A simulated sequential analysis based on data from two MRC trials

Development of negative feedback during successive growth cycles of black cherry

Negative feedback between plant and soil microbial communities can be a key determinant of vegetation structure and dynamics. Previous research has shown that negative feedback between black cherry (Prunus serotina) and soil pathogens is strongly distance dependent. Here, we investigate the temporal dynamics of negative feedback. To examine short-term changes, we planted successive cycles of seedlings in the same soil. We found that seedling mortality increased steadily with growth cycle when sterile background soil was inoculated with living field soil but not in controls inoculated with sterilized field soil. To examine long-term changes, we quantified negative feedback across successive growth cycles in soil inoculated with living field soil from a mature forest system (more than 70 years old) versus a younger successional site (ca. 25 years old). In both cases negative feedback developed similarly. Our results suggest that negative feedback can develop very quickly in forest systems, at the spatial scale of a single seedling.

Repeated significance tests on accumulating survival data

The aim of the study was to compare the properties of two well-known group sequential methods and to demonstrate the effect of performing interim analyses on accumulating survival data without making appropriate adjustments of the nominal significance level. The properties of a group sequential method with fixed nominal significance level (Pocock stopping boundaries) and a method with increasing nominal level with each interim analysis (O'Brien-Fleming boundaries) were compared by stochastic simulation. Simulation experiments with survival times sampled from a breast cancer trial and from exponential distributions were performed. The true overall significance level with unplanned interim analyses increased from 5% to 14% when a maximum of five tests were performed. Both group sequential methods maintained the desired overall significance level. The O'Brien-Fleming method had higher power than Pocock's method. It also reduced the risk of early stopping based on immature data and should usually be preferred.

Sequential methods based on the boundaries approach for the clinical comparison of survival times

The earliest formal sequential procedure, the sequential probability ratio test, involved the plotting of certain test statistics and comparison with straight line parallel boundaries. The boundaries approach can now be used with a wide variety of test statistics, including those appropriate to the analysis of survival data. The boundaries can take various forms, although the use of straight lines still eases the underlying mathematical theory while at least approximating to the requirements of the majority of clinical trials. The implementation of sequential methods needs to be made flexibly and sensitively, with each clinical trial meriting an individualized approach.