Saibal Chattopadhyay

Indian Institute of Management Calcutta

Exponential clinical trials: Sequential comparison under asymmetric penalty

Suppose that two divisions of the same pharmaceutical company have been independently studying response times for two comparable treatments via separate clinical trials under identical protocols. Each division has been experimenting with just one treatment. The response times in each case follows a two-parameter exponential model, with all parameters unknown. The physical separation of these two divisions is an important input, and sequential design and allocation of units to these two treatments is ruled out. We consider the case where the two divisions independently estimate the minimum guarantee times (i.e., the thresholds) under some asymmetric linear-exponential (linex) loss function having unequal penalties for over and under estimation. Individual divisions have certain notion of ‘fixed-precision’ (such as bounded risk point estimation) tied with their individual problems. In the absence of fixed-sample size procedures, each division independently performed some sequential experimentation, and came up with independent stopping rules. The present study attempts to combine the results obtained from these two independent sequential studies and proposes to estimate the difference of these two thresholds under a similar asymmetric loss function. Asymptotic expansion of the sequential risk is derived under a general class of stopping rules. Examples of combining specific sequential methodologies such as purely sequential, accelerated sequential etc. are provided.