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3 papers

A Multi-Stage Drop-the-Loser Design With Superiority Boundaries.

Greenstreet P et al. · Jul 1, 2026

Multi-arm multi-stage (MAMS) trials have gained popularity, due to their improved efficiency in evaluating multiple treatments. A traditional MAMS trial often decreases the expected sample size of the trial compared with just running a multi-arm approach, but with the drawback of an increase in maximum sample size. For academic led trials, this poses a particular challenge, as funding is typically based on the maximum required sample size. To address this, drop-the-loser designs were introduced, where a fixed number of treatments are dropped at each interim stage, thereby reducing the maximum sample size. In this work, we propose an enhanced multi-stage drop-the-loser design that also allows for early stopping of the entire trial for superiority. This approach aims to retain the benefits of a reduced maximum sample size while also lowering the expected sample size. The proposed design is motivated by a trial in atrial fibrillation. We derive analytical expressions for the type I error rate, power, and expected sample size, and compare the proposed design's performance to alternative methods. We outline the key requirements for implementing the proposed design and discuss the contexts in which it should be considered. For the motivating example, the results show that the proposed design substantially reduces the expected sample size compared to a standard drop-the-loser design, while lowering the maximum sample size relative to running a traditional MAMS trial or multiple separate trials.

Mathematics

The Empirical Bayes Variational Autoencoder-A Neural ODE Approach for Population Modeling in Pharmacology.

Baaz M et al. · Jul 1, 2026

Variational autoencoders (VAEs) combined with neural ordinary differential equations provide a flexible framework for exploring neural latent-variable models in population pharmacokinetics. In this work, we investigate an empirical Bayes VAE formulation that integrates encoder-decoder architectures with covariate-dependent population priors, enabling correlated latent representations and probabilistic inference. We evaluate the proposed framework using controlled simulation studies and a small clinical benchmark dataset. The simulation experiments assess the ability to recover known population structures and covariate effects, while the clinical study evaluates subject-specific prediction and model diagnostics. In simulation studies with correlated individual parameters, the empirical Bayes VAE consistently captured population-level variability, whereas a fixed-prior VAE baseline exhibited systematic biases. In our experiments, extrapolation beyond the training dosing schedules showed more stable predictive behavior when using the proposed input-response normalization, relative to models trained without normalization, within a limited range. Diagnostic analyses indicated clear relationships between inferred latent variables and true parameters, and estimated observation noise was consistent with simulated values. In the clinical case study, cross-validation experiments suggested predictive performance comparable to previously reported neural ODE-based approaches. Overall, the results illustrate the feasibility of combining empirical Bayes inference with neural ODE-based decoders for population modeling. The proposed framework should be viewed as a methodological proof-of-concept, highlighting both the potential and the current limitations of variational neural approaches in pharmacometric applications.

Mathematics

Caveats on Using Firth's Penalization in the Model-Based Regression Standardization for Rare Diseases.

Hashibe S et al. · Jul 1, 2026

Model-based regression standardization, also known as the parametric g-formula, is widely used to estimate marginal effect measures. However, in rare disease settings, the small number of observed events relative to the number of covariates can lead to (quasi-)complete separation, resulting in non-convergent estimates in the regression models. Firth's penalized likelihood estimates are a common solution to this issue, ensuring finite parameter estimates even for separated data. While effective for estimating regression coefficients, Firth's method introduces bias into model-based regression standardization because of its tendency to shrink the predicted probabilities to 0.5, leading to discrepancies between the predicted and observed event rates. We examined the implications of applying Firth's method to model-based regression standardization, illustrating its potential bias through an empirical study on surgical site infections (SSI) in orthopedic surgeries. We also proposed two ad hoc corrections (i.e., Firth's logistic regression with intercept correction and added covariate) to mitigate this bias and evaluated these methods via simulation studies, comparing them with propensity score-based approaches. Finally, we applied the proposed method to assess the association between SSI, a rare disease, and smoking status in a clinical database of orthopedic surgeries.

Mathematics