A simulation approach for power calculation in large cohort studies based on multistate models

Realistic power calculations for large cohort studies and nested case control studies are essential for successfully answering important and complex research questions in epidemiology and clinical medicine. For this, we provide a methodical framework for general realistic power calculations via simulations that we put into practice by means of an R‐based template. We consider staggered recruitment and individual hazard rates, competing risks, interaction effects, and the misclassification of covariates. The study cohort is assembled with respect to given age‐, gender‐, and community distributions. Nested case‐control analyses with a varying number of controls enable comparisons of power with a full cohort analysis. Time‐to‐event generation under competing risks, including delayed study‐entry times, is realized on the basis of a six‐state Markov model. Incidence rates, prevalence of risk factors and prefixed hazard ratios allow for the assignment of age‐dependent transition rates given in the form of Cox models. These provide the basis for a central simulation‐algorithm, which is used for the generation of sample paths of the underlying time‐inhomogeneous Markov processes. With the inclusion of frailty terms into the Cox models the Markov property is specifically biased. An “individual Markov process given frailty” creates some unobserved heterogeneity between individuals. Different left‐truncation‐ and right‐censoring patterns call for the use of Cox models for data analysis. p‐values are recorded over repeated simulation runs to allow for the desired power calculations. For illustration, we consider scenarios with a “testing” character as well as realistic scenarios. This enables the validation of a correct implementation of theoretical concepts and concrete sample size recommendations against an actual epidemiological background, here given with possible substudy designs within the German National Cohort.     

Environmental regulation of surface conductance for evaporation from vegetation

We examine conductances for evaporation from both vegetation and soil in response to environmental variables. Data from a vertically-structured pristine forest of Nothofagus are presented as an example of the effects of biodiversity on the scaling of conductances between tiers of plant organisation. Available data sets of maximum leaf stomatal conductances (g _lmax ) and bulk vegetation surface conductances (G _smax ) are compared. Overall, the ratio G _smax /g _lmax is consistently close to 3 for seven major vegetation types of diverse structure. An analytical model accounts for this close relationship, and in particular how G _smax is conservative against changes in leaf area index because of the compensating decrease in plant canopy transpiration and increase in soil evaporation as leaf area index diminishes. The model is also successfully tested by comparison with canopy conductances of emergent trees measured in the Nothofagus forest. The constraint of vegetation surface conductance and evaporation via environmental regulation by irradiance, air saturation deficit and root zone water supply are discussed.     

Effect of feeding boxes on the behavior of stereotyping amur tigers (Panthera tigris altaica) in the Zurich Zoo,Zurich, Switzerland

The stereotyped pacing shown by the two Amur tigers in the Zurich Zoo was hypothesized as being caused by permanently frustrated appetitive foraging behavior. Several electrically controlled feeding boxes were installed and access to each box was possible only twice a day for 15 min at semi‐random times. The boxes had to be opened actively by the tigers. Two trials were carried out: one with solitary confinement, and one with paired confinement. During box feeding, the female's stereotyped pacing was significantly reduced from 16% (solitary confinement, conventional feeding) and 7% (paired confinement, conventional feeding) to 1% (solitary confinement) and less than 0.01% (paired confinement) of the daily observed time. The female's sleeping increased significantly in both solitary and paired confinement. The male only showed a significant reduction in stereotyped pacing behavior when kept with the female (conventional feeding: 10%; box feeding: <0.01% of the daily observed time). On days with a box‐feeding regime in paired confinement, the male spent 25% (83 min) of the observed time with active behavior at the feeding boxes. The results support the hypothesis that permanently frustrated appetitive foraging behavior causes stereotyped pacing in adult tigers. Zoo Biol 21:573–584, 2002. © 2002 Wiley‐Liss, Inc.