Some considerations concerning covariates in clinical trials
Department of Statistics, University of Glasgow
The closer you get to registration in drug development, the greater the resistance to using covariate information. There is a lamentable prejudice against modelling that is reflected in a series of superstitions, in particular
- That randomisation means that prognostic information can safely be ignored.
- That simpler approaches (for example the log-rank test) are more robust than more sophisticated ones (such as for example proportional hazards regression).
- That nonparametric methods are more exact than parametric ones.
- That marginal predictions require marginal models.
- That change from baseline uses baseline information adequately.
I consider these points and provide some examples. I show that using covariates information can often bring benefits equivalent to studying more patients. As a technical matter, I consider the relationship between stratification, which is generally more widely accepted, and analysis of covariance which has greater resistance.
In addition to adjusting for main effects, covariates can be modelled as ‘effect modifiers'. This raises more difficult issues, in particular of bias-variance trade-off. A simple illustration using mean square error is illuminating of the general philosophical issue but the precise solution remains difficult to agree.
I conclude that the analysis of phase III trials could be improved by adopting some of the spirit of the ‘population school'.
. Senn, SJ. An unreasonable prejudice against modelling?, Pharmaceutical Statistics 2005; 4: 87-89.
. Senn, SJ. Baseline Balance and Valid Statistical Analyses: Common Misunderstandings, Applied Clinical Trials 2005; 14: 24-27.
. Lee, Y, Nelder, JA. Conditional and marginal models: Another view, Statistical Science 2004; 19: 219-228.
. Senn, SJ. Three things every medical writer should know about statistics, The write stuff 2009; 18: 159-162.