ABSTRACT
We argued in Section 4.1 that, in general, it is not a good idea to perform such an analysis as the main analysis of a study, because we get two effect estimates. A regression analysis providing one overall effect estimate is more useful, in particular, if we are interested in demonstrating the existence of an effect. The latter is basically an argument about power: The confidence interval of the overall effect is substantially more narrow than the confidence intervals in each stratum, as we have in the overall analysis a larger sample size than in the single strata. Similarly, the test on the null hypothesis of “no effect” using all data is typically much more powerful than the corresponding tests in each stratum. However, if a study is large enough, we may have sufficient power in each stratum, and a corresponding, stratified analysis may be a feasible and interesting alternative. As an example, let us take a look at a reanalysis of the breast cancer data set introduced in Exercise 10.5. If we are interested in demonstrating that the lymph node status has an effect on the survival of the patients that we cannot explain by confounding with the effect of grading, we can take a look at the effect of the lymph node status on survival within the three strata corresponding to the three levels of grading. And as within each stratum we are only interested in the effect of one covariate, we can simply use a graphical approach to visualise the effect, that is, in this case Kaplan-Meier plots as shown in Figure 28.1.
