![]() ![]() Statistical performance metrics: Exact calculations are illustrated for statistical power, expected time of surveillance given that the null hypothesis is rejected, expected time of surveillance, and maximum maximum sample size. All calculations are exact, based on iterative numerical procedures, rather than using asymptotic theory, computer simulations, or normal distribution approximations.įor either Poisson or binary 0/1 data, this tutorial covers the following topics: 12 R Sequential is an easy‐to‐use tool for both the design and the practical implementation of sequential analysis. The calculations for the illustrative examples are run with the R Sequential package. For this, we present step‐by‐step calculations accompanied with explanations on the underlying theory and proper interpretations of illustrative data analysis results. 9, 10, 11 This is the approach of the present tutorial, which is devoted to offer practical examples on designing and conducting sequential hypothesis testing with binary and Poisson data. 8 Recent developments have shown that exact calculations are possible for many applications. Statistical performance evaluations and critical values calculations for sequential testing are usually obtained through asymptotic theory and/or normal distribution approximations. This way, as an adaptive design, no matter the frequency at which the chunks of data arrive, or the cumulative sample size available at each test, the alpha spending function enables to find the thresholds accordingly. Therefore, the alpha spending function dictates, in advance, the amount of Type I error probability to be spent at each of the multiple tests. 8 The alpha spending function is a non‐decreasing function taking values in the interval, where α is the significance level. Instead of thresholds given in the scale of a test statistic, sequential testing can be based on alpha spending functions. 5 For post‐market safety surveillance, recent methods are the maximized sequential probability ratio test (MaxSPRT), 6 and the conditional MaxSPRT (CMaxSPRT). Classical methods for sequential analysis are Wald's sequential probability ratio test (SPRT), 1, 2 Pocock's test, 3 O‘Brien‐Fleming's test, 4 and Wang‐Tsiatis' method. The sequential analysis is stopped as soon as the test statistic crosses one of the thresholds. Usually, the sequential analysis is based on monitoring a test statistic in comparison to a lower and an upper signaling threshold at each of the multiples sequential looks at the data. ![]() The sequential approach is essential for many applications when it is urgent to reach a conclusion or decision, such as in post‐market medical product safety surveillance, or when it is unethical to continue a clinical trial when there is clear evidence of benefit or harm affecting one group. Each test is performed when new data-that is, new observations-arrive, while guaranteeing the overall significance level by the end of the analysis. Alternatively, with sequential hypothesis testing, one prospectively performs multiple hypothesis tests. The regular practice for hypothesis testing is to conduct a single analysis based on a single data sample. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |