arXiv subjects

Andrew Titman

Publications and source records attributed to Andrew Titman.

3 recordsLinked to original sources

arXiv2026

A continuous-time Markov chain framework for population size estimation from multi-list data: accounting for absorbing lists and asymmetric interactions

We introduce a continuous-time Markov chain framework for estimating population size from multi-list data, which allows directional interactions to be modelled and can accommodate absorbing lists, such as death records, or more general data collection processes. The standard model of the continuous-time Markov chain framework and the log-linear model for multi-list data are equivalent when lists are independent and we show empirically that they give similar results in the presence of dependencies between lists. Through a simulation study, we highlight the need to account for an absorbing list by using the Markov model or the log-linear model with forced absorbing interactions, observing biased estimates of the population size otherwise. We motivate our approach with an epidemiological dataset concerning individuals suffering from a first ever stroke in North-West England, in which one of the lists is a death record. We illustrate a further use of our approach by considering a case of ordered lists on drug use data from the City of London.

stat.ME↗

arXiv2025

Comparison of Estimators for Multi-State Models in Potentially Non-Markov Processes

Various estimators for modelling the transition probabilities in multi-state models have been proposed, e.g., the Aalen-Johansen estimator, the landmark Aalen-Johansen estimator, and a hybrid Aalen-Johansen estimator. While the Aalen-Johansen estimator is generally only consistent under the rather restrictive Markov assumption, the landmark Aalen-Johansen estimator can handle non-Markov multi-state models. However, the landmark Aalen-Johansen estimator leads to a strict data reduction and, thus, to an increased variance. The hybrid Aalen-Johansen estimator serves as a compromise by, firstly, checking with a log-rank-based test whether the Markov assumption is satisfied. Secondly, landmarking is only applied if the Markov assumption is rejected. In this work, we propose a new hybrid Aalen-Johansen estimator which uses a Cox model instead of the log-rank-based test to check the Markov assumption in the first step. Furthermore, we compare the four estimators in an extensive simulation study across Markov, semi-Markov, and distinct non-Markov settings. In order to get deep insights into the performance of the estimators, we consider four different measures: bias, variance, root mean squared error, and coverage rate. Additionally, further influential factors on the estimators such as the form and degree of non-Markov behaviour, the different transitions, and the starting time are analysed. The main result of the simulation study is that the hybrid Aalen-Johansen estimators yield favourable results across various measures and settings.

stat.ME↗

arXiv2020

A Seamless Phase I/II Platform Design with a Time-To-Event Efficacy Endpoint for Potential COVID-19 Therapies

In the search for effective treatments for COVID-19, initial emphasis has been on re-purposed treatments. To maximise the chances of finding successful treatments, novel treatments that have been developed for this disease in particular, are needed. In this manuscript we describe and evaluate the statistical design of the AGILE platform, an adaptive randomized seamless Phase I/II trial platform that seeks to quickly establish a safe range of doses and investigates treatments for potential efficacy using a Bayesian sequential trial design. Both single agent and combination treatments are considered. We find that the design can identify potential treatments that are safe and efficacious reliably with small to moderate sample sizes.

stat.AP↗