1. Case-control studies Overview of different types of studies Review of general procedures Sampling of controls –implications for measures of association –implications for bias Logistic regression modeling

2. Learning Objectives To understand how the type of control sampling relates to the measures of association that can be estimated To understand the differences between the nested case-control study and the case-cohort design and the advantages and disadvantages of these designs To understand the basic procedures for logistic regression modeling

3. Overview of types of case-control studies No designated cohort, but should treat source population as cohort Within a designated cohort Nested case controlCase-cohort Cases only Case-crossover Cases and controls 1) Type of sampling - incidence density - cumulative “epidemic” 2) Source of controls - population-based - hospital - neighborhood - friends - family

4. Review of General Procedures Obtaining cases 1) Define target cases 2) Identify potential cases 3) Confirm diagnosis 4) *Obtain physician’s consent 5) Contact case 6) Confirm case’s eligibility 7) *Obtain case’s consent 8) Obtain exposure data *need to account for nonresponse Obtaining controls 1) Define target controls 2) Define mechanism for identifying controls 3) Contact control 4) Confirm control’s eligibility 5) *Obtain control’s consent 6) Obtain exposure data

5. Pros/Cons of Different Methods

6. Case cohort study T 0 Assemble cohort, sample subcohort to be used in all future analyses First case Additional cases, compare all cases to the subcohort selected at T 0

7. Nested case-control Study T 0 Assemble cohort First case; randomly select control from remaining cohort Likewise, select controls again at each separate time point; note: each of these cases was eligible to be a control for the first case

8. Crossover designs Period the subject is exposed Period the subject is unexposed Case-crossover: variation of crossover; case has a pre-disease period which is used as the control period Good method for control of confounding May have limited applications Assumes that neither exposure nor confounders are changing over time in a systematic way

9. Source Population Think of all case-control studies as nested within a cohort, even when the cohort is not designated Source population is this underlying cohort Source population describes the cohort giving rise to the cases; controls are also from this source population Source population reflects the disease under study, difficulties in diagnosing disease, routine procedures for recording the disease occurrence, and the frequency of disease

10. Classic case-control Cases Controls ExposedAB UnexposedCD Odds ratio = AD/BC If sampling: OR = f1*A*f2*D = AD f1*C*f2*B BC

11. Incidence Density Sampling 1) Collect information on each case 2) Collect control at the same time each case is observed; collect control from the underlying source population giving rise to the cases 3) Controls can be cases

12. Cumulative-based sampling 1) Start after the event has happened 2) Ascertain cases 3) Collect controls from the noncases after event (e.g., epidemic)

13. Measures of Association Key concept, sampling fraction, independent of exposure Incidence density sampling/nested case-control studies –if exposure odds in controls(B/D) approximates person-time ratio for source population, odds ratio will approximate rate ratio –without rare disease assumption

14. Measures of Association Case cohort –if ratio B/D approximates overall prevalence of exposure in source population, odds ratio will approximate risk ratio – without rare disease assumption Cumulative “Epidemic” case-control studies –odds ratio will approximate rate ratio if proportion diseased in each exposure group is low (< 20%) and remains steady during study period

15. When is the rare disease assumption needed? Cumulative-based sampling if want to approximate the relative risk Otherwise –nested case-control and incidence density sampling will give an estimate of rate ratio without rare disease assumption –case-cohort will give an estimate of risk ratio without rare disease assumption If disease is rare, all three measures will be very close

16. A closer look Recall: Note: in R&G notation A 1 = A A o = C B 1 = B B 0 = D If sampling does not lead to bias and the sample can approximate the person-years of distribution, a case- control study is a more efficient design (i.e. for same number of people, more precision). However not as precise as if you use the full cohort.

