# Adaptive Gaussian Process Search for Simulation-Based Sample Size Estimation in Clinical Prediction Models: Validation of the pmsims R Package

arXiv: https://arxiv.org/abs/2603.23688 · HTML: https://mlsanity.com/paper/2603.23688/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 24 Mar 2026.

## Builds on (most cited first, 8 of 8)

- [Using simulation studies to evaluate statistical methods](https://mlsanity.com/paper/1712.03198/) (2017)
- [Minimum Sample Size for Developing a Multivariable Prediction Model using Multinomial Logistic Regression](https://mlsanity.com/paper/2207.12892/) (2022)
- [A general sample size framework for developing or updating a clinical prediction model](https://mlsanity.com/paper/2504.18730/) (2025)
- [The Root Finding Problem Revisited: Beyond the Robbins-Monro procedure](https://mlsanity.com/paper/2508.17591/) (2025)
- [Formalising Sample Size Calculations for the Development of Risk Prediction Models: The Importance of Accounting for Performance Variability](https://mlsanity.com/paper/2509.14028/) (2025)
- [Efficient and flexible simulation-based sample size determination for clinical trials with multiple design parameters](https://mlsanity.com/paper/1908.07769/) (2019)
- [Bayesian sample size calculations for external validation studies of risk prediction models](https://mlsanity.com/paper/2504.15923/) (2025)
- [Sample Size Calculations for Developing Clinical Prediction Models: Overview and pmsims R package](https://mlsanity.com/paper/2602.23507/) (2026)

## Abstract (arXiv)

Background: Determining an adequate sample size is essential for developing reliable and generalisable clinical prediction models, yet practical guidance on selecting appropriate methods remains limited. Existing analytical and simulation-based approaches often rely on restrictive assumptions and focus on mean-based criteria. We present and validate pmsims, an R package that uses Gaussian process surrogate modelling to provide a flexible and computationally efficient simulation-based framework for sample size determination across diverse prediction settings. Methods: We conducted a comprehensive simulation study with two aims. First, we compared three search engines implemented in pmsims: a Gaussian process-based adaptive method, a deterministic bisection method, and a hybrid approach, across binary, continuous, and survival outcomes. Second, we benchmarked the best-performing pmsims engine against existing analytical (pmsampsize) and simulation-based (samplesizedev) methods, evaluating recommended sample sizes, computational time, and achieved performance on large independent validation datasets. Results: The Gaussian process-based method consistently produced the most stable sample size estimates, particularly in low-signal, high-dimensional settings. In benchmarking, pmsims achieved performance close to prespecified targets across all outcome types, matching simulation-based approaches and outperforming analytical methods in more challenging scenarios. Conclusions: pmsims provides an efficient and flexible framework for principled sample size planning in clinical prediction modelling, requiring fewer model evaluations than non-adaptive simulation approaches.