The log rank test is often used to test the hypothesis of equality for the survival functions of two treatment groups in a randomised controlled trial. Alongside this, trials often estimate the hazard ratio (HR) comparing the hazards of failure in the two groups. Typically the HR is estimated by fitting Cox's proportional hazards model, and a 95% confidence interval is used to indicate the precision of the estimated HR.
Yesterday the Advanced Analytics Centre at AstraZeneca publicly released the InformativeCensoring package for R, on GitHub. Standard survival or time to event analysis methods assume that censoring is uninformative - that is that the hazard of failure in those subjects at risk at a given time and who have not yet failed or been censored, is the same as the hazard at that time in those who have been censored (with regression modelling, this assumption is somewhat relaxed).
Today I listened to a great Royal Statistical Society webinar, with Alan Phillips and Peter Diggle (current RSS president) presenting. The topic was a particularly hot one in the clinical trials world right now, namely estimands.
Alan's presentation gave an excellent overview of the work of a PSI/EFSPI special interest group on estimands. Topics discussed included defining exactly what is meant by an estimand, whether there should be a standardised set of estimands which could be used across trials conducted in different disciplines, and what the estimand discussion means in terms of implementation and statistical analysis.
A common situation arises when one wants to estimate the effect of a treatment or exposure at some time point t in an observational cohort or randomised trial. For example, what is the mean difference in some outcome Y at time t between the two groups of interest. To make things a bit simpler, let's suppose that subjects were allocated to the two groups (e.g. two treatments A and B) randomly, as in a randomised trial. Now suppose that some of the subjects die before time t, such that their outcome Y is not observed. Then we can no longer compare Y between the two groups in all subjects, because some values of Y are missing, or truncated by death.
Yesterday I was re-reading the recent nice articles by Brennan Kahan and Tim Morris on how to analyse trials which use stratified randomization. Stratified randomization is commonly used in trials, and involves randomizing in a certain way to ensure that the treatments are assigned in a balanced way within strata defined by chosen baseline covariates.
Multiple imputation (MI) is a popular approach to handling missing data. In the final part of MI, inferences for parameter estimates are made based on simple rules developed by Rubin. These rules rely on the analyst having a calculable standard error for their parameter estimate for each imputed dataset. This is fine for standard analyses, e.g. regression models fitted by maximum likelihood, where standard errors based on asymptotic theory are easily calculated. However, for many analyses analytic standard errors are not available, or are prohibitive to find by analytical methods. For such methods, if there were no missing data, an attractive approach for finding standard errors and confidence intervals is the method of bootstrapping. However, if one is using MI to handle missing data, and would ordinarily use bootstrapping to find standard errors / confidence intervals, how should these be combined?