Use of a side effect as a covariate in a problem of sequential analysis. (English) Zbl 0752.62053
Summary: A drug is administered sequentially to incoming patients. A response \(Y\) to treatment and a covariate \(X\) is measured (\(X\) might be a side effect). The experiment is stopped when the covariate falls outside some acceptable region. We study the effect that this optional stopping has on the significance level of the test and we found that this effect is surprisingly small in the examples considered. An approximation to the problem is found. This approximation does not depend on the distribution of the variable \(X\) but only on the correlation coefficient between \(X\) and \(Y\).
MSC:
| 62L10 | Sequential statistical analysis |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 90C90 | Applications of mathematical programming |
| 60F15 | Strong limit theorems |
| 62L15 | Optimal stopping in statistics |
Keywords:
estimation; clinical trials; backward induction; dynamic programming; binary binomial case; testing without batches; Wiener process; conditional expectation; binomial example; testing; central limit theorem; covariate; optional stopping; significance level; approximation; testing with batchesReferences:
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