Sequential testing for efficacy in clinical trials with non-transient effects

This paper describes a new type of sequential testing for clinical trials. The sequential nature of the data is not from additional patients, but rather from longer follow-up times. At each analysis, the null hypothesis that all treatments are equivalent in effect on the outcome after that amount of time is tested. The trial might still have staggered entry or not, but the key feature is that a different statistical hypothesis is tested at each analysis. It is assumed that any effect of treatment is non-transient, allowing a conclusion to be drawn in favour of one treatment or the other based on a difference at a single follow-up time. It is shown that a general method based on the Bonferroni inequality can be used to obtain critical cutpoints for sequential testing, that controls the chance of a type I error for the clinical decision. This method is applicable regardless of the test used at each analysis. In the case of a two-armed trial with a Gaussian outcome variable, it is shown how simulation can be used to obtain critical cutpoints that maintain the chance of a type I error for the clinical decision. The methods are compared by Monte-Carlo simulation, and it is seen that in most practical cases the Bonferroni method is not very conservative. The Bonferroni procedure is illustrated on the results of a real clinical trial of Pirfenidone on pulmonary fibrosis in Hermansky-Pudlak Syndrome.