17. Pseudo Rates This assumes that the sampling rates are the same for the exposed and unexposed

18. Pseudo Risks This assumes that the sampling rates are the same for the exposed and unexposed

19. Summary Odds Ratio approximates Rate Ratio –incidence density sampling –nested case- control studies –cumulative sampling is proportion exposed is steady and relatively low Odds Ratio approximates Risk Ratio –case-cohort design –cumulative sampling if disease is rare

20. Source of Controls population-based: not necessarily equal probability, control selection probability is proportional to the individual’s person time at risk neighborhood: need to think about referral patterns (e.g., not good for veteran’s hosp); also need to worry about overmatching hospital: need to be especially concerned that sampling was independent of exposure; try to use a variety of diagnoses for controls. friends: main problem is with overmatching; cedes the control selection to the case rather than to the investigator family:may be worthwhile design to control for certain variable (e.g., spouse control, environment, twin control genetics and environment)

21. Review of control selection Select from source population Select independent of exposure status Probability of selection should be proportion to amount s/he would have contributed to person-time in the denominator Not eligible to be a control, if during same time would not have been eligible to be a case

22. Ille-et-Vilaine study (epidat1.txt) conducted between January 1972 and April 1974 French department of Ille-et-Vilaine (Brittany) Men diagnosed in regional hospitals Controls sampled from electoral lists in each commune of department

23. Other methodological points exposure opportunity –interest is in the fact of exposure –think about cohort design –make same exclusions to cases as to controls comparability of information –may not want comparability if errors are not independent number of different types of control groups –may be appropriate in some situations (e.g., spouse, siblings), but generally not recommended prior disease history

24. Regression Modeling Regression model- simpler function used to estimate the true regression function Benefit of Regression Modeling: overcome the numerical limitations of categorical analysis Cost of Regression Modeling: assumptions of model; invalid inferences if model is misspecified E(Y|X = x) Y = dependent variable, outcome variable, regressand X = set of independent variables, predictors, covariates, regressors

25. Logistic Regression R(x1) Logistic risk model, bounded by 0 and 1

26. Likelihood in logistic regression Cases Controls

27. Interpreting Coefficients If X is continuous, B represents the impact of a one-unit change in X to Y, the exponential of B will give you the OR for a one unit change Note: both modeling variables as either ordered categorical variables or continuous variables assumes the one unit change in X is the same irrespective of the level of X

28. Logistic Modeling Y Linear Model   Log ( Y ) (1-Y) Logistic Model   Not bounded by 0 and 1

29. Assessing Linearity Create categories of continuous variable; categories should represent the same amount of units (e.g., 0-39 grams, 40-79 grams, 80-119, etc) Plot Beta coefficients; if pattern is approximately linear, keep variable as a continuous variable in model

30. Log ( Y ) (1-Y) Logistic Model 11 22 33 44 * * * * * * * *

31. Creating Indicator Variables Also referred to as categorical regressors, dummy variables Need to pick a reference level Number of indicator variables created = # categories - 1 The intercept term picks of the effect of the left out category Note: The precision of the estimate will depend on which category you pick as the referent

32. Things to keep in mind Note: For some variables, nonusers/nonconsumers are different than users/consumers, therefore may want to keep separate zero category Last category may be too heterogeneous Balance between homogeneity and parsimony

33. Changing units One Unit IncreaseX unit increase (e.g., X=10) Point esimate Lower 95% CL Upper 95% CL Note: can also rescale, see pg 371 of R&G

34. Examining confounding and mediation 1) Run a model with exposure only 2) Run a model with exposure and potential confounder (and/or mediator) 3) Examine the changes in the estimate with exposure between model 1 and 2 - if different keep in confounder - many use a 10% change in estimate - if estimate is different but B is still associated with outcome -- partial confounder - data cannot distinguish b/w confounder and mediator

35. Comparing Models Model B: Model A: If model B is no worse than model A, we want to use model B. Always favor parsimony if we don’t have to give up anything One way of comparing models is using the log likelihood ratio test

36. Likelihood Ratio Tests ~ Chi Square with df = (total number of parameters in larger model - total number of parameters in smaller model)

37. Comparing models: Subtract the log likelihoods (part of SAS output) Can use following code or look up in a Chi Square table: data; p = (1-probchi(diff, df)); put p; run; diff = difference in -2 *log likelihoods df = degrees of freedom see above