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.

# Randomized controlled trials

## 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.

## Robustness to misspecification when adjusting for baseline in RCTs

It is well known that adjusting for one or more baseline covariates can increase statistical power in randomized controlled trials. One reason that adjusted analyses are not used more widely may be because researchers may be concerned that results may be biased if the baseline covariate(s)' effects are not modelled correctly in the regression model for outcome. For example, a continuous baseline covariate would by default be entered linearly in a regression model, but in truth it's effect on outcome may be non-linear. In this post we'll review an important result which shows that for continuous outcomes modelled with linear regression, this does not matter in terms of bias - we obtain unbiased estimates of treatment effect even if we mis-specify a baseline covariate's effect on outcome.

## Clustering in randomized controlled trials

Randomized clinical trials often involve some sort of clustering. The most obvious is in a cluster randomized trial, where clusters form the unit of randomization. It is well known that in this case the clustering must be allowed for in the analysis. But even in the common setting where individuals are randomized, clustering may be present. Perhaps the most common situation is where a trial involves a number of hospitals or centres, and individuals are recruited into the trial when they attend their local centre. Another example is where the intervention is administered to each individual by some professional (e.g. surgeon, therapist), such that outcomes from individuals treated by the same professional may be more similar to each other. In both of these situations, an obvious question is whether we need to allow for the clustering in the analysis?

## Leveraging baseline covariates for improved efficiency in randomized controlled trials

In a previous post I talked about the issue of covariate adjustment in randomized controlled trials, and the potential for improving the precision of treatment effect estimates. In this post I'll look at one of the (fairly) recently developed approaches for improving estimates of marginal treatment effects, based on semiparametric theory.