arXiv subjects

Jonathan Rathjens

Publications and source records attributed to Jonathan Rathjens.

2 recordsLinked to original sources

arXiv2024

Prediction intervals for overdispersed binomial endpoints and their application to toxicological historical control data

For toxicology studies, the validation of the concurrent control group by historical control data (HCD) has become requirements. This validation is usually done by historical control limits (HCL), which should cover the observations of the concurrent control with a predefined level of confidence. In many applications, HCL are applied to dichotomous data, e.g. the number of rats with a tumor vs. the number of rats without a tumor (carcinogenicity studies) or the number of cells with a micronucleus out of a total number of cells. Dichotomous HCD may be overdispersed and can be heavily right- (or left-) skewed, which is usually not taken into account in the practical applications of HCL. To overcome this problem, four different prediction intervals (two frequentist, two Bayesian), that can be applied to such data, are proposed. Based on comprehensive Monte-Carlo simulations, the coverage probabilities of the proposed prediction intervals were compared to heuristical HCL typically used in daily toxicological routine (historical range, limits of the np-chart, mean plus minus 2 SD). Our simulations reveal, that frequentist bootstrap calibrated prediction intervals control the type-1-error best, but, also prediction intervals calculated based on Bayesian generalized linear mixed models appear to be practically applicable. Contrary, all heuristics fail to control the type-1-error. The application of HCL is demonstrated based on a real life data set containing historical controls from long-term carcinogenicity studies run on behalf of the U.S. National Toxicology Program. The proposed frequentist prediction intervals are publicly available from the R package predint, whereas R code for the computation of the two Bayesian prediction intervals is provided via GitHub.

stat.AP↗

arXiv2021

Bivariate Analysis of Birth Weight and Gestational Age Depending on Environmental Exposures: Bayesian Distributional Regression with Copulas

In this article, we analyze perinatal data with birth weight (BW) as primarily interesting response variable. Gestational age (GA) is usually an important covariate and included in polynomial form. However, in opposition to this univariate regression, bivariate modeling of BW and GA is recommended to distinguish effects on each, on both, and between them. Rather than a parametric bivariate distribution, we apply conditional copula regression, where marginal distributions of BW and GA (not necessarily of the same form) can be estimated independently, and where the dependence structure is modeled conditional on the covariates separately from these marginals. In the resulting distributional regression models, all parameters of the two marginals and the copula parameter are observation-specific. Besides biometric and obstetric information, data on drinking water contamination and maternal smoking are included as environmental covariates. While the Gaussian distribution is suitable for BW, the skewed GA data are better modeled by the three-parametric Dagum distribution. The Clayton copula performs better than the Gumbel and the symmetric Gaussian copula, indicating lower tail dependence (stronger dependence when both variables are low), although this non-linear dependence between BW and GA is surprisingly weak and only influenced by Cesarean section. A non-linear trend of BW on GA is detected by a classical univariate model that is polynomial with respect to the effect of GA. Linear effects on BW mean are similar in both models, while our distributional copula regression also reveals covariates' effects on all other parameters.

stat.ME↗