Biostatistics Lesson 4 PDF

Stefanos Bonovas, MD, MSc, PhD Associate Professor of Medical Statistics Department of Biomedical Sciences Humanitas University Course: Biostatistics Lesson 4. April 13, 2023 Measures of association Risk Odds Two-by-two table (contingency table) Measures of association A measure of associ...

Stefanos Bonovas, MD, MSc, PhD Associate Professor of Medical Statistics Department of Biomedical Sciences Humanitas University Course: Biostatistics Lesson 4. April 13, 2023 Measures of association Risk Odds Two-by-two table (contingency table) Measures of association A measure of association quantifies the relationship between an exposure and a particular disease. Exposure is used loosely to mean not only exposure to foods, mosquitoes, a toxic substance, or a partner with a sexually transmissible disease, but also inherent characteristics of persons (for example, age, race, sex), biologic characteristics (immune status), acquired characteristics (marital status), activities (occupation, leisure activities), or conditions under which they live (socioeconomic status, or access to medical care). Measures of association The measures of association described here compare disease occurrence among one group with disease occurrence in another group. Examples of measures of association include:  Risk Ratio  Rate Ratio  Odds Ratio Risk Ratio Definition: A risk ratio compares the risk of a health event (e.g. disease, injury, risk factor, or death) among one group, with the risk among another group. It does so by dividing the risk in group 1 by the risk in group 2. Often, the group of primary interest is labeled as the “exposed group”, and the comparison group is labeled the “unexposed group”. Risk Ratio The formula:    A risk ratio of 1.0 indicates identical risk among the two groups. A risk ratio greater than 1.0 indicates an increased risk for the group in the numerator (exposed group). A risk ratio less than 1.0 indicates a decreased risk for the exposed group, indicating that perhaps exposure actually protects against disease occurrence. Risk Ratio Example 1: In an outbreak of tuberculosis (TB) among prisoners in South Carolina, 28 of 157 inmates residing on the “East wing” of the dormitory developed TB, compared with 4 of 137 inmates residing on the “West wing”. Data are summarized in the following 2x2 table... Risk Ratio Risk Ratio Risk Ratio Example 2: In an outbreak of varicella (chickenpox) in Oregon, varicella was diagnosed in 18 of 152 vaccinated children compared with 3 of 7 unvaccinated children. Data are summarized in the following 2x2 table... Risk Ratio Risk Ratio Risk Ratio Example 3: Risk Ratio Risk Ratio Rate Ratio Definition: A rate ratio compares the incidence rates, person-time rates, or mortality rates of 2 groups. The rate for the group of primary interest is divided by the rate for the comparison group… Rate Ratio The formula: The interpretation of a rate ratio is similar to that of the risk ratio.  A rate ratio of 1.0 indicates equal rates in the two groups…  A rate ratio greater than 1.0 indicates an increased risk for the group in the numerator…  A rate ratio less than 1.0 indicates a decreased risk for the group in the numerator… Solution: 1. Rate ratio comparing current smokers with nonsmokers = rate among current smokers / rate among non-smokers = 1.30 / 0.07 = 18.6 2. Rate ratio comparing ex-smokers who quit at least 20 years ago with nonsmokers = rate among ex-smokers / rate among non-smokers = 0.19 / 0.07 = 2.7 3. The lung cancer rate among smokers is 18 times as high as the rate among non-smokers. Smokers who quit can lower their rate considerably, but it never gets back to the low level seen in never-smokers. So the public health message is: “If you smoke, quit. But better yet, don’t start!” Odds Ratio An odds ratio is another measure of association that quantifies the relationship between an exposure with two categories and health outcome. Referring to the two-by-two table, the odds ratio is calculated as: Calculate the Odds Ratio, and compare with the Risk Ratio… Example 1: Calculate the Odds Ratio, and compare with the Risk Ratio… Example 1: Risk Ratio = 5.0 / 1.0 = 5.0 Calculate the Odds Ratio, and compare with the Risk Ratio… Example 1: Risk Ratio = 5.0 / 1.0 = 5.0 Odds Ratio = (100 x 7,920) / (80 x 1,920) = 5.2 Calculate the Odds Ratio, and compare with the Risk Ratio… Example 2: Calculate the Odds Ratio, and compare with the Risk Ratio… Calculate the Odds Ratio, and compare with the Risk Ratio… Example 3: Calculate the Odds Ratio, and compare with the Risk Ratio… Odds Ratio = (139 x 10,795) / (239 x 10,898) = 0.576 (The Risk Ratio was 0.582…) Important note: The odds ratio is the measure of choice in case-control studies (see next Lessons). A case-control study is based on enrolling a group of persons with the disease of interest (i.e. the case-patients) and a comparable group of persons without the disease (controls). The # of persons in the control group is decided by the investigator. Often, the size of the population from which the case-patients came is not known. As a result, risks, rates, risk ratios or rate ratios cannot be calculated from the typical case-control study. However, we can calculate an odds ratio and interpret it as an approximation of the risk ratio, particularly when the disease is uncommon in the population. Important note: The odds ratio is the measure of