Estimating Risk Binder PDF

Estimating Risk Presentation By: Ann M Vuong, DrPH MPH Objectives of Epidemiology  To determine rates of disease by person, place, and time  Absolute Risk  Incidence, Prevalence  To identify the risk factors for the disease  Relative Risk, Odds Ratio  To develop approaches for disease preventi...

Estimating Risk Presentation By: Ann M Vuong, DrPH MPH Objectives of Epidemiology  To determine rates of disease by person, place, and time  Absolute Risk  Incidence, Prevalence  To identify the risk factors for the disease  Relative Risk, Odds Ratio  To develop approaches for disease prevention  Attributable Risk Absolute Risk Absolute Risk  The likelihood of an individual in a defined population developing a disease or adverse health problem  The incidence of a disease in a population  Can indicate the magnitude of risk in a group with a certain exposure  Your risk of developing a disease over a period of time Incidence: Measures the occurrence of new cases in a population over time Purpose: Indicator of the force of the disease or the conversion of health status Cumulative Incidence Incidence Density # new cases during follow-up # of people at the start of follow-up # new cases during follow-up Accumulated person-time Absolute Risk  The likelihood of an individual in a defined population developing a disease or adverse health problem  The incidence of a disease in a population  Can indicate the magnitude of risk in a group with a certain exposure  Your risk of developing a disease over a period of time  Does not indicate whether the exposure is associated with an increased risk of the disease, because there is no comparison Absolute Risk Examples  Congenital rubella appears in 80-100% of infants if maternal infection of rubella occurs during the first trimester1  Vertical transmission of parvovirus B19 is ~35%1  ~90% of infants perinatally or infected during the first year of life develop chronic hepatitis B virus infection1 * 1 Implicit comparison made, but to address whether an association exists – we need to make explicit comparisons Neu et al. (2015) Does an Association Exist?  Must determine whether there is an excess risk of disease among people who have been exposed to a certain agent  The stronger the association, the more likely the relationship is causal in absence of known biases  May be misleading due to confounding Measures of Associations  Cohort and case control studies are designed to address the association between exposure and disease  Association involves the comparison between two measures  Cohort Studies: Relative Risk  Case Control Studies: Odds Ratio Steps in Epidemiologic Research  Generate a research question of interest  Define the population of interest  Conceptualize and create measure of exposures and health outcomes  Take a sample of the population  Estimate measures of association between exposures and health outcomes  Rigorously evaluate whether the association observed suggests a causal association  Assess the evidence for causes working together  Assess the extent to which the result matters, is externally valid, to other populations Contingency Table: 2 by 2 Table  Important tool in evaluating the association between exposure and disease  Cross-classifies exposure status and disease status  Represents the association between exposure and disease status  Columns represent disease or outcome status (yes/no)  Rows represent exposure status (yes/no) Exposure Status 2 by 2 Table Exposure Present No Exposure Disease Status People with Disease People without Disease A B Exposure & Disease Present Exposure Present, No Disease C D No Exposure, Disease Present No Disease, No Exposure A+C B+D Total of Diseased Total of Nondiseased A+B Total Exposed C+D Total Unexposed N Sample Total Relative Risk Relative Risk  Probability of an event occurring in exposed people compared to the probability of the event in non-exposed people  Measures the size of the effect on the disease rates of the risk factor and the strength of the association in epidemiology  Cannot be calculated from case control studies  No incidence data in the exposed or non-exposed  Odds ratio can provide an acceptable estimate of relative risk  Ratio of two incidence rates Relative Risk Cumulative Incidence in Exposed Cumulative Incidence in Unexposed Exposure Status Measure of Association in Cohort Studies: Disease Status RR A B C D A / (A+B) C / (C+D) Relative Risk Interpretation RR=1 No evidence of association Risk exposed = Risk unexposed RR>1 Positive association Risk exposed > risk unexposed RR Coffee consumption is associated with 5 times higher risk of anxiety Statistically Significant?  Sample, by chance, may not represent exact disease and exposure experience of the population  Confidence intervals can help us understand the variability in the study estimates due to chance in sampling process  How confident are you of that your estimated measure of association reflects the true measure of association?  95% Confidence Interval  Range of values in which you can be 95% certain contains the true estimate  There is 95% chance that the confidence interval calculated contains the true measure of association  If the 95% CI contains the null value of 1.00, then the results are NOT statistically significant and should be interpreted as no association between exposure and outcome.  RR = 2.1, 95% CI (0.7-2.4)  Not statistically significant! Interpret as there is no association between exposure and disease 95% Confidence Interval for RR 1. Take the natural log of RR ln(RR) 2. Estimate standard error (SE) 1 1 1 1 A (A + B) C (C + D) 3. Estimate upper and lower bounds on log scale ln(RR) - 1.96(SE) 4. Exponentiate upper and lower bounds eLowerBound eUpperBound ln(RR) + 1.96(SE) Let’s revisit Relative Risk Example 2 to determine whether associations are statistically significant! Research Objective: To examine whether history of sexual abuse is associated with suicide attempts in adolescents Relative Risk Example 2 RR Deykin & Buka (1994) History of Sexual Abuse Suicide Attempt 14 49 9 149 2.46 1 1 1 1 A (A + B) C (C + D) 1 1 1 1 14 (23) 49 (198) SE 0.21 60.8% 24.7% LB ln(RR) - 1.96(SE) ln(2.46) - 1.96(0.21) 0.49 UB ln(RR) + 1.96(SE) ln(2.46) + 1.96(0.21) 1.31 LB UB e(LB) e(0.49) 1.63 e(UB) e(1.31) 3.71 RR=2.46, 95% CI 1.63-3.71 Considerations  Central Limit Theory  Validity of confidence interval dependent on the central limit theory  Assumptions  Large sample size  Each cell must have at least 5 participants Attributable Risk Attributable Risk  Clinical and Public Health Impact  How much of the disease that occurs can be attributed to a certain exposure?  Amount of disease incidence (risk) that can be attributed to a specific exposure  How much of the risk of disease can we prevent if we eliminate the exposure Attributable Risk  Attributable Risk (AR) is the amount of the incidence of disease in the exposed that is due to the exposure  It is the incidence of a disease in the exposed that would be eliminated if exposure was removed  Difference in incidence of disease between exposed and unexposed individuals  Incidence in unexposed = background risk AR Ie Iu Incidence of Exposed Incidence of Unexposed Attributable Risk Percent  AR% is the percent of the incidence of a disease in the exposed that is due to the exposure  It is the percentage or proportion of the incidence of a disease in the exposed that would be eliminated if exposure was eliminated AR% AR Iu Ie Ie 100 Population Attributable Risk (PAR)  Represents the amount of the outcome (in a specified time) in the whole population that may be prevented if a cause of the outcome was totally eliminated Attributable Risk 35% 30% Type II Diabetes 25% 23% 20% 15% 10% 5% 7% 0% Overweight/Obese 7% Normal Weight Attributable Risk Example 1  Attributable Risk = Risk of type II diabetes attributed to being overweight/obese  AR = Type II diabetes among overweight/obese individuals – Type II diabetes among normal weight individuals  AR = 30 per 100 overweight/obese individuals – 7 per 100 normal weight individuals  AR = 23 of the 30/100 instances of type II diabetes among individuals who are overweight/obese are attributed to the fact that they are overweight/obese Attributable Risk 35% 30% Type II Diabetes 25% 23% 20% Due to being overweight/obese Background rate 15% 10% 5% 7% 0% Overweight/Obese 7% Normal Weight Attributable Risk Example 1  Attributable Risk = Risk of type II diabetes attributed to being overweight/obese  AR = Type II diabetes among overweight/obese individuals – Type II diabetes among normal weight individuals  AR = 30 per 100 overweight/obese individuals – 7 per 100 normal weight individuals  AR = 23 of the 30/100 instances of type II diabetes among individuals who are overweight/obese are attributed to the fact that they are overweight/obese  Attributable Risk Percent = 23 30 100 77%  77% of type II diabetes among overweight/obese group may be attributed to being overweight/obese and could presumably be prevented by decreasing adiposity to that of the normal weight category Attributable Risk Example 2 Stroke Incidence Fish Consumption Totals Almost daily RR 1 82 1549 1631 Never * Sauvaget et al (2003) 23 779 Incidence in non-fish eaters Incidence in fish eaters 802 5.03 2.87 82 1631 5.03 per 100 23 802 2.87 per 100 Incidence in fish eaters 105 2433 4.32 per 100 Incidence in population 1.75 Incidence in nonfish eaters Attributable Risk Example 2 5.03 per 100 Incidence in nonfish eaters AR = Inofish – Ifish AR% = 2.87 per 100 4.32 per 100 Incidence in fish eaters Incidence in population = 5.03 – 2.87 = 2.16 per 100 = AR