Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / Estimation of exposure-specific risks (ESRs) using estimates of the overall risk and relative risk of disease given exposure has been performed in previous studies, but the performance of such an estimator has not been assessed nor has a variance for such an estimate been proposed. In this project I evaluated the performance of a simple product-based ESR and its variance derived using the delta method. I used the variance to estimate the 95% confidence interval. I found that this point estimate was biased and that the accompanying 95% confidence interval did not attain 95% coverage. I also proposed a revised product-based estimator and found that this estimator was unbiased. I used the delta method to derive a variance for this estimator and estimated the 95% confidence interval. The coverage of this interval attained 95% coverage in most situations. According to the CONSORT statement, subgroup analyses in randomized controlled trials (RCTs) should be pre-planned and accompanied with a formal test of interaction. I considered the interaction between treatment and a dichotomous prognostic factor with a continuous outcome. I examined the impact of misspecifying the distribution of the prognostic factor on power and sample size for interaction effects. I found that power for the interaction test was decreased when the misspecification of the distribution of the prognostic factor was away from a balanced design. I also proposed three methods for improving the power under misspecifications. Quota sampling maintained the power at 80%, but trial completion may be delayed under misspecifications. Modified quota sampling improved the power, but results were related to the proportion of trials switching to the quota sampling procedure. Sample size re-estimation improved the power, but did not always attain 80% power. All three methods maintained appropriate type I error. Lastly, I examined the impact of unplanned cross-over on power and sample size for interaction effects in RCTs. Unplanned cross-over is common in surgical trials and can diminish the magnitude of the interaction effect. Due to this, the sample size re-estimation procedure performed better than quota sampling and modified quota sampling in the presence of unplanned cross-over. / 2031-01-02