Parameterization of European perch Perca fluviatilis length-at-age data using stochastic Gompertz growth models

Three stochastic versions of the Gompertz growth model were used to parameterize total length (L(T) )-at-age data for perch Perca fluviatilis, an important target species for commercial and recreational fishers and a food species for predatory fishes and aquatic birds. Each model addresses growth heterogeneity by incorporating random parameters from a specific positive distribution: Weibull, gamma or log-normal. The modelling outputs for each version of the model provide L(T) distributions for selected ages and percentiles of L(T) at age for both males and females. The results highlight the importance of using a stochastic approach and the logistic-like growth pattern for analysing growth data for P. fluviatilis in Curonian Lagoon (Lithuania). Outputs from this modelling can be extended to a stochastic analysis of fish cohort dynamics, incorporating all length-based biological relationships, and the selectivity-related interactions between fish cohorts and fishing gear.     

Estimation of a Secondary Parameter in a Group Sequential Clinical Trial

In this article, we investigate estimation of a secondary parameter in group sequential tests. We study the model in which the secondary parameter is the mean of the normal distribution in a subgroup of the subjects. The bias of the naive secondary parameter estimator is studied. It is shown that the sampling proportions of the subgroup have a crucial effect on the bias: As the sampling proportion of the subgroup at or just before the stopping time increases, the bias of the naive subgroup parameter estimator increases as well. An unbiased estimator for the subgroup parameter and an unbiased estimator for its variance are derived. Using simulations, we compare the mean squared error of the unbiased estimator to that of the naive estimator, and we show that the differences are negligible. As an example, the methods of estimation are applied to an actual group sequential clinical trial, The Beta-Blocker Heart Attack Trial.