Inofish(exp) 2.16 5.03 100 43% PAR = Ipop – Iunexp = 4.32 – 2.87 = 1.45 per 100 PAR% = PAR Ipop = 1.45 4.32 100 33.6% Interpretations  RR = 1.75  Individuals who never eat fish have 1.75 times higher risk of stroke as those who eat fish almost daily  AR = 2.16 per 100  If those who do not eat fish change their eating habits and begin to eat fish almost daily, then their incidence of strokes will decrease by 2.16 per 100 individuals  AR% = 43%  There would be a 43% reduction in stroke incidence if exposure, no fish consumption, were eliminated among nonfish eaters  This represents a 43% reduction in stroke incidence among the exposed individuals (nonfish eaters) Interpretations  PAR = 1.45 per 100  A reduction of 1.45 new cases of stroke per 100 population is expected if everybody eats fish almost daily  PAR% = 33.6%  There would a reduction of 33.6% in the incidence of stroke in the population if everyone eats fish almost daily Attributable Risk for Lung Cancer in Springfield Lung Cancer Location of Residence Totals Springfield 20 80 100 AR = ISpringfield – IShelbyville = 20 – 10 = 10 AR% = Shelbyville 10 90 100 AR ISpringfield = 10 20 100 50%  50% of lung cancer cases can be attributed to living in Springfield  If we removed Springfield (the exposure) then we could reduce the risk of lung cancer by 50% Attributable vs. Relative Risk  Relative Risk  Measure of the strength of the association, which is an important consideration in deriving a causal inference  Valuable in etiologic studies of disease, whereas the attributable risk has major applications in clinical practice and public health  Attributable Risk  Measure of how much the disease risk is attributable to a certain exposure Attributable vs. Relative Risk Age adjusted death rates per 100,000 Lung cancer CHD Smokers Nonsmokers RR AR AR% 140 10 14.0 130 92.9 669 413 1.6 256 38.3  256 deaths per 100,000 from CHD would be prevented if smokers would no longer smoke  130 deaths per 100,000 from lung cancer would be prevented if smokers would no longer smoke ? Why are there fewer deaths prevented for lung cancer if smoking was eliminated when the proportion of deaths attributed to smoking is higher among lung cancer patients (92.9%) compared to CHD (38.3%) Attributable vs. Relative Risk  Prevented: 256 deaths per 100,000 from CHD  Prevented: 130 deaths per 100,000 from lung cancer ? Why are there fewer deaths prevented for lung cancer if smoking was eliminated when the proportion of deaths attributed to smoking is higher among lung cancer patients (92.9%) compared to CHD (38.3%)  Mortality level (number of people) in smokers is much higher for CHD (669) than for lung cancer (140)  Attributable risk (the difference between total risk in smokers and the background risk) is much greater for CHD than for lung cancer Odds Ratio Odds Ratio  Can be calculated in case control and cohort studies  Appropriate measure of association for studies in which individuals with or without the disease are recruited and then there is a retrospective assessment of exposure status  Case Control Study  The proportion of cases who were exposed compared to the proportion of controls who were exposed  Cohort Study  Proportion of exposed with disease development compared to the proportion of unexposed with disease development Cohort studies can also calculate an OR, because an OR does not require the establishment of temporality. However, a case control (unless it is a nested case control or a case-cohort) cannot calculate a RR, because it lacks the ability to establish temporality. Although cohort studies can calculate both measures of association, when you think of a cohort study, think of a RR !! Probability and Odds Probability Measures the number of times the outcome of interest occurs relative to the number of observations (sample size) Odds Measures the number of times the outcome occurs relative to the number of times it does not Odds Ratio Compares the odds of those exposed to the risk factor and the odds of those unexposed Risk vs. Odds  The chance of something happening can be expressed as a risk and/or as an odds Risk Odds Chances of something happening Chances of ALL things happening Chances of something happening Chances of it NOT happening If I choose a student randomly from a class size of 6, how likely is it that I will choose you? Risk Odds Chances of something happening 1 Chances of ALL things happening 6 Chances of something happening 1 Chances of it NOT happening 5 0.16 0.20 Odds Ratio in Case Control Studies  Ratio of the odds that a case was exposed compared with the odds that a control was exposed Odds Ratio Odds of Exposure in Diseased Odds of Exposure in Nondiseased Calculating Odds Ratio for a Case Control Disease What are the odds that a case was exposed Exposure Odds by disease group A B Cases Controls Number of times exposure occurs among cases C ? A C D Number of times exposure occurs among controls B D Calculating Odds Ratio for a Case Control Odds ratio Disease Exposure in diseased group versus nondiseased group Exposure Number of times exposure occurs among cases A B A C Number of times exposure occurs among controls B D C D A C AD B BC D Odds Ratio Sample Calculation of an Odds Ratio Gastric Cancer Population-based case control study in Mexico City of the relationship between chili pepper consumption and gastric cancer risk Chili Pepper Consumption A 1 204 552 Lopez-Carillo et al (1994) C AD B BC D 9 145 204×145 552×9 Odds Ratio 5.95 Interpretation of the Odds Ratio OR=1 No evidence of association Odds of exposure among cases = Odds of exposure among controls OR>1 Positive association Odds of exposure in cases > Odds of exposure in controls OR 204×145 552×9 Odds Ratio 5.95 Gastric cancer individuals have a 6-fold higher odds of chili pepper consumption compared to controls Are the findings statistically significant? 95% Confidence Interval for Odds Ratio 1. Take the natural log of OR ln(OR) 2. Estimate standard error (SE) 1 1 1 1 A B C D 3. Estimate upper and lower bounds on log scale ln(OR) - 1.96(SE) 4. Exponentiate upper and lower bounds eLowerBound eUpperBound ln(OR) + 1.96(SE) Relative Risk Example 2 Chili Pepper Consumption Gastric Cancer SE 204 552 9 145 0.35 Lopez-Carillo et al (1994) OR 552×9 1 1 1 1 A B C D 1 1 1 1 204 552 9 145 LB ln(OR) - 1.96(SE) ln(5.95) - 1.96(0.35) 1.10 UB ln(OR) + 1.96(SE) ln(5.95) + 1.96(0.35) 2.47 LB UB 1 204×145 e(LB) e(1.10) 3.00 e(UB) e(2.47) 11.82 5.95 OR=5.95, 95% CI 3.00, 11.82 Are the findings statistically significant? Yes! The 95% CI does not include the null value of 1.00. We would interpret this finding as, “Gastric cancer is associated with ~6-times higher odds of chili pepper consumption.” Odds Ratio Question Disease Exposure  Investigators want to determine whether vitamin D deficiency was associated with birth defects. By reviewing the birth certificates during a single year, the researcher located 189 infants born with NTDs. A total of 600 other births were selected at random from the certificates. Mothers were given a dietary questionnaire. Among mothers who gave birth to an infant with an NTD, 84 reported no use of supplementary vitamins; a total of 137 control mothers did not use a vitamin supplement. Construct the appropriate 2 by 2 table and calculate the OR between vitamin use and NTDs. Are the results statistically significant? A B C D Odds Ratio Question Vitamin Supplementation  Investigators want to determine whether vitamin D deficiency was associated with birth defects. By reviewing the birth certificates during a single year, the researcher located 189 infants born with NTDs. A total of 600 other births were selected at random from the certificates. Mothers were given a dietary questionnaire. Among mothers who gave birth to an infant with an NTD, 84 reported no use of supplementary vitamins; a total of 137 control mothers did not use a vitamin supplement. Construct the appropriate 2 by 2 table and calculate the OR between vitamin use and NTDs. Are the results statistically significant? NTDs Odds Ratio Question Vitamin Supplementation  Investigators want to determine whether vitamin D deficiency was associated with birth defects. By reviewing the birth certificates during a single year, the researcher located 189 infants born with NTDs. A total of 600 other births were selected at random from the certificates. Mothers were given a dietary questionnaire. Among mothers who gave birth to an infant with an NTD, 84 reported no use of supplementary vitamins; a total of 137 control mothers did not use a vitamin supplement. Construct the appropriate 2 by 2 table and calculate the OR between vitamin use and NTDs. Are the results statistically significant? NTDs 105 463 84 137 189 600 AD 105×137 BC 463×84 0.37 NTDs  Investigators want to determine whether vitamin D deficiency was associated with birth defects. By reviewing the birth certificates during a single year, the researcher located 189 infants born with NTDs. A total of 600 other births were selected at random from the certificates. Mothers were given a dietary questionnaire. Among mothers who gave birth to an infant with an NTD, 84 reported no use of supplementary vitamins; a total of 137 control mothers did not use a vitamin supplement. Construct the appropriate 2 by 2 table and calculate the OR between vitamin use and NTDs. Are the results statistically significant? > Vitamin Supplementation Odds Ratio Question AD BC 105 463 84 137 189 600 105×137 463×84 0.37 The odds of NTDs is 63% lower among infants with mothers who took vitamin supplementation during pregnancy. Odds Ratio Question Vitamin Supplementation NTDs 105 84 137 