Biostatistics Lesson 3 PDF

Stefanos Bonovas, MD, MSc, PhD Associate Professor of Medical Statistics Department of Biomedical Sciences Humanitas University Course: Biostatistics Lesson 3. April 04, 2023 Measures of disease occurrence Uncertainty in Medical Research Medical research is not an exact science… …uncertainty...

Stefanos Bonovas, MD, MSc, PhD Associate Professor of Medical Statistics Department of Biomedical Sciences Humanitas University Course: Biostatistics Lesson 3. April 04, 2023 Measures of disease occurrence Uncertainty in Medical Research Medical research is not an exact science… …uncertainty is always present Uncertainty can be expressed either: – Qualitatively using terms like ‘probable’, ‘possible’, ‘likely’ – Quantitatively using probabilities (P) • Advantage: explicit interpretation, exactness • Disadvantage: may force one to be more exact than is justified! Probability and Odds • Probability (P) = a measure of the likeliness that a random event will occur (mathematically, it is a function that assigns random events numbers between 0 and 1) • Odds = ratio of the probability of having an event to the probability of not having the event or P/(1–P) Example: 1 out of 5 patients have flu… Probability and Odds • Probability (P) = a measure of the likeliness that a random event will occur (mathematically, it is a function that assigns random events numbers between 0 and 1) • Odds = ratio of the probability of having an event to the probability of not having the event or P/(1–P) Example: 1 out of 5 patients have flu… • Prob = 1/5 = 0.20 or 20% is the probability of having flu • Odds = (P) / (1-P) Odds = 0.2/0.8 = 0.25 or “1 flu case to 4 persons without flu” Probability and Odds • Probability (P) = a measure of the likeliness that a random event will occur (mathematically, it is a function that assigns random events numbers between 0 and 1) • Odds = ratio of the probability of having an event to the probability of not having the event or P/(1–P) Example: 1 out of 5 patients have flu… • Prob = 1/5 = 0.20 or 20% is the probability of having flu • Odds = (P)/(1-P) Odds = 0.2/0.8 = 0.25 or “1 flu case to 4 persons without flu” Risk, Odds, and 2×2 tables Exposed Case a Non-case b a+b Non Exposed c d c+d a+c b+d Risk, Odds, and 2×2 tables Exposed Case a Non-case b a+b Non Exposed c d c+d a+c b+d Risk of being a case in exposed = a / a+b Risk of being a case in non exposed = c / c+d Risk, Odds, and 2×2 tables Exposed Case a Non-case b a+b Non Exposed c d c+d a+c b+d Risk of being a case in exposed = a / a+b Risk of being a case in non exposed = c / c+d Odds of being a case in exposed = a / b Odds of being a case in non exposed = c / d Relationship between probability and odds Probability and odds are more alike the lower the absolute P (risk) Probability Odds 0.80 4.0 0.67 2.0 0.60 1.5 0.50 1.0 0.40 0.67 0.33 0.50 0.25 0.33 0.20 0.25 0.10 0.11 0.05 0.053 0.01 0.0101 • Odds = P/(1–P) Example: if P = 0.67 Odds = 0.67/(1–0.67) Odds = 0.67/0.33 = 2.0 Measuring disease occurrence Odds of a rare event equal the risk of rare event The number of hepatitis A cases during an outbreak Cases Non-cases 30 49,970 Hepatitis A Risk of disease = 30 / 50,000 Total 50,000 = 0.0006000 30 / 50,000 Odds of disease = -------------------- = 0.0006004 49,970 / 50,000 Measuring disease occurrence counts number of cases “we have 2 cases of cancer” On its own very little informative!! Who is in the denominator ???? In what time period did they occur??? Measuring disease occurrence Ratio Proportion Rate What, who is in the denominator ???? In what time period did they occur ??? Ratio • The division of two numbers • Numerator NOT INCLUDED in the denominator • It allows to compare quantities of different nature males = 5 / 2 = 2.5 /1 females beds = 850 / 10 doctors = 85 / 1 Ratio Ratio Ratio Ratio Proportion • The division of 2 numbers • Numerator INCLUDED in the denominator • In general, quantities are of same nature • In general, it ranges between 0 and 1 • Percentage = proportion x 100 males = 2,000/5,000 population = 40% Proportion Rate • The division of 2 numbers • TIME INCLUDED in the denominator • Speed of occurrence of an event over time HBV+ in 2015 Population in 2015 = 2,000 / 15,000,000 * 1 = = 0.00013 = 1.3 per 10,000 