Subject allocation and study curtailment for fixed event comparative Poisson trials

Comparative Poisson trials of prophylactic interventions, such as vaccines, can be lengthy and costly. We evaluate two easily implemented approaches to reduce numbers of disease cases and person years of follow up (N(u+t)) for comparative Poisson trials with fixed numbers of cases (T); (i) altering k the portion of N(u+t) allocated to treatment and (ii) curtailed stopping before T cases if numbers of cases in the treatment or control group indicate that H(0) has already been rejected or will not be rejected at T cases. Normal and arcsine approximations as well as discrete exact tests are evaluated. For studies not stopped early, allocating about 1/(1+sqrt r_a) of person years to treatment roughly minimizes T needed for given size and power (where r(a) is the alternative hypothesized relative disease incidence in treated subjects used to power the study). This reduces T moderately vs equal allocation (k=0.5) by 2-3 cases in our examples with exact tests. However, the common practice of allocating k=0.5 of the person years to treatment may be the overall best strategy to minimize N(u+t) for studies that are not stopped early. For studies analysed by exact test and planned with a one-sided alpha ranging from 0.005 to 0.025, beta from 0.1 to 0.2 and r(a) from 0.2 to 0.5, curtailed stopping reduces both the number of disease cases and N(u+t) by 6-40 per cent depending on true treatment benefit. With curtailed stopping, allocating k=0.5 person years to treatment approximately minimizes the numbers of cases and person years under most conditions, although k as large as 0.6 often performs comparably well. If a specific localized k is selected to minimize disease cases for a study analysed by exact test, the study may be underpowered should the final allocation deviate even slightly from that k when it is conducted.