0.18 Lopez-Carillo et al (1994) 463×84 1 1 1 1 A B C D 1 1 1 1 105 463 84 137 LB ln(OR) - 1.96(SE) ln(0.37) - 1.96(0.18) -1.35 UB ln(OR) + 1.96(SE) ln(0.37) + 1.96(0.18) -0.64 LB UB 1 OR SE 463 105×137 e(LB) e(-1.35) 0.26 e(UB) e(-0.64) 0.53 0.37 OR=0.37, 95% CI 0.26-0.53 Interpreting ORs Which of the following statements is NOT correct regarding the interpretation of the results? A) No association was observed between living with at least one household smoker during the postnatal period and children ever having or currently having asthma B) No association was noted between maternal smoking during pregnancy and children ever having or currently having asthma. C) Children currently having asthma had significantly higher odds of having a mother who smoked prior to pregnancy. D) There was no relationship between maternal smoking, either prior or during pregnancy, and childhood asthma (ever or current). Tanaka K, Arakawa M, Miyake Y. (2020). Allergol Immunopathol. Interpreting ORs Which of the following statements is NOT correct regarding the interpretation of the results? A) No association was observed between living with at least one household smoker during the postnatal period and children ever having or currently having asthma B) No association was noted between maternal smoking during pregnancy and children ever having or currently having asthma. C) Children currently having asthma had significantly higher odds of having a mother who smoked prior to pregnancy. D) There was no relationship between maternal smoking, either prior or during pregnancy, and childhood asthma (ever or current). Adjusted ORs for postnatal living with at least one household smoker and ever and current asthma are not statistically significant (includes the null value 1.0), which means there is no association. Tanaka K, Arakawa M, Miyake Y. (2020). Allergol Immunopathol. Interpreting ORs Which of the following statements is NOT correct regarding the interpretation of the results? A) No association was observed between living with at least one household smoker during the postnatal period and children ever having or currently having asthma B) No association was noted between maternal smoking during pregnancy and children ever having or currently having asthma. C) Children currently having asthma had significantly higher odds of having a mother who smoked prior to pregnancy. D) There was no relationship between maternal smoking, either prior or during pregnancy, and childhood asthma (ever or current). Adjusted ORs for maternal smoking during pregnancy and ever and current asthma are not statistically significant (includes the null value 1.0), which means there is no association. Tanaka K, Arakawa M, Miyake Y. (2020). Allergol Immunopathol. Interpreting ORs Which of the following statements is NOT correct regarding the interpretation of the results? A) No association was observed between living with at least one household smoker during the postnatal period and children ever having or currently having asthma B) No association was noted between maternal smoking during pregnancy and children ever having or currently having asthma. C) Children currently having asthma had higher odds of having a mother who smoked prior to pregnancy. D) There was no relationship between maternal smoking, either prior or during pregnancy, and childhood asthma (ever or current). Adjusted ORs for maternal smoking prior to pregnancy and a current asthma condition in children is not statistically significant (includes the null value 1.0), which means there is no association. Even though the OR is >1.0, which would be a positive association, the results cannot be interpreted as such UNLESS it is statistically significant. Tanaka K, Arakawa M, Miyake Y. (2020). Allergol Immunopathol. Interpreting ORs Which of the following statements is NOT correct regarding the interpretation of the results? A) No association was observed between living with at least one household smoker during the postnatal period and children ever having or currently having asthma B) No association was noted between maternal smoking during pregnancy and children ever having or currently having asthma. C) Children currently having asthma had significantly higher odds of having a mother who smoked prior to pregnancy. D) There was no relationship between maternal smoking, either prior or during pregnancy, and childhood asthma (ever or current). All adjusted ORs are not statistically significant and should be interpreted as null associations. The statement is correct. Tanaka K, Arakawa M, Miyake Y. (2020). Allergol Immunopathol. Interpreting ORs Which of the following statements is NOT correct regarding the interpretation of the results? A) No association was observed between living with at least one household smoker during the postnatal period and children ever having or currently having asthma B) No association was noted between maternal smoking during pregnancy and children ever having or currently having asthma. C) Children currently having asthma had significantly higher odds of having a mother who smoked prior to pregnancy. D) There was no relationship between maternal smoking, either prior or during pregnancy, and childhood asthma (ever or current). Tanaka K, Arakawa M, Miyake Y. (2020). Allergol Immunopathol. Odds Ratio in Cohort Studies  Ratio of the odds of a disease in the exposed compared with the odds of the disease in the unexposed Odds Ratio Odds of Disease in Exposed Odds of Disease in Unexposed Calculating Odds Ratio in Cohort Studies Disease Exposure Odds Ratio A C B D A A+B 1 A (A+B) C C+D 1 C (C+D) A B AD C BC D Odds Ratios in Case Control and Cohort Studies OR Disease A B C D Exposure Exposure Disease Odds of Exposure in Diseased Odds of Exposure in Nondiseased A OR A B C D Odds of Disease in Exposed Odds of Disease in Unexposed A C AD B AD B BC C BC D D Case Control Calculation of Odds Ratio Neuroblastoma Status What are the odds of congenital malformations for cases Congenital Malformations Number of times exposure occurs in cases 23 116 217 2284 A Odds Ratio C B 23 217 ? 0.105 AD BC D 23 × 2284 116 × 217 2.1 Cohort Calculation of Odds Ratio Congenital Malformations Neuroblastoma Status 23 116 217 2284 What are the odds of a child with congenital malformations developing neuroblastoma Number of times those with congenital malformations develop neuroblastoma A Odds Ratio B C 23 116 ? 0.20 AD BC D 23 × 2284 116 × 217 2.1 Example: Death by sex Death Totals 709 142 851 Sex Male Female 154 308 462 > Males are more likely to die than females ? How much more likely? What are the odds of dying for each sex? Example: Death by Sex Death Totals 709 142 851 Sex Male Female 154 308 462 Odds Ratio C 154 D 308 A 709 B 142 AD 709×308 BC 154×142 > There is a ten-fold greater odds of death for males than females 0.5 5.0 10.0 What about the Relative Risk? Death Totals 709 142 851 Sex Male Female 154 308 462 RR C 154 C+D 462 A 709 A+B 851 0.33 0.83 A/(A+B) 0.83 C/(C+D) 0.33 > There is a 2.5 greater probability of death for males than females 2.5 Odds Ratio vs Relative Risk Odds Ratio There is a ten-fold greater odds of death for males than females Relative Risk There is a 2.5 greater probability of death for males than females  Both measurements indicate that men were more likely to die on the Titanic  Odds ratio implies that men are much worse off than the relative risk estimate  Which number is a fairer comparison?  RR measures events in a way that is interpretable and consistent with the way people really think  RR cannot always be computed in a research design Instances when the Odds Ratio can estimate the Relative Risk  When the cases studied are representative, with regard to history of exposure, of all people with the disease in the population from which the cases were drawn  When the controls studied are representative, with regard to history of exposure, of all people without the disease in the population from which the controls were drawn  When the disease being studied is rare Odds Ratio in Matched Samples  In a matched case-control study, each case is matched to a control according to variables that are known to be related to disease risk  Data analyzed in terms of case-control pairs rather than for individual subject  Four combination of pairs Odds Ratio in Matched Samples Concordant Pairs Discordant Pairs  Pairs in which both the case and the control were exposed  Pairs in which the case was exposed, but the control was not  Pairs in which neither the case nor the control was exposed  Pairs in which the control was exposed, but the case was not Controls Exposure status Cases Exposure status Concordant Discordant Discordant Concordant Odds Ratio in Matched Samples Controls  Concordant pairs are ignored since they do not contribute in the calculation of the effect estimate  Matched OR = Ratio of discordant pairs B # of pairs in which cases were exposed C # of pairs which controls were exposed Cases  Discordant pairs of cases and controls are used to calculate the matched OR Exposure status Exposure status Concordant Discordant Discordant Concordant Example for Matched Case Control Study  Study Aim: To examine the risk factors for brain tumors in children  Hypothesis: Children with certain childhood cancers are more likely to have higher birth weight Cases Children with brain tumors Controls Children without brain tumors Exposure Birth weight > 8 lbs Example for Matched Case Control Study Controls Hypothesis: Children with brain tumors are more likely to have higher birth weights Exposure status >8 lbs ≤8 lbs Exposure status Cases Matched OR >8 lbs 9 18 B # of pairs in