choice in case-control studies (see next Lessons). A case-control study is based on enrolling a group of persons with the disease of interest (i.e. the case-patients) and a comparable group of persons without the disease (controls). The # of persons in the control group is decided by the investigator. Often, the size of the population from which the case-patients came is not known. As a result, risks, rates, risk ratios or rate ratios cannot be calculated from the typical case-control study. However, we can calculate an odds ratio and interpret it as an approximation of the risk ratio, particularly when the disease is uncommon in the population. Important note: The odds ratio is the measure of choice in case-control studies (see next Lessons). A case-control study is based on enrolling a group of persons with the disease of interest (i.e. the case-patients) and a comparable group of persons without the disease (controls). The # of persons in the control group is decided by the investigator. Often, the size of the population from which the case-patients came is not known. As a result, risks, rates, risk ratios or rate ratios cannot be calculated from the typical case-control study. However, we can calculate an odds ratio and interpret it as an approximation of the risk ratio, particularly when the disease is uncommon in the population. Measures of Public Health Impact A measure of public health impact is used to place the association between an exposure and an outcome into a meaningful public health context. While a measure of association quantifies the relationship between exposure and disease, and thus begins to provide insight into causal relationships, the “measures of public health impact” reflect the burden that an exposure contributes to the frequency of disease in the population. Measures of public health impact often used are:  the attributable proportion, and  the efficacy or effectiveness. Attributable proportion The attributable proportion (also known as “attributable risk”) is a measure of the public health impact of a causative factor. The calculation of this measure assumes that the occurrence of disease in the unexposed group represents the baseline risk (or expected risk) for that disease. It also assumes that if the risk of disease in the exposed group is higher than the risk in the unexposed group, the difference can be attributed to the exposure. Thus, the attributable proportion is the amount of disease in the exposed group attributable to the exposure.  It represents the expected reduction in the disease if the exposure could be removed (or never existed). Attributable proportion Example: Calculation of Attributable proportion In a study of smoking and lung cancer, the lung cancer mortality rate among non-smokers was 0.07 per 1,000 persons per year. The respective rate among those who smoked 1–14 cigarettes/day was 0.57 lung cancer deaths per 1,000 persons per year. Attributable proportion = (0.57–0.07) / 0.57 x 100% = 87.7% Given the proven causal relationship between cigarette smoking and lung cancer, and assuming that the groups are comparable in all other ways, one could say that about 88% of the lung cancer among smokers of 1-14 cigarettes/day may be attributable to their smoking. The remaining 12% of the lung cancer cases in this group would have occurred anyway. Vaccine efficacy & vaccine effectiveness Vaccine efficacy and vaccine effectiveness measure the proportionate reduction in cases among vaccinated persons. Vaccine efficacy is used when a study is carried out under ideal conditions, for example, during a clinical trial. Vaccine effectiveness is used when a study is carried out under typical field (i.e. less than perfectly controlled) conditions. Vaccine efficacy/effectiveness (VE) is measured by calculating the risk of disease among vaccinated and unvaccinated persons and determining the percentage reduction in risk of disease among vaccinated persons relative to unvaccinated persons. The greater the % reduction of illness in the vaccinated group, the greater the vaccine efficacy/effectiveness. Vaccine efficacy & vaccine effectiveness Vaccine efficacy & vaccine effectiveness Vaccine efficacy/effectiveness is interpreted as the % reduction in disease among the vaccinated group. So a VE of 90% indicates a 90% reduction in disease occurrence among the vaccinated group, or a 90% reduction from the number of cases you would expect if they have not been vaccinated. Example: Vaccine efficacy & vaccine effectiveness In an outbreak of varicella (chickenpox) in Oregon, varicella was diagnosed in 18/152 (11.8%) vaccinated compared with 3/7 (42.9%) unvaccinated children. Example: Vaccine efficacy & vaccine effectiveness In an outbreak of varicella (chickenpox) in Oregon, varicella was diagnosed in 18/152 (11.8%) vaccinated compared with 3/7 (42.9%) unvaccinated children. VE = (42.9–11.8) / 42.9 = 72% So, the vaccinated group experienced 72% fewer varicella cases than they would have if they had not been vaccinated. Workshop 2 Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5 Exercise 6 Exercise 7 Exercise 8 Exercise 9 Exercise 10 Bibliography: Principles of Epidemiology in Public Health Practice. An Introduction to Applied Epidemiology and Biostatistics. U.S. Department of Health and human Services, Centers for Disease Control and Prevention (CDC). https://www.cdc.gov/ophss/csels/dsepd/ss1978/ss1978.pdf