Sequential analysis of matched dichotomous data from prospective case-control studies

Sequential analysis of randomized controlled clinical trials and epidemiological prospective (matched) case-control studies can have ethical or economical advantages above a fixed sample size approach. It offers the possibility to stop early when enough evidence for an apparent effect of the risk factor or lack of the expected effect is achieved. In clinical trials it is well accepted to stop the trial early in favour of the alternative hypothesis. In epidemiological studies, in general, the need is not felt to stop early in case of a clear exposure effect. Little attention has been paid, however, to early stopping and accepting the null hypothesis. In metabolic epidemiological studies, where analysis destroys the biological material, the question of efficient use of samples, for example, those stored in a biobank, becomes crucial. Also a slow accrual of cases or the costs of follow-up of a cohort nested study can make it desirable to stop a study early once it becomes clear that no relevant exposure effect will be found. Matching can further reduce the amount of information necessary to reach a conclusion. We derived test statistics Z (efficient score) and V (Fisher's information) for the sequential analysis of studies with dichotomous data where each case can be matched to one or more controls. A variable matching ratio is allowed. These test statistics can be entered into the software PEST to monitor the course of the study. The double sequential probability ratio test and the double triangular test were evaluated with simulated data for odds ratios equal to 1.5, 2.0 and 2.5 and various type I and type II error probabilities both under H(0) and under H(1). Our simulations resulted in average and median values for the amount of information (V) that are far less than those for a fixed sample size study. Efficiency gain ranges from 32 per cent to 60 per cent. The proposed sequential analysis was applied in an investigation on the possible relationship between the polymorphism of the MTHFR-gene and rectal cancer in a cohort of women with cases matched by age to one and to three controls. A sequential analysis of matched data can lead to early stopping in favour of H(0) or H(1), thus conserving valuable resources for future testing. A sequentially designed study can be more economical and less arbitrary than a study that makes use of conditional power or conditional coverage probability calculations to decide early stopping.