The Art of Statistics: Learning from Data

by David Spiegelhalter

Statisticians in the US and UK, working independently, developed what became known as the Sequential Probability Ratio Test (SPRT), which is a statistic that monitors accumulating evidence about deviations, and can at any time be compared with simple thresholds – as soon as one of these thresholds is crossed, then an alert is triggered and the production line is investigated.fn8 Such techniques led to more efficient industrial processes, and were later adapted for use in so-called sequential clinical trials in which accumulated results are repeatedly monitored to see if a threshold that indicates a beneficial treatment has been crossed. I was one of a team that developed a version of the SPRT that could be applied to the Shipman data. This is plotted in Figure 10.4 for both men and women, assuming an alternative hypothesis that Shipman had double the mortality rate of his colleagues. The test has thresholds that control the Type I (alpha) and Type II (beta) error probability to the specified values of 1 in 100, 1 in 10,000 and 1 in 1,000,000: the Type I error is the overall probability of the test statistic crossing the threshold at some point, given that Shipman had the expected mortality rates, and the Type II error is the overall probability of the test statistic not crossing the threshold at some point, given that Shipman had double the expected mortality rate.7 Given there are around 25,000 GPs, then a threshold P-value of 0.05/25,000 or 1 in 500,000 might be reasonab...

Sequential probablity ratio test