which cases were exposed C # of pairs which controls were exposed 18 7 ≤8 lbs 7 38 > 2.6 There is a 2.6-fold greater odds of children with brain tumors having a birth weight >8 lbs compared to having a birth weight ≤8 lbs Questions? Estimating Risk - Part 1: Introduction An es&ma&ng risk We'll mainly be learning about how to calculate measures which are important in public health and epidemiological research, par&cularly for those measures of associa&ons related to case control studies and cohort studies which are rela&ve risk and odds ra&os. When we think of Abby and the aims of epidemiology, they mainly pertain to disease preven&on, either by determining race of disease, iden&fying risk factors, or developing strategies that would best result in disease preven&on. To meet these objec&ves, we need to rely on several measures, and that's what we're going to learn about today. For instance, when we want to determine race of disease by person, place and &me, we turn to absolute risk, more specifically, incidence and prevalence, which you're all very familiar with already. Another objec&ve of epidemiology is to iden&fy risk factors for disease. We accomplished this by designing studies like cohort studies, case control studies. But how do we actually conclude or pinpoint what par&cular exposure is associated with our disease of interest? We use measures of associa&ons. For cohort studies, we use rela&ve risk. For case control studies we use odds ra&os. And lastly, when we're thinking about poten&al strategies to combat disease, we would like to have the highest yield in terms of disease reduc&on. To do this, we need to know how much of the disease would be reduced if we eliminated a certain risk factor. That way, we can target our strategies to focus on exposures that are contribu&ng the most to disease development. To do this, we rely on the measure of aEributable risk. Let's talk about absolute risk first. Absolute risk is the likelihood of an individual in a popula&on developing a certain disease. It's essen&ally the incidence of disease within a given popula&on. This measure provides an indica&on of the magnitude of risk and a group of people who have a certain exposure the risk that you will get a disease over a period of &me. If we look back to incidents, we recall that incidence measures the new cases in a popula&on over &me. This essen&ally indicates the force of the disease or conversion of health status. You can either be expressed as cumula&ve incidence as shown in the top formula, or as incidence density which takes into account accumulated person &me. S does not, however, provide any informa&on about the associa&on between the exposure and the disease because there is no comparison that is made. If we look at some absolute risk examples, you see that there is an implicit comparison made. But to properly determine if an associa&on exists, we need to make an explicit comparison. You see on the slide 3 examples of absolute risk. The first one is congenital rubella appears in 80 to 100% of infants if maternal infec&on of rubella occurs during the first trimester pregnancy. This statement provides us informa&on about the absolute risk, but it doesn't give us informa&on about the measure of associa&on between maternal rubella infec&on during the first trimester and congenital rubella in the infant because we lack a comparison group. What about the infants who had mothers who had maternal infec&on in the second trimester or the 3rd? And the second example is states ver&cal transmission of parvovirus B19 is approximately 35%. While this is important informa&on, it provides us with the absolute risk of parvovirus B19 from mother to child during gesta&onal development. But what it does not have is a comparison group that would lend addi&onal informa&on that is needed to determine associa&ons. The same is said about the last example. Approximately 90% of infants perinatally or infected during the first year of life develop chronic hepa&&s B virus infec&on. Again, the comparison is only implicit. There is no explicit comparison which is needed to determine whether an associa&on exists. Thus, these examples are considered only as absolute risk. To truly examine whether an associa&on exists between exposure and a disease or health outcome, we need to have comparison groups. Groups without the disease, groups without the exposure. This way we can see if there is an excess risk of disease and the group that is. Exposed. If the socia&on is strong, then there is more evidence to support that the rela&onship is causal. A court team is always considered the influence of confounding factors, as we discussed in the previous lectures. Several studies are u&lized to help inves&gators examine research ques&ons that seek to learn more of the rela&onship between exposure and outcome, in par&cular case control studies and cohort studies. Each study design has a measure of associa&on that is linked to it, for example. The color study is able to yield a rela&ve risk. It can also yield an odds ra&o because of the way it's designed. But for the most part, a rela&ve risk is seen as a stronger measure of associa&on. So when people ask what the measure of associa&on for in a cohort study is, the answer is a rela&ve risk. Case central studies, on the other hand, cannot calculate rela&ve risk. They are only able to determine odds ra&os. So when you think of a case control study, you should immediately think of the odds ra&o. Before we go into calcula&on and interpreta&on of these measures, let's revisit the general steps in every research. We first start with an idea, a research ques&on we would like to address and find out more about. We hone our ques&on, and we look to see what our popula&on of interest is. We think about exposure assessment defini&on of our outcome of interest. We sample our popula&on and determine exposure and disease status based on our conceptualized measures of them. We then es&mate whether an associa&on exists between our exposure and disease using appropriate sta&s&cal models and evaluate whether the findings support of poten&al causal. Socia&on. These two steps are where we are now in the semester here today to discuss es&ma&ng risk. To do this, we rely on the handy dandy con&ngency table, otherwise known as the two by two table. This is an important tool that's u&lized to help determine the associa&on between exposure and disease by cross classifying exposure status and disease status. The columns of a two by two table represent disease status, yes or no and the rows represent exposure status, yes or no. Some people switch it up depending on what they're examining. My sugges&on is to only s&ck with one format as to not get confused with the formulas as you start the calcula&ons. As men&oned earlier, your columns are disease status. First column consists of people who have the disease, the second column is of people without the disease. The rules represent exposure status. The first row is for everyone who is exposed, The 2nd row is for everyone who is not exposed. So what you end up with are 4 categories of people and block A. You have people who are disease but who are also exposed and block B. You have people who were exposed but do not have the disease, and block C you have people who have the disease but were not exposed. And then in block T you have not diseased people who were not exposed. You can have your totals on the sides of the table. At the far right you have your total number exposed as a sum of A + B. You have your total unexposed right underneath with C + D. Then your totals for disease on the very boEom le\ with A + C and the total number of undisclosed with B + D This table is really important as you move forward in calcula&ng measures of associa&ons for case control and cohort studies.When you're asked to construct a two by two table, refers to the side and set up the two by two table. This way you fill in the table with the informa&on that is given the prompt. Estimating Risk - Part 2: Relative Risk Rela&ve risk is the probability of an event happening in exposed people compared to the probability of the event happening and the non exposed people. So think back to the design of a cohort study. You start with exposure status and you follow people for a specified period of &me to determine whether disease develops. So it makes sense that the rela&ve risk, the measure of associa&on for coerce studies is defined as a probability of disease development and exposed compared to the probability of disease development and the unexposed. It's essen&ally a ra&o of two incidence rates. Remember, we cannot calculate a rela&ve risk and. Case control study because case control studies do not have incidence data because they start with disease and then go to exposure. The rela&ve risk has and the numerator the condi&onal risk of disease among the exposed. The denominator has the condi&onal risk of disease among the unexposed. This translates to the formula on the boEom right of the slide and the numerator we have A / A + B. Which is the number of exposed people who get the disease over the total number of people exposed? And the denominator we have C / C + D, which is the number of unexposed people who get the disease divided by the total number of people who were unexposed. The calcula&on itself is preEy easy, but what does this number mean? If we were to get a rela&ve risk of one, that means that the risk of the exposed is equal to the risk of the unexposed. So there's no evidence to suggest that there's any associa&on. But if the rela&ve risk is greater than one, then there is a