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.

# Randomized controlled trials

## Estimands and assumptions in clinical trials

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.

## Matching analysis to design: stratified randomization in trials

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.

## Multiarm trials - should we allow for multiplicity?

Last week I listened to a great presentation about new trial designs by Mahesh Parmar, director of the Medical Research Council Clinical Trial Unit in London. Among the topics he touched on were multi-arm trials (and extensions), as an attractive alternative to the classic two arm trial. There seem to be a number of advantages to such a trial design, in which in the simplest case, the trial randomizes patients to either control or one of a number of experimental treatments.

## Improving efficiency in RCTs using propensity scores

Propensity scores have become a popular approach for confounder adjustment in observational studies. The basic idea is to model how the probability of receiving a treatment or exposure depends on the confounders, i.e. the 'propensity' to be treated. To estimate the effect of exposure, outcomes are then compared between exposed and unexposed who share the same value of the propensity score. Alternatively the outcome can be regressed on exposure, weighting the observations using the propensity score. For further reading on using propensity scores in observational studies, see for example this nice paper by Peter Austin.

But the topic of this post is on the use of propensity scores in randomized controlled trials. The post was prompted by an excellent seminar recently given by my colleague Elizabeth Williamson, covering the content of her recent paper 'Variance reduction in randomised trials by inverse probability weighting using the propensity score" (open access paper here).

## Is the two sample t-test/ANOVA really biased in RCTs?

A couple of months ago I came across this paper, "Bias, precision and statistical power of analysis of covariance in the analysis of randomized trials with baseline imbalance: a simulation study", published in the open access online journal BMC Medical Research Methodology, by Egbewale, Lewis and Sim. Using simulation studies, as the title says, the authors investigate the bias, precision and power of three analysis methods for a randomized trial with a continuous outcome and a baseline measure of the same variable, when there is an imbalance at baseline in the baseline measure. The three methods considered are ANOVA (a two-sample t-test here), an analysis of change (CSA, change from baseline to follow-up) scores, and analysis of covariance (ANCOVA), which corresponds to fitting a linear regression model with outcome measurement as the dependent variable, with randomized treatment and baseline measure as covariates.