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Background Typical survival studies follow individuals to an event and measure explanatory variables for that event, sometimes repeatedly over the course of follow up. The Cox regression model has been used widely in the analyses of time to diagnosis or death from disease. The associations between the survival outcome and time dependent measures may be biased unless they are modeled appropriately. Methods In this paper we explore the Time Dependent Cox Regression Model (TDCM), which quantifies the effect of repeated measures of covariates in the analysis of time to event data. This model is commonly used in biomedical research but sometimes does not explicitly adjust for the times at which time dependent explanatory variables are measured. This approach can yield different estimates of association compared to a model that adjusts for these times. In order to address the question of how different these estimates are from a statistical perspective, we compare the TDCM to Pooled Logistic Regression (PLR) and Cross Sectional Pooling (CSP), considering models that adjust and do not adjust for time in PLR and CSP. Results In a series of simulations we found that time adjusted CSP provided identical results to the TDCM while the PLR showed larger parameter estimates compared to the time adjusted CSP and the TDCM in scenarios with high event rates. We also observed upwardly biased estimates in the unadjusted CSP and unadjusted PLR methods. The time adjusted PLR had a positive bias in the time dependent Age effect with reduced bias when the event rate is low. The PLR methods showed a negative bias in the Sex effect, a subject level covariate, when compared to the other methods. The Cox models yielded reliable estimates for the Sex effect in all scenarios considered. Conclusions We conclude that survival analyses that explicitly account in the statistical model for the times at which time dependent covariates are measured provide more reliable estimates compared to unadjusted analyses. We present results from the Framingham Heart Study in which lipid measurements and myocardial infarction data events were collected over a period of 26 years. Electronic supplementary material The online version of this article (doi:10.1186/s12874-016-0248-6) contains supplementary material, which is available to authorized users.

Background: Interaction in clinical trials presents challenges for design and appropriate sample size estimation. Here we considered interaction between treatment assignment and a dichotomous prognostic factor with a continuous outcome. Our objectives were to describe differences in power and sample size requirements across alternative distributions of a prognostic factor and magnitudes of the interaction effect, describe the effect of misspecification of the distribution of the prognostic factor on the power to detect an interaction effect, and discuss and compare three methods of handling the misspecification of the prognostic factor distribution. Methods: We examined the impact of the distribution of the dichotomous prognostic factor on power and sample size for the interaction effect using traditional one-stage sample size calculation. We varied the magnitude of the interaction effect, the distribution of the prognostic factor, and the magnitude and direction of the misspecification of the distribution of the prognostic factor. We compared quota sampling, modified quota sampling, and sample size re-estimation using conditional power as three strategies for ensuring adequate power and type I error in the presence of a misspecification of the prognostic factor distribution. Results: The sample size required to detect an interaction effect with 80% power increases as the distribution of the prognostic factor becomes less balanced. Misspecification such that the actual distribution of the prognostic factor was more skewed than planned led to a decrease in power with the greatest loss in power seen as the distribution of the prognostic factor became less balanced. Quota sampling was able to maintain the empirical power at 80% and the empirical type I error at 5%. The performance of the modified quota sampling procedure was related to the percentage of trials switching the quota sampling scheme. Sample size re-estimation using conditional power was able to improve the empirical power under negative misspecifications (i.e. skewed distributions) but it was not able to reach the target of 80% in all situations. Conclusions: Misspecifying the distribution of a dichotomous prognostic factor can greatly impact power to detect an interaction effect. Modified quota sampling and sample size re-estimation using conditional power improve the power when the distribution of the prognostic factor is misspecified. Quota sampling is simple and can prevent misspecification of the prognostic factor, while maintaining power and type I error.

Background Previous studies have proposed a simple product-based estimator for calculating exposure-specific risks (ESR), but the methodology has not been rigorously evaluated. The goal of our study was to evaluate the existing methodology for calculating the ESR, propose an improved point estimator, and propose variance estimates that will allow the calculation of confidence intervals (CIs). Methods We conducted a simulation study to test the performance of two estimators and their associated confidence intervals: 1) current (simple product-based estimator) and 2) proposed revision (revised product-based estimator). The first method for ESR estimation was based on multiplying a relative risk (RR) of disease given a certain exposure by an overall risk of disease. The second method, which is proposed in this paper, was based on estimates of the risk of disease in the unexposed. We then multiply the updated risk by the RR to get the revised product-based estimator. A log-based variance was calculated for both estimators. Also, a binomial-based variance was calculated for the revised product-based estimator. 95% CIs were calculated based on these variance estimates. Accuracy of point estimators was evaluated by comparing observed relative bias (percent deviation from the true estimate). Interval estimators were evaluated by coverage probabilities and expected length of the 95% CI, given coverage. We evaluated these estimators across a wide range of exposure probabilities, disease probabilities, relative risks, and sample sizes. Results We observed more bias and lower coverage probability when using the existing methodology. The revised product-based point estimator exhibited little observed relative bias (max: 4.0%) compared to the simple product-based estimator (max: 93.9%). Because the simple product-based estimator was biased, 95% CIs around this estimate exhibited small coverage probabilities. The 95% CI around the revised product-based estimator from the log-based variance provided better coverage in most situations. Conclusion The currently accepted simple product-based method was only a reasonable approach when the exposure probability is small (< 0.05) and the RR is ≤ 3.0. The revised product-based estimator provides much improved accuracy.