Epidemiologic cohort studies frequently make use of a comparison group to infer what background rate of death or disease might have occurred in the exposed cohort in the absence of exposure. Unlike cohort analyses utilizing the standardized risk ratio, regression analyses of risk can often be performed without the need for a comparison group, avoiding possible bias in the risk estimate. Demographic factors related to the background rate may also modify the risk (effect modification). Including the comparison group can improve the precision of effect-modification parameter estimates, but if there is inadequate adjustment for heterogeneity between exposed and comparison groups in the background effects of these factors, the effect-modification parameter estimates can be biased. We studied this bias and the precision of effect-modification parameter estimates using theory and simulation. The problem is illustrated using data from studies of radiation exposure of atomic-bomb survivors that include a comparison group selected from distal geographic areas having different gender-specific rates of death. We conclude that, for studies of effect modification in cohorts covering a wide range of exposures including doses close to zero, there may be no advantage to including a comparison group, as long as internal standardization is feasible.
We conducted a simulation study to see how much bias reduction occurred where an intermediate variable was included in imputation model but not in analysis model for multiple imputation method, if missing depends on the intermediate variable. We compared the results with those of complete case analysis. We assumed the causal pathway that obesity causes coronary heart disease (CHD) only through hypertension as an intermediate variable. We further assumed that the missing on the CHD depends on hypertension status. The data sets of systolic blood pressure, occurrence of CHD and missing on the CHD were obtained by the normal and binomial random number generator. Using these data sets, we obtained parameter estimates of obesity by logistic regression model for the multiple imputation and the complete case analysis. The variable of hypertension was included in the imputation model only for the multiple imputation. The proportions of missing data were set to 10, 20, and 30 % and the number of simulation for each condition was set to 2000 times. Analyses with complete data sets were also conducted. Unbiased estimates were obtained by applying the multiple imputation where the intermediate variable was included in the imputation model only.
In clinical trials, some patients are dropped-out of the trials by the different causes and their outcomes may happen to be missing. In such a case, analyses ignoring the missing mechanisms lead a biased estimator. One of the methods for taking them into account is the IPCW (Inverse Probability of Censoring Weighted) method, which accounts for the observed past histories of time-dependent factors that are predictors of drop-outs and are correlated with the outcomes. In this method, the probability of being censored is usually modeled via a logistic regression without considering the causes of drop-outs. We developed the IPCW method including the causes of drop-outs such as improvement or aggravation. As an example, we analyzed the data from a randomized clinical trial of a drug for osteoporosis. To evaluate the efficacy, the difference of the rate of increasing in the lumber vertebral mineral density at 48 weeks from baseline in the two dose groups were estimated. We compared the results of the proposed IPCW methods with those of the usual IPCW methods, complete-case analysis, and LOCF method. Although the results of the two IPCW estimators did not change much, the missing mechanisms could be modeled reasonably and could be interpreted clinically by the proposed method compared with the usual IPCW method.