inhabitants per year • Rate may be expressed in any power of 10: 100, 1000, 10000, 100000, etc. Measuring disease occurrence Number of cases of disease Population – Number of cases of a disease in a given population at a specific time – Proportion of the population that had the disease at a given time – Probability of having the disease (values between 0 and 1) prevalence Measuring disease occurrence Number of NEW cases of disease during a period Healthy population (at risk) at the beginning of that period – Number of new cases of a disease in a given population at a specific time period – Proportion of the population that acquire or develop a disease in a period of time – Probability of developing a disease (values between 0 and 1) incidence Measuring disease occurrence Incidence rate Speed of developing a disease (ranges from 0 to infinity… it is not a proportion!) Number of NEW cases of disease Total person-time of observation Denominator: - is a measure of time - the sum of each individual’s time at risk (the subject is free from disease) Incidence and incidence rate Person 1 l Person 2 l Person 3 l Person 4 Person 5 l l Person 6 l 3 yrs x 4 yrs 6 yrs x x 3 yrs 1 yrs 5 yrs 22 p.y 2003 2004 2005 Incidence = ? Incidence rate = ? 2006 2007 2008 2009 Incidence and incidence rate Person 1 l Person 2 l Person 3 l Person 4 Person 5 l l Person 6 l 3 yrs x 4 yrs 6 yrs x x 3 yrs 1 yrs 5 yrs 22 p.y 2003 2004 2005 2006 2007 2008 Incidence = 3 cases / 6 persons = 50% Incidence rate = ? 2009 Incidence and incidence rate Person 1 l Person 2 l Person 3 l Person 4 Person 5 l l Person 6 l 3 yrs x 4 yrs 6 yrs x x 3 yrs 1 yrs 5 yrs 22 p.y 2003 2004 2005 2006 2007 2008 2009 Incidence = 3 cases / 6 persons = 50% Incidence rate = 3 cases / 22 person-years = 0.14 or 14 cases / 100 person-years Incidence rate Subject Period of follow-up Years of follow-up Outcome 1 1980–1984 5 years Healthy 2 1981–1983 3 years HIV+ 3 1980–1984 5 years Healthy 4 1980–1983 4 years Lost 5 1980–1984 5 years Healthy 6 1982 1 year HIV+ 7 1980–6/1982 2.5 years HIV+ 8 6/1983–1984 1.5 years Drop-out 9 1980–1984 5 years Healthy Total 32 person-years Incidence rate ? Incidence rate Subject Period of follow-up Years of follow-up Outcome 1 1980–1984 5 years Healthy 2 1981–1983 3 years HIV+ 3 1980–1984 5 years Healthy 4 1980–1983 4 years Lost 5 1980–1984 5 years Healthy 6 1982 1 year HIV+ 7 1980–6/1982 2.5 years HIV+ 8 6/1983–1984 1.5 years Drop-out 9 1980–1984 5 years Healthy Total 32 person-years Incidence rate 3/32=0.094 or 9.4 HIV infections per 100 individuals per year Measuring disease occurrence Attack rate Cumulative incidence during an outbreak – Expressed for the entire epidemic period, from the first to the last case – Not really a rate but a proportion! Outbreak of gastroenteritis in a wedding ceremony Number of cases 20 Population Attack rate 200 10% Interpretation… Measuring disease occurrence Descriptive Prevalence Probability of having the disease Burden Incidence Probability of developing the disease Risk Concept of the prevalence “pool” New cases (Incidence) Recovery rate Death rate Relationship between Prevalence and Incidence • Prevalence is a function of: – the incidence of the condition, and – the average duration of the condition • duration is influenced in turn by the recovery rate and the mortality rate • Prevalence ~ Incidence × Duration Incidence – Prevalence Important note: "Population at risk" An important factor in calculating measures of disease occurrence is the correct estimate of the numbers of people under study. Ideally these numbers should only include people who are potentially susceptible to the diseases being studied. For instance, men should not be included when calculating the frequency of cervical cancer… The people who are susceptible to a particular disease are called the population at risk, and can be defined by demographic, geographic or environmental factors. For instance, occupational injuries occur only among working people, so the population at risk is the workforce; in some countries brucellosis occurs only among people handling infected animals, so the population at risk consists of those working in farms or slaughter houses… Workshop 1 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/csels/dsepd/ss1978/SS1978.pdf