posi&ve associa&on because the risk among the exposed is higher than the risk among the unexposed. In some instances, you will see that the rela&ve risk is less than one indica&ng an inverse associa&on. Because the risk among the exposed is actually less than that of the unexposed. This means that there is a protec&ve associa&on. An example could be between physical ac&vity and obesity development. The rela&ve risk would most likely be less than one for a study examining this research ques&on, so let's take a look at some examples. In the first example, we are examining the associa&on between cigareEe smoking, defined as greater than or equal to 1 pack per day, and heart aEacks yes or no. And we are looking at a five year follow up number for each group's exposure and disease status is within the two by two table If we want to calculate a rela&ve risk, we need to look at the incidence and the exposed compared to the incidence and the unexposed. So let's start with incidents and the exposed. We would take the number of people who smoked and who got heart aEacks and divided by the total number of people who smoked, which was 1074. So we would get 8.2% for the five year incidence rate among smokers or among our exposed group. For unexposed, we would take the 26 non-smokers who got heart aEacks and divide that by the total number of people who did not smoke or who were unexposed, which was 1076. For unexposed we would take the 26 non-smokers who got heart aEacks and divide that by the total number of people who did not smoke or who were unexposed. So that would be 1076. Using this formula we would get it incidence among no cigareEe users as 2.4%. We can use these numbers to get our rela&ve risk. The formula for the rela&ve risk can be seen on the boEom of this line. We plug the values of the incidences that we just calculated into the formula 8.2% for the numerator because this is incidence among the exposed, and then 2.4%. For the denominator, because this is the cumula&ve incidence of the unexposed and then we will calculate this out to be a rela&ve risk of 3.4. So what do these numbers even mean? Or how do we go about interpre&ng these numbers? So let's start with the five year incidence we calculated for smokers and non-smokers. As you recall, the incidence for smokers was 8.2%. This means that the probability of heart aEacks is 8.2% among people who smoke at least one pack a day. The probability of a heart aEack among people who were unexposed or people who did not smoke is 2.4%. The rela&ve risk we obtained was 3.4. This means that there is a 3.4 greater probability of heart aEacks for people who smoke at least one pack of cigareEes per day compared to people who did not smoke at all. This indicates a posi&ve associa&on in excess risk among the exposed of our disease of interest. And the second example. We are examining the rela&onship between history of sexual abuse and suicide aEempts and adolescents. We have our numbers for each group listed in the table. We again calculate the incidence rate among the exposed and the unexposed. We get 60.8% as the incidence of suicide aEempts for people who had a history of sexual abuse. Compared to 24.7% among people who did not have a history of sexual abuse. We can take the incidence among our exposed and our unexposed groups to calculate our rela&ve risk. We plug the incidence values into the formula with 16.8% going into the numerator because this represents the instance of our outcome suicide aEempt among people who were exposed, meaning that people who had a history of sexual abuse. And then we take 24.7% and we plug that into our denominator because this represents the incidence among adolescents with no history of sexual abuse. We calculated this out to get a rela&ve risk of 2.46. So let's quickly review what we found. We found that the probability of suicide aEack among adolescents with the history of sexual abuse was 60.8%. Among our exposed group, we found that the probability of suicide aEempts was only 24.7%. This rela&ve risk of 2.46 indicates a posi&ve associa&on, an excess of suicide aEempts among adolescents who were sexually abused compared to adolescents who were not sexually abused. Based off of this value, we can say that there is a 2.5 fold greater probability of a suicide aEempt for adolescents with a history of sexual abuse compared to adolescents with no history of sexual abuse. And the third example, we would like to compare the incidence of lung cancer between two ci&es, Springfield and Shelbyville. Both ci&es have a small popula&on of 100 residents and Springfield there is polluted air. Thus this city is going to be categorized as our exposed other Springfield residents we. 20 cases of lung cancer. And our second city, we have Shelbyville. Shelbyville does not have polluted air, thus they're going to be considered as our unexposed group. And Shelbyville, there are 10 cases of lung cancer. We again construct our two by two table using the informa&on that we were given. This &me for our exposure status rose. We have Springfield for exposed and Shelbyville for unexposed. We calculate the incidence rate for each city. Springfield has an incidence rate of 20% because 20 out of the 100 residents developed lung cancer. And Shelbyville? This number is halved because only 10 out of the hundred of his residents were diagnosed with lung cancer. In this scenario, because our exposure status is basically being a resident in either Springfield or Shelbyville, we can calculate the rela&ve risk for each city. So let's start with Springfield. What is the rela&ve risk for lung cancer among Springfield residents? We would have the incidence of Springfield and the numerator, and then in the denominator we will put the incidence of lung cancer among Shelbyville residents. So we plug in 20% / 10%, which will result in a rela&ve risk of two. So what if we look at the rela&ve risk from the other ci&es perspec&ve from Shelbyville being the exposed. So let's bring up all the numbers that we already have, 20% incidents in Springfield, 10% incidence in Shelbyville. Now in the rela&ve risk formula you have in the numerator the incidence of lung cancer among Shelbyville because now Shelbyville is considered your exposed group and that would be 10% and the and the denominator you have the incidence of lung cancer in Springfield because now it's flipped. We are going to consider Springfield as our unexposed group. And this was 20%. You end up with a rela&ve risk of 0.5 for lung cancer among Shelbyville residents. So how do we interpret these findings? First, let's quickly review our probabili&es. The probability of lung cancer among Springfield residents was 20%. The probability of lung cancer among Shelbyville residents was 10%. We calculated A rela&ve risk of lung cancer for Springfield as two, with Springfield being the exposure. We can interpret this as there's a two fold greater probability of lung cancer among Springfield residents compared to residents of Shelbyville. When we looked at it from Shelbyville's perspec&ve, you think Shelbyville as the exposed group, we calculated A rela&ve risk of 0.5. We can say that residents of Shelbyville have a 50% reduc&on in risk of lung cancer compared to residents of Springfield. If you want to interpret the finding or inverse associa&on based off a rela&ve risk less than one. Then you can interpret this as a reduc&on in risk. Now the rela&ve risk here is 0.5. To get the percentage of reduc&on in risk, you would do 1 -, 0.5, which equals to 0.5. So that would be a 50% reduc&on here. Now if the rela&ve risk was let's say 0.7. Then it would be 1 -, 0.7. And then you would interpret this statement as resonance of Shelbyville have a 30% reduc&on in risk of lung cancer compared to residents of Springfield. So when you want to interpret it as a reduc&on in risk is always a difference from the null value 1 minus whatever rela&ve risk you got. That was less than one. Now, if you don't want to go that route in terms of interpre&ng it as a reduc&on in risk, you can simply use the rela&ve risk of 0.5 in your interpreta&on and you can state residents of Shelbyville have 0.5 &mes the risk of lung cancer compared to residents of Springfield. Both these interpreta&ons are correct. The interpreta&on was the percentage of reduc&on in risk is a liEle bit tricky because you do have to remember to do that subtrac&on. If you put solely the rela&ve risk there for the percentage and reduc&on of risk, then the interpreta&on is going to be inaccurate. So let's go ahead and calculate the rela&ve risk for this research ques&on, the prompt states. A course study was conducted to study the associa&on of coffee drinking and anxiety and a popula&on based sample of adults. Among 10,000 coffee drinkers, 500 develop anxiety among 20,000 non coffee drinkers. 