For the analysis of count data from comparative clinical study with patient screening which refers to the baseline observation, Cook and Wei (2003) proposed a conditional Gamma-Poisson model as a natural extension of ANCOVA. However, in some cases this model suffers from its insufficient capacity in expressing the inter-patient heterogeneity. As alternative we propose extended models that include an additional random effect into the conventional Poisson mixture, which can be estimated through conditioning by total sum of count or baseline. The resulting models can offer improved summary of patient heterogeneity, as well as other population parameters. The proposed models are illustrated with seizure count data from a clinical experiment for an anti-epileptic drug.

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Recently, flexible approaches with updating of sample size during the course of clinical trials have been proposed; the weighted Z-statistic approach and the 50 %-conditional power approach. In this paper, we propose a modification of the 50 %-conditional power approach, which increases the sample size only when the conditional power based on the unblinded interim results is greater than 50 %. Our method can control the type I error rate due to the restriction on the minimum required sample size ratio under the decision of increasing sample size. Simulation studies showed that the proposed method increased power about 10 % compared with the fixed sample size design and attained higher power than the original 50 %-conditional power approach. Compared with the weighted Z-statistic approach, the proposed method had several promising operating characteristics; a substantial gain in conditional power given the decision of sample size adjustment, a low probability of reaching the maximum sample size, a substantial decrease in the conditional type II error rate given the maximum sample size, and a conservative property of not increasing sample size erroneously under no treatment effect.

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Fixation or extinction of neutral genes by genetic drift is especially important for understanding the evolution of small populations. Assuming a monoecious diploid species, I derived expressions for the fixation probability of a neutral gene in age-structured populations with cyclic change in size. Stochastic simulation with a small population showed that the obtained formulae give a good prediction of the fixation probability. Extension to a dioecious diploid species was also presented.

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Assuming a random mating population of monoecious diploid, I derived an expression for the effective size of an age-structured population that varies the size over time in cycles of a given length. From the asymptotic contributions of age groups to the coancestry after many repetitions of cycles, an equation for the effective population size per cycle was derived, which showed a different expression from the previously published equation. Effect of the discrepancy was numerically evaluated with a hypothetical ladybird population with seasonal periodicity in size. The equation derived in this study gave a reasonably precise value, while the published one underestimated the effective size. The effect of estimation error of the census population size on the estimate of the effective size was also evaluated with the obtained formulae.

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