From: Ingeborg van der ¹weel Centre for Biostatistics, C122 ºtrecht ºniversity Padualaan 14 3584 CH ºtrecht ¹he Netherlands Paul A. H. van Noord Julius Centre for Patient Oriented Research ºtrecht ºniversity PO Box 80035 3508 ¹A ºtrecht ¹he Netherlands
It is with interest that we read the article of Stro¨mberg addressing the methodology of efficient analysis in epidemiology by proposing early stopping rules. We feel encouraged to respond since Stro¨mberg explicitly states on p. 2328 that 'A goal of the present paper is also to stimulate further discussion concerning early stopping of epidemiological studies'. Although a plan for an interim analysis was not explicitly stated in his investigation, the need was felt to evaluate the data on the first 25 cases and 25 controls, because blood samplings and assessments were time-and cost-consuming.
In the literature a number of areas can be found where the need for early stopping is also recognized and where sequential methods are advocated, such as quality control, genetic studies, clinical trials and epidemiology, -so it is interesting that this idea has not caught on further. In clinical trials ealy stopping for ethical or economical reasons is well accepted. We agree with Stro¨mberg that also in observational epidemiologic studies it might be desirable to stop when the data indicate no significant effect and analyses of biological samples are costly, time-consuming or destructive. - Stro¨mberg proposes a method for deciding to stop early and accept the null hypothesis based on the conditional coverage probability (CCP). The CCP as well as other proposed methods for early stopping, such as conditional power (CP) and stochastic curtailing, are, however, based on rather arbitrary choices. Plausible values for the parameter (based on the data obtained so far or an upper bound of an arbitrary confidence interval, the parameter value under the null hypothesis or under the alternative hypothesis) have to be chosen, a choice for the critical value for the CCP to decide early stopping (or the choice of the 'futility index') and the choice of the optimal initial fraction of total sample size or the optimal information time must be made. Furthermore, the type I and type II error probabilities are affected by these strategies.
These arbitrary choices do not apply to a study that is sequential by design. A sequential study design requires definition in advance of the difference that is considered relevant to detect and the type I and type II error probabilities, a matter of good statistical practice and also required for the design of a fixed sample size study.
Hunsberger et al. and Stro¨mberg estimate the CP and the CCP, respectively, from the first part of the data. Based on these results they decide either to stop the study or to continue until the anticipated total sample size. In the latter case they could also have considered continuing the study sequentially. That could have reduced the costs of their studies considerably, particularly when the null hypothesis or the alternative LETTER TO THE EDITOR