200 of these individuals developed anxiety. So what is the rela&ve risk of anxiety associated with coffee use? So I went ahead and helped you guys out here and I'll label the columns with our outcome which is anxiety and I label the rows with your exposure which is coffee consump&on. So go ahead and pause the lecture and give it a try. Calculate the rela&ve risk and this scenario. To the prompt says that there are 500 of the 10,000 coffee drinkers that developed anxiety. Coffee drinking the AR, exposure and anxiety being our outcome. So based off of these numbers, we would take 500 and put that number in cell A. We know that 10,000 people were exposed, so to obtain the number for cell B we would subtract 500 from 10,000, which would result in 9500. Let's look at the prompt again to get our last row of numbers. It says that a total of 20,000 people were non coffee drinkers. So these 20,000 people are are unexposed people. So of the unexposed people, these 20,200 of them had anxiety. So then we would take 200 and put it in block C. That would make Cell did 19,800. So let's go ahead and sum up all the rows so we have our numbers of exposed and unexposed handies for our calcula&on. So we have 10,000 people who were exposed, 20,000 people who were unexposed. These numbers will serve as our denominators when we calculate out the incidence of anxiety among the two groups, the exposed group and the unexposed group. The formula for the rela&ve risk is displayed on the slide. We have A / A + b and the numerator and the denominator we have C / C + d. We plug in the respec&ve numbers from the table and we get a rela&ve risk of five, which indicates a posi&ve associa&on. We can't interpret this as coffee consump&on is associated with five &mes higher risk of anxiety. But is this result sta&s&cally significant? Our sample popula&on may not represent the exact disease and exposure that is seen in the target popula&on. We are going to consider Spring0ield as our unexposed group, with a probability of lung cancer among residents being 20%. In comparison, Shelbyville residents have a 10% probability of lung cancer, resulting in a relative risk of 0.5. This means that there is a twofold greater probability of lung cancer among Spring0ield residents compared to Shelbyville residents. However, when looking at it from Shelbyville's perspective, the relative risk is 0.5, indicating a 50% reduction in risk of lung cancer for Shelbyville residents compared to Spring0ield residents. To interpret this as a reduction in risk, we can calculate the percentage by subtracting the relative risk from 1. For example, a relative risk of 0.7 would result in a 30% reduction in risk for Shelbyville residents. It is important to remember to subtract the relative risk from 1 when interpreting as a reduction in risk. Alternatively, we can state that residents of Shelbyville have 0.5 times the risk of lung cancer compared to residents of Spring0ield. Both interpretations are correct. Now, let's calculate the relative risk for the research question provided. The study aimed to investigate the association between coffee consumption and anxiety in a population-based sample of adults. Among 10,000 coffee drinkers, 500 developed anxiety, while among 20,000 non-coffee drinkers, 200 developed anxiety. This results in a relative risk of 5, indicating a positive association between coffee consumption and anxiety. However, it is important to note that this result may not be statistically signi0icant as our sample population may not accurately represent the target population. Estimating Risk - Part 3: Attributable Risk The aEributable risk is a measure that has more of a clinical and public health impact. When we want to ask how much a disease is linked to a certain exposure, we're going to refer to the aEributable risk, which is defined as the amount of disease incidence that is aEributed to a specific exposure. This measure is used to help. Let's figure out how much of the disease risk can't be prevented if we remove the exposure itself. It is the incidence of a disease and the exposed popula&on that would be eliminated if exposure was removed. We can get aEributable risk by taking the difference in the incidence of disease and the exposed by the incidence of disease and the unexposed. We subtract the incidence of disease and the unexposed because this represents the background risk. The aEributable risk percent is the percent of disease incidence and the expose that is due to the exposure itself. I know this sounds very familiar to AEributor risk, but there is a slight dis&nc&on. While the aEributable risk is the amount of disease incidents that can be aEributed to a specific exposure, at Trudeau risk percent is a propor&on or percentage. So is the propor&onal percentage of the incidence of disease and exposed that would be eliminated if exposure was removed. So aEributable risk looks at amount, aEributable risk percent looks at percent. To calculate the aEributable risk percent, we would take the aEributable risk and divide that by the disease incidence and the exposed, followed by mul&plying this value by 100. Popula&on aEributable risk represents the amount of disease in the whole popula&on that may be prevented if one risk factor was completely removed. If we look at an example of aEributable risk graphically, we see the rate of type 2 diabetes among the exposed, which in this case is being either overweight or obese. We also see the rate of type 2 diabetes among individuals who are considered as unexposed. So these individuals have a normal weight. From this graph, we know that the rate of type 2 diabetes among individuals who are overweight or obese is 30%, whereas among normal weight individuals it is only 7%. That would mean that 23% of the rate of type 2 diabetes among those who are exposed, meaning that those who are overweight or obese is actually due to being exposed, or in this case, is actually due to being overweight or obese. This 23 percent is your tribunal risk. So why is this 23% considered the aEributable risk? Well, to calculate aEributable risk, we would take the type 2 diabetes among the exposed and subtract the type 2 diabetes among the unexposed. As you recall, it was 30 for the exposed and seven for the unexposed. So this will result in 23 of the 30 instances of type 2 diabetes and the overweight or obese group being aEributed to the fact that they were overweight or obese. Looking at the graph again, we see the doEed horizontal line running across the graph at 7%. This represents type 2 diabetes rate among the normal weight individuals, or in other words the unexposed. So this 7% is the background rate. Any excess amount a\er 7% that we see in the exposed group, the overweight or obese would be due to the exposure itself, which is basically high out of pacity. So this 23 percent is their total risk of Type 2 diabetes due to being overweight or obese. If we wanted to calculate the aEributable risk percent, we would take the aEributable risk and divide that by type 2 diabetes among those who were exposed. Which was again 30. A\er which we will mul&ply it by 100 to get 77%. AEributable risk percent represents A propor&on or percentage, whereas aEributable risk is the amount itself. So for aEributable risk percent, 77% of the type 2 diabetes among the exposed group may be aEributed to being overweight or obese, which would mean that 77% of type 2 diabetes. Diagnosis could be prevented if we were able to decrease adiposity in the popula&on to the point that everyone is within the normal weight category. So let's look at another example where an inves&gators would like to look at fish consump&on and stroke. Now this example non fish eaters are those who report never ea&ng fish and they are considered to be the exposed group. So keep that in mind as we move forward daily fish consump&on is considered as non exposed or unexposed. We have on the right side of the slide several incidents calcula&ons for various groups. We have incidents among our exposed group, so our non fish eaters being 5.03 per 100 by taking the number of people who had a stroke and dividing it by the total number of people who were exposed. So that was 82 / 1631. The second incidence we have on the screen is the incidence among our unexposed group people who eat fish daily. We calculated this by taking the number of unexposed people who have a stroke, 23, and dividing it by the total number of unexposed people, which was 802. And lastly, we have our incidence of stroke and the en&re popula&on. So that's the en&re study popula&on and this is regardless of exposure status Here we're taking the total number of strokes, 105 and then we're going to divide that by the total number of people in the en&re study, which was 2433. To get an incidence of 4.32 per 100. We can use these numbers to calculate a rela&ve risk. We take the incidence among the exposed and then we divide it by the incidence among the unexposed to get a rela&ve risk of 1.75, indica&ng that there is a posi&ve associa&on. So people who never consume fish have 1.7 &mes higher risk of a stroke compared to people who eat fish on a daily basis. All these summers can help us calculate all the forms of a tribunal risk we've learned so far. These incidence values are displayed on the le\ hand side of the slide now, so let's use some in our calcula&ons star&ng with AEribute or Risk, which tells us the amount of disease incidents that can be aEributed to a specific exposure. We will take the incidence and the exposed and subtract that by the incidents and the unexposed, which gives us an atrial risk of 2.16 per 100. For the aEribu&ve risk percent, we would take that amount and divide it by the incidence among the exposed, and then we apply a mul&plier. Doing this, we get in a chorus percent of 43. For popula&on aEributable risk, we take the incidence of stroke in the popula&on and subtract the incidence among the unexposed, here being the incidence among fish eaters, and then we get a 1.4 per 100. If we would like to get popula&on aEributable risk, which gives us the propor&on rather than the amount, we would divide the popula&on aEributable risk by incidents in the total popula&on and apply the mul&plier to get 33.6%. In terms of the interpreta&ons, A rela&ve risk of 1.75 would mean that people who are exposed, so people who never eat fish, have 1.7 &mes higher risk of a stroke compared