Gerstman Case-Control Studies 1 Epidemiology Kept Simple Section 11.5 Case-Control Studies

GerstmanCase-Control Studies2 Introduction  The goal of analytic epidemiologic studies is to elucidate exposure – disease relations  For rare diseases, cohort studies require large sample sizes  Case-control methods were developed to overcome the statistical efficiency of cohort sampling

GerstmanCase-Control Studies3 Case-Control Sampling  Study all cases  Select a random sample of non-cases from source population  Compare exposure status in cases and controls Source Population Identify m 1 c ases Select m 0 noncases Determine % exposed

GerstmanCase-Control Studies4 Historical Example: Levin (1950)  Identify 236 individuals with lung cancer cases  Identify 481 individuals with other non-cancerous conditions  156 of the 236 cases (66%) smoked  212 of the 481 non-cases (44%) smoked  Because smoking was more common is cases, we can infer that there was a positive association between suggesting that smoking and lung cancer Note: Incidence and prevalence can NOT be calculated from case- control samples because sizes of the populations at risk are not known.

GerstmanCase-Control Studies5 Notation Disease + Disease - Total Exposed + A1A1A1A1 B1B1B1B1 N1N1N1N1 Exposed - A0A0A0A0 B0B0B0B0 N0N0N0N0 Total M1M1M1M1 M0M0M0M0N  Disease status indicated by letters A (cases) A (cases) B (controls) B (controls)  Exposure status indicated by subscript [subscript] 1 = exposed [subscript] 1 = exposed [subscript] 0 = nonexposed [subscript] 0 = nonexposed

GerstmanCase-Control Studies6 Calculation of Odds Ratio () Calculation of Odds Ratio (  ) Disease + Disease − Total Exposed + A1A1A1A1 B1B1B1B1 N1N1N1N1 Exposed − A0A0A0A0 B0B0B0B0 N0N0N0N0 Total M1M1M1M1 M0M0M0M0N The odds ratio (denoted ψ ) is simply the cross- product ratio of the counts in the 2-by-2 table Use the Odds Ratio as an estimate of the Risk Ratio

GerstmanCase-Control Studies7 Illustrative Example: Tampon Use and Toxic Shock, Wisconsin Data (p. 215)  Exposure = tampon use  Disease = toxic shock syndrome D+D- E+3071 E-122 Total3193 Tampon-exposed individuals have 9.3× risk

GerstmanCase-Control Studies8 Small Sample Size Formula For the Odds Ratio (Optional)  Some statisticians recommend adding ½ to each cell before calculating the odds ratio, esp. when some cells have very few counts (This is known as the “small sample odds ratio formula”) For the illustrative data:

GerstmanCase-Control Studies9 Why the OR is used as an estimate of the RR  We use the OR as an estimate of the RR  There are two justifications for this  The classical justification described in  The classical justification described in Cornfield, J. (1951). A method of estimating comparative rates from clinical data. Application to cancer of the lung, breast, and cervix. Journal of the National Cancer Institute, 11,  The modern justification described in  The modern justification described in Miettinen, O. (1976). Estimability and estimation in case-referent studies. American Journal of Epidemiology, 103,

GerstmanCase-Control Studies10 Miettinen’s (1976) Justification of the OR Imagine 5 people followed for occurrence of disease D. At time t 1, D occurs in person 1. At t 1 (shaded), select at random a non- cases to serve as a control. (Note: person #2 becomes a case later on, but can still as a control at time t 1 ). Justification (optional): Let A  no. of cases in population and T  person-time in population. The ratio of rates in the exposed (1) and nonexposed (0) populations can be estimated as the ratio of (A 1 /A 0 ) to (T 1 /T 0 ). (A1/A0) is available in the case series and (T1/T0) is stochastically equivalent to B 1 /B 0 in the control series if the controls are a random sample of the population.

GerstmanCase-Control Studies11 Multiple Levels of Exposure E xample: Wynder & Graham (1950) SmokingCasesControls Chain12364 Excessive18698 Heavy Moderate61147 Light1482 None8115 Total  Break-up data into separate 2- by-2 tables using the least exposed group as reference  e.g., Compare chain-smokers vs. non-smokers SmokingCasesControlsChain12364 None8115

GerstmanCase-Control Studies12 Multiple Levels of Exposure (cont) Smoking level CasesControls Chain smokers OR 5 = (123)(115)/(64)(8) = 27.6 Excessive smokers OR 4 = (186)(115)/(98)(8) = 27.3 Heavy smokers OR 3 = (213)(115)/(274)(8) = 11.2 Mod. heavy smokers OR 2 = (61)(115)/(147)(8) = 6.0 Light smokers 1482 OR 1 = (14)(115)/(82)(8) = 2.5 Non-smokers8115 reference group Total Notice increasing risk with increasing exposure: dose- response relationship (biological gradient)

GerstmanCase-Control Studies13 Matched-Pairs  Matching is employed to help adjust for confounding  e.g., matching on age and sex will adjust for these factors  Each pair now represents a single observation  Cross-tabulate pairs to determine odds ratio Control E+ Control E− Case E+ tu Case E− vw Odds ratio formula for matched pairs

GerstmanCase-Control Studies14 Example (Matched Pairs) Control E+ Control E− Case E+ 530 Case E− 105 Exposure triples risk

GerstmanCase-Control Studies15 Comparison of Sampling Methods Although sampling methods differ, all have the same of goal: to elucidate exposure – disease relationships

GerstmanCase-Control Studies16 Comparisons Study Designs Randomized Trials CohortCase-Control ExperimentalObservationalObservational Randomly assign exposure Select fixed number of exposed and non-exposed individuals Select fixed number of cases and non- cases (efficient sampling design) Can calculate RDs and RRs Can calculate ORs only Convenient for studying multiple outcomes Convenient for studying multiple exposures Must be prospective Can be prospective or retrospective Exposure must be retrospective