Trial sequential analysis: plain and simple
Alessandro De Cassai et al.
The use of trial sequential analysis (TSA) in the medical literature is increasing in recent times. However, not all readers may be familiar with this statistical technique. This correspondence aims to provide readers with the essentials to understand and interpret TSA. Adequately conducted meta-analyses (MAs) are considered the best evidence in the scientific literature. Nonetheless, MAs are exposed to misleading significant results (type I errors; α) or erroneously insignificant results (type II errors; β) caused by low quality or inadequately powered trials, publication bias, and repeated significance testing . TSA is a cumulative MA method developed  to weigh α and β errors while estimating when the effect is large enough to be unlikely to be affected by further studies. TSA is displayed as a Cartesian graph with cumulative z-score on the y-axis and number of patients on the x-axis, subdivided into four zones by four lines: monitoring boundaries for benefit, and harm, and two futility boundaries (Fig. 1). Two lines parallel to the x-axis are usually displayed, showing the conventional statistically significant line at z, corresponding to 1.96. The cumulative z statistic line is constructed adding a study sequentially with chronological criteria. The end of the line corresponds to the lastly added study. It will lie in one of the following zones: “benefit”, “harm”, “inner wedge” or “not statistically significant”, representing a statistically significant result for the first two areas (“benefit” and “harm”) or a strong evidence that further studies will hardly be able to change the no-effect results (“inner wedge” area). Presence in the “not statistically significant” area means that further studies are needed. Control of α and β errors may be managed by decreasing the test statistic using a penalizing factor λ (law of the iterated logarithm) or adjusting the significance threshold. The last described strategy is managed in TSAs using α-and β-spending functions. The α spending function determines both the benefit and harm boundaries, while the beta spending function is displayed on the graph as the futility boundaries. The spending functions used in TSA are based on the O’BrienFleming’s function. Although several examples of such functions have been described, O’BrienFleming’s function is the only function implemented in the TSA software. The spending function is a monotonically increasing function that distributes the α error along the entire analysis for a pre-decided α. The function is defined from 0 to 1, where 0 corresponds to “no patient enrolled” and 1 to the “reached information size” with the information fraction (IF) as the independent variable. The IF is given by the accumulated sample divided by the required sample.