Rejoinder to comments on ‘The statistics of linear models: back to basics’

Conclusion The discussion has shown, I fear, that the formulation of linear models, one of the basic tools of our trade, is in an unsatisfactory state; also that the argument is not just one between Nelder and the rest of the world. Why the sorry state? I believe that the problem is that statistical theory is driven too often by mathematics rather than by the requirements of scientific inference. None of the hypotheses I have described as uninteresting are mathematically wrong; rather I contend that they do not correspond to any inferential quantities of interest. Searle points out that in the first example of Section 5 the original authors did not specify a nested structure of the type I discussed. However, without such a prior nested structure the hypotheses being discussed are, to me, pointless. They are mathematically specifiable but do not correspond to anything of inferential interest. Even with the prior structure two of the three remain uninteresting. The contributions of Aitkin and van Eeuwijk show what a mess the applied literature is in, as the result of some of the confusions I discussed. This confusion is not something that statisticians can or should ignore.     

Rejoinder

Kaplan–Meier graphs of survival and other timed events are an extremely effective way to summarize outcome data from some types of clinical studies, but information on dates and the interaction among events is lost. A new mode for presenting such data is proposed, an Eventchart, that aids in looking at the study as a whole by simultaneously displaying the timing of 2–3 different types of events, including censoring and time-dependent covariate events. The chart helps to monitor accrual and can be used to “guesstimate” the amount of information resulting from additional enrollment and/or follow-up. Eventcharts are designed to supplement, not replace, quantitative methods of analysis or conventional survival graphs. Data from bone marrow transplantation and AIDS studies are used to illustrate the method. Terminology is suggested for describing the concepts and distinguishing among the complex of events studied in modern clinical trials, including timed events, loss and date censoring, and time-braided events.