to people who are not exposed, so those who eat fish on a daily basis. The aEributable risk is 2.16 per 100. This means that if people who do not eat fish change their ea&ng habits and begin to eat fish on a daily basis, then their incidence of strokes would decrease by 2.16 per 100 individuals. For a child to risk percent, we can interpret this in two ways. We can either say that there would be a 43% reduc&on in stroke incidence if exposure was completely eliminated, or we can simply say that it represents a 43% reduc&on in stroke incidence among the exposed individuals. For popula&on aEributable risk and popula&on of tribal risk percent, we're thinking about trivial risk in terms of the popula&on instead of focusing on the exposed group. So star&ng with popula&on of total risk of 1.45 per 100, this could be interpreted as there would be a reduc&on of about 1.45 new cases of stroke per 100 individuals in the popula&on. If everyone eats fish on a daily basis. For popula&on of Trudeau risk, there would be a reduc&on of 33.6% and stroke incidence in the popula&on if everyone eats fish on a daily basis. So let's revisit our example of lung cancer and air pollu&on in our two ci&es of Springfield and Shelbyville, and we can calculate aEributable risk and aEributable risk percent. We can do this from the standpoint of Springfield because Springfield is considered as exposed due to its air pollu&on. So for a Trudeau risk, we would again take the incidence of lung cancer in Springfield and subtract the incidence of one cancer in Shelbyville. When we do this, we get 10. For aEribute risk percent, this is a propor&on of aEributable risk. So we take a trivial risk and divide that by the incidence of lung cancer and they expose and we get 50%. We can say that 50% of lung cancer cases can be aEributed to living in Springfield. If we remove Springfield the exposure to air pollu&on, we reduce the risk of lung cancer by 50%. You can also say that if individuals moved away from Springfield or no longer lived there. Remember that a rela&ve risk is a measure of associa&on. It's important for determining whether an associa&on is present between exposure and disease, and to see if there is enough evidence to support a causal inference. It is a measure of associa&on in court studies when researchers are inves&ga&ng disease ideology. However, the aEribu&ve risk measure is important when we think of clinical prac&ce and public health. It tells us how much the disease risk is aEributed to a certain exposure. It helps people in the public decide which strategies to focus on for reducing disease. This slide displays the aEributable risk, aEribute risk percent and rela&ve risk for smoking and lung cancer, as well as coronary heart disease. We see that the rela&ve risk for smoking lung cancer is 14 compared to smoking and coronary heart disease which is 1.6. We have our aEributed risks telling us that 256 per 100,000 deaths from coronary heart disease could be prevented if smokers would quit. 130 deaths per 100,000 from lung cancer would be prevented if smokers would quit. So why is it that fewer deaths are prevented from lung cancer 130 if smoking was eliminated compared to 256 for coronary heart disease, when their children risk percent as lower for coronary heart disease compared to lung cancer? This is because of the number of people who smoke who die from coronary heart disease is much higher than for lung cancer. You have 669 smokers who die of coronary heart disease compared to 140 smokers who die of lung cancer. So the aEributable risk is much higher for coronary heart disease than for lung. It has to do with the amount, not necessarily the propor&on. Estimating Risk - Part 4: Odds Ratio Are generally thought of when you think of case control studies, even though you can calculate it, and cohort studies as well. When you think of the case control study, you merely think of an odds ra&o as the measure of associa&on because of the design itself. OZ ra&os are used when studies start with disease status and informa&on on exposure status is collec&ve retrospec&vely. As I men&oned, oscilla&ons can be calculated in cohort studies as well. For the case control study, the odds ra&o is propor&on of cases who were exposed compared to the propor&on of controls who were exposed. Course studies have as their measure of associa&on the rela&ve risk. This is because they are powerful enough to their ability to establish temporality. That being said, if they can calculate a rela&ve risk which requires temporality, then they can calculate an odds ra&o which does not require temporality. But I want you to remember that even though the cohort study can calculate both a rela&ve risk and an odds ra&o, whenever you think of a cohort study, think of rela&ve risk. For cohort studies, the ICE ra&o is the propor&on of exposed people who developed the disease compared to the propor&on of unexposed people who developed the disease. Before we get into how to calculate an Oz ra&o and how to interpret them, let's backtrack a bit to cover probability and odds. So what is probability? Probability measures the number of &mes the outcome occurs rela&ve to the number of observa&ons or sample size. Odds, on the other hand, measures the number of &mes the outcome occurs. Relate. Times it does not. So the difference is that probability compares it to a sample size and Oz compares it to the number of &me diseases not occur. And finally, the Osprey show compares the odds of those exposed to the risk factor and the odds of those unexposed. What's the difference between risk and odds? This looks at the chances of something happening rela&ve to the chances of everything happening, whereas all Z is a chance of something happening, rela&vely chance of it not happening. If I were to choose someone from the Classic, what's the likelihood that I will pick you? If we say that the class is only comprised of 60 word for simplicity, what is the risk? The IQ? It would be one out of six because the chances of it happening is 1. The chances of all things happening is 6. This is because the class is made of six people, including yourself. The odds are that you are going to plan out of five or 20% because the chance I picked this one and the chance that I won't pick was five since I can pick any of the five other students in the class. So then that would mean that the all the you is about 20% compared to the risk of Edu which is only 16%. The odds ra&o is the ra&o of odds that cases were. As shown in the formula display. To calculate an observa&on on a case control study, we'll start by focusing on our two groups. Here says it's a case control study. We look at disease status, so by the columns. We look at the odds by disease group, your cases, and your controls. What is the number of &mes exposure occurs among? That would be a / C everyone in. The. Keep on the. Some&mes exposure. This would be divided by. If you. Yep. Eight &mes. This is. Let's calculate an oscilla&on recently case which was. And this paper they. Chili. 1st. This. The numbers. Which is? A\er we do this, we. The interpreta&on for the osprey. To the direc&ons. The interpreta&on that. But again, the odds ra&o. There is no associate. This means that the odds of. PreEy much the same as the. If the odds ra&o is greater than one, that there's a. Because the. Cases is going to be greater than the. However, if the odds ra&o is less. Specia&on. This is because the odds of exposure in your. In our case, study examining the rela&onship with Interprets. So there is a posi&ve aspect. These findings sta&s&cally signify. We have the steps to calculate the. It's slightly different for Osman. If you're. Is slightly. Table. Let's first look at her standing. Need to plug in the. Why this? And then we get a. We have one more. To get. We. 3. So. Measure with socia&on. But no&ce. This is because. So now it's your turn to calculate the odds. And this example the inves&gators want to examine vitamin D. They found that. Single year in the United. 600. Mothers were given a dietary. Deficiency. 84 said they did not divide. Of the control. Did not use. Construct. Table and calculate the odds. Also figure out if the odds ra&o is sta&s&cally signific. Go ahead and pause the lecture. So we have the outcome. And then? Supplementa&on on the. With five in use, yes, and. States that. Dicta&on. Number of. I did. So that would be 180. Controls were exposed to the. Dicta&on. We know that. Of 600. Without. Off. 37. So that's. A\er. 30. PreEy easy. It should be 84. Just a. Taxi. Plug. And we get an Oscar. This. Use has. There's. The reason why? Because for all. Less than one. Pause. That would be. If you want you can also. As. 7 hours odds. During. What are the? To determine this. First calculate. You goEa stand. East. Uses. It comes out. This is your. Based on the 95% confidence. There's been some &me interpret. This table is from a study. Perspec&ve. Examine the associate. And. About. They usually just suppress. And. Let's take a look at the. Happening. But before we do. We have two varia&ons of the outcome here, one being ever. I had it in the past. And the second outcome varia&on is currently. The exposure. See Return of smoking. For this exposure, they actually had three category. Instead of. They. Then they have two other. 