Use of a side effect as a covariate in a problem of sequential analysis

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.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29874/1/0000223.pd