A Maximized Sequential Probability Ratio Test for Drug and Vaccine Safety Surveillance

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Abstract
Because of rare but serious adverse events, pharmaceutical drugs and vaccines are sometimes withdrawn from the market, either by a government agency such as the Food and Drug Administration (FDA) in the United States or by the manufacturing pharmaceutical company. In other cases, a drug may be generally safe but increase the risk for serious adverse events for certain subpopulations such as pregnant women or people with heart problems. Due to limited sample size and selected study populations, rare adverse events are often impossible to detect during phase 3 trials conducted before the drug is approved for general use. It is then important to conduct post-approval drug safety surveillance, using, for example, health insurance claims data. In such surveillance, the goal should be to detect serious adverse events as early as possible without too many false alarms, and it is then natural to use a continuous or near-continuous sequential test procedure that reevaluates the data on a daily or weekly basis. In this article, we first show that Wald's classical sequential probability ratio test (SPRT) for continuous surveillance is very sensitive to the choice of relative risk required in the specification of the alternative hypothesis, making it difficult to use for drug and vaccine safety surveillance. We instead propose the use of a maximized sequential probability ratio test (MaxSPRT) based on a composite alternative hypothesis, which works well across a range of relative risks. We illustrate the use of this method on vaccine safety surveillance and compare it with the classical SPRT. A table of critical values for the MaxSPRT is provided, covering most parameter choices relevant for vaccine and drug safety surveillance. The critical values are based on exact numerical calculations. We also calculate the statistical power, the expected time until the null hypothesis is rejected, and the average length of surveillance.