1. They also examined. This. Someone else? This miracle is a douche. Either. You see the value? We. This. Not. Table. Just. OSU ra&o. Just. Which of the following statements about the table is not? He says that there is no associa&on between the. Smoke during the post employment and children ever have. If you look at the results between coastal living with the household smoker and ever in current. The findings are not sta&s&cally significant because the 95. Because of this, the statement is true. The results you must do so on the adjusted. Because the adjusted model is the final model. Takes it to the. Here the inves&gators adjusted for a number of import. These are listed on the boEom of the table. You said that. Please. The number of children at baseline. Dicta&on. History of. As well. So they took it to account number. This is why I always these argumenta&ons of essay on the. Let's go ahead and move. It says that there is no associa&on. Pregnancy. It also specifies that it's referring to both ever and current asthma. Par&cular. The adjusted oscilla&ons from this exposure outcome rela&onship is also not. Because of this, the statement is. The third statement says that children currently have an absconding higher. Specials for this. Which would indicate a posi&ve rela&onship, but as stated, we cannot conclude that there is a posi&ve rela&onship. 95%. Readers from 0.64 meters here in the studio with. Mode. Pinnacle really applies to the volunteer because that is where Donald Trump is trying to scramble constantly to figure out what he's going to do. And they really don't have any idea how they're gonna handle this and they are just days away now when it comes to the. Was moving confirmed that he is. It says that there is no rela&onship between. Whether it be at any&me recently? Second one. They are not ci&zens. Now. You get the access of star&ng your expose and divide that by 1 minus. That is, this does not to the right and the denominator you would get the incidence of disease and the unexposed and divide that by 1 minus that incidents. Once you simplify all that down you get the formula that looks. Which is 8 * B / B * C and o\en if we look at the calcula&ons for Oz ra&os for case control studies and core studies side by side, we see the differences and the similari&es. So what are the differences? Well for the case control study we're looking at it from a disease status, also exposure and cases rela&ve to odds of exposure and controls. For the cohort study, we're looking at it from an exposure status posi&ve disease and exposed rela&ve to odds of disease and unexposed. A\er we simplify everything, we end up with the exact same equa&on, A * D / B * C so that makes things a lot easier. We can use the same formula to calculate the odds ra&o in a case control study. As a cohort study. So let's look at observa&ons from case control studies and AUZ ra&os from cohort studies. We can look at this and an example of a study that looks at the rela&onship between congenital malforma&ons and metal blastoma status. First, this complete and odds ra&o from a case material perspec&ve. What are the odds of congenital malforma&ons? For cases? It would be 23 / 217 because that would be the number of cases exposed, which is 23 divided by the number of cases are not exposed, which is 2/17. This one is sought in 0.105 for the oz ra&o you can calculate using the standard formula. 8 * b / b * C to get 2.1. When we talk about an ostrich or using the same example but as if the study was a course that you were asking what the odds of a child would be exposure is of developing neuroblastoma. You would take the number of exposed to have neuroblastoma rela&ve to the exposed who do not have neuroblastoma. So that would be 23 / 116. And this equals to 0.2. We can again calculate an odds ra&o using the same formula and then we get 2.1 which is the same number. Let's visit another example focusing on a historical event, the Sinking Representa&ve. Here we're examining the rela&onship between sex and death. Just glancing at the numbers in the con&ngency table, we can see that the mail is risk factor of death on the Titanic. But how much more likely is a mellow to dive than a female? What are the odds of dying for each sex? Trial for females, you have 154 who die rela&ve to 308 did not die, resul&ng in 0.5 medical. The odds are two to one against dying for females Now you have 709 miles dying rela&ve to 142 live, resul&ng in five. This means the osmer 5 to one in favor of death for melts. Now we should calculate the odds ra&o using the formula A * D / B * C. He's going out a\er recording ar&st from the table we get in Oswayo of 10. We would interpret that as there's a tenfold greater odds of death when Bell sends emails. We should calculate rela&ve risks using the same table. For females, the probability of death is 33% as 154 out of the 462 female style. For males, the probability of death is 83% since 709 out of the 851 mels died The rela&ve risk of death is 2.5 a\er we do the calcula&on, meaning that there is a posi&ve associa&on. We would interpret this as there is a 2.5 greater probability of death from males than females. So let's stop these measures of associa&on. For an OSS ra&o we got 10. There is a tenfold greater odds of death from males and females. For rela&ve risk, we got a 2.5, meaning that there is a 2.5 greater risk of death from males and females. Both these measures come to the same conclusion, saying that males are more likely to die on the Titanic. But the odds ra&o implies that men's likelihood of dying is far worse than females than the rela&ve risk es&mate 10 versus 2.5. So which of these is the fair comparison? Well, there really isn't a right or wrong way, but we just need to remember that a rela&ve risk measures events in a way that is more interpretable and is more in line with the way people think from exposure to disease. But our rela&ve risk can't always be computed, it's only possible in court semngs. So some&mes you must rely on an OZ ra&o. And remember that the Oz racial interpreta&on should be carefully wriEen. You shouldn't save risk of disease because it doesn't measure risk, it measures odds. And that is why for the interpreta&on here is states that there's a temporal greater odds of death for mills than females. And some instances the OZ ra&o can es&mate the rela&ve risk. There are three instances in which it can do this. 1st, when the cases and your case control study are representa&ve of all the people with the disease with regard to exposure prevalence. Same goes for controls. So when controls are representa&ve of all the people without the disease with regard to exposure prevalence, then at this point the odds ra&o can possibly es&mate rela&ve risk. So basically for those two bullets, when cases and controls are representa&ve. And lastly if the disease being studied is rare. So we covered how to calculate your standard OZ ra&o, but what about case control studies where you match based off of a confounder? Do you have a mashed cakes Mitchell study? Then you would need to calculate the odds ra&o using a different formula. You cannot use the standard A * C divided by me &mes C. You need to analyze the data based off of case control pairs rather than individual subjects. So we would have four combina&on of pairs. Two sets of pairs would be concordant pairs, wherein pairs of cases and controls would both be exposed, and pairs of cases and controls would both be unexposed so they match according to their exposure status. Then you have two sets of pairs that are considered as discordant. Among the discorded pairs you have pairs where the case was exposed with control was not and then and the second set of this coordinate pair you would have controls over exposed and cases who were not. So the discordant pairs would have pairs that differ with regard to exposure status. For a match case control study, we set up the two by two table differently. We have controls for the columns and cases for the rows. So previously we had disease for the columns and exposure for the Rose. But here the columns and the rows have two sets of informa&on, so in square A. This would represent a concordant pair, a pair that was essen&ally matched with regard to exposure status. Both your cases and your controls are exposed here. And square B we have a discordant pair with a control that is not exposed in a case that is exposed. Foresee this is also a discordant pair. We have a controller exposed in a case not exposed. And finally, it's weird. We have our last concordant pair with both cases and controls that were not exposed. To calculate odds ra&os and match samples, we focus solely on the discorded pairs, so we ignore the concordant Paris because they don't contribute to the calcula&on of effect es&mate. Remember they are the same with regard to exposure status. So the match odds ra&o is a ra&o of discordant pairs, the number of pairs in which the cases were exposed rela&ve to the number of pairs in which the controls were exposed. So B / C. An example of a match case control study that examines the risk factors of brain tumors in children. Inves&gators hypothesized that children with certain childhood cancers are more likely to have higher birth weight. Cases are children with brain tumors. Controls were those without brain tumors and exposure is based off a cut off of birth rate greater than. 8 lbs. To calculate the match oz ra&o, we would use the formula B / C and focus on the discordant pairs. We refilled the formula with 18 / 7 to get 2.6 as the match oz ra&o. This indicates a posi&ve associa&on. We can interpret this. There's a 2.6 Volt greater odds of children with brain tumors having a birth rate greater than 8 lbs compared to having a birth rate less than or equal to 8 lbs. The calcula&on of a 95% confidence interval in a match case control study is a bit more complicated, so we won't be calcula&ng it in this course.