Alpha Spending

A group sequential trial method allocating the overall acceptable risk of a false positive across multiple planned interim analyses.

Source: Lan & DeMets 1983

Alpha spending solves the problem that looking at a trial's data repeatedly, at several interim analyses, inflates the chance of a false positive, because each look is another opportunity to cross a significance threshold by chance. It divides the total acceptable risk of a false positive across the planned looks, spending a small portion at each so that the overall risk stays at the intended level. This lets a trial stop early for benefit or harm without abandoning statistical rigour. Rationing the false-positive risk across looks is its purpose. Friedman and colleagues (2015) describe this method.

Source: Friedman et al. 2015

Alpha spending is needed because examining trial data at multiple interim analyses and testing for significance each time inflates the overall chance of a false positive, so without control the type I error would exceed the intended level. Alpha spending apportions the allowable error across the looks to keep the total at the intended level. So alpha spending is needed to allow interim analyses, which are valuable for stopping trials early for benefit, harm, or futility, without inflating the false positive rate, since repeatedly testing accumulating data would otherwise make a spurious significant result more likely than the nominal alpha suggests.

Source: Lan & DeMets 1983

Alpha spending works by defining a spending function that specifies how much of the total alpha is used, or spent, by each interim analysis as a function of the proportion of information accrued, with the cumulative amount reaching the full alpha only at the final analysis. The boundaries for significance at each look are derived from this function. So alpha spending works by allocating portions of the overall error rate across interim analyses according to a chosen spending function, which sets how conservative the early looks are, allowing flexible interim monitoring while ensuring the total type I error does not exceed the intended level over the whole trial.

Source: Lan & DeMets 1983

The advantages of alpha spending include flexibility in the number and timing of interim analyses, since the spending function does not require these to be fixed exactly in advance, only the information fractions; control of the overall type I error across the looks; and the ability to stop a trial early for convincing benefit, harm, or futility while preserving statistical validity. So alpha spending is advantageous for interim monitoring of trials, allowing accumulating data to be examined repeatedly and trials to be stopped early when justified, without inflating the false positive rate, which makes it a widely used approach for the group sequential design and monitoring of clinical trials.

Source: Lan & DeMets 1983

Alpha spending relates to interim analysis as the method that makes repeated interim testing statistically valid: interim analyses examine accumulating trial data before the planned end, and alpha spending controls the error rate across these examinations by allocating the alpha among them. Without such control, interim analyses would inflate the false positive rate. So alpha spending underpins the interim analysis of trials by distributing the overall false positive risk across the interim looks, enabling data monitoring committees to review results periodically and stop trials early when warranted, while ensuring the total type I error remains at the intended level.

Source: Lan & DeMets 1983