A model-based approach for historical borrowing, with an application to neovascular age-related macular degeneration.

Bayesian historical borrowing has recently attracted growing interest due to the increasing availability of historical control data, as well as improved computational methodology and software. In this article, we argue that the statistical models used for borrowing may be suboptimal when they do not adjust for differing factors across historical studies such as covariates, dosing regimen, etc. We propose an alternative approach to address these shortcomings. We start by constructing a historical model based on subject-level historical data to accurately characterize the control treatment by adjusting for known between trials differences. This model is subsequently used to predict the control arm response in the current trial, enabling the derivation of a model-informed prior for the treatment effect parameter of another (potentially simpler) model used to analyze the trial efficacy (i.e. the trial model). Our approach is applied to neovascular age-related macular degeneration trials, employing a cross-sectional regression trial model, and a longitudinal non-linear mixed-effects drug-disease-trial historical model. The latter model characterizes the relationship between clinical response, drug exposure and baseline covariates so that the derived model-informed prior seamlessly adapts to the trial population and can be extrapolated to a different dosing regimen. This approach can yield a more accurate prior for borrowing, thus optimizing gains in efficiency (e.g. increasing power or reducing the sample size) in future trials.

Tracking elimination of HIV transmission in men who have sex with men in England: a modelling study.

BACKGROUND: To manage the HIV epidemic among men who have sex with men (MSM) in England, treatment as prevention strategies based on test and treat were strengthened between 2011 and 2015, and supplemented from 2015 by scale-up of pre-exposure prophylaxis (PrEP). We examined the effect of these interventions on HIV incidence and investigated whether internationally agreed targets for HIV control and elimination of HIV transmission by 2030 might be within reach among MSM in England. METHODS: We used a novel, age-stratified, CD4-staged Bayesian back-calculation model to estimate HIV incidence and undiagnosed infections among adult MSM (age ≥15 years) during the 10-year period between 2009 and 2018. The model used data on HIV and AIDS diagnoses routinely collected via the national HIV and AIDS Reporting System in England, and knowledge on the progression of HIV through CD4-defined disease stages. Estimated incidence trends were extrapolated, assuming a constant MSM population from 2018 onwards, to quantify the likelihood of achieving elimination of HIV transmission, defined as less than one newly aquired infection per 10 000 MSM per year, by 2030. FINDINGS: The peak in HIV incidence in MSM in England was estimated with 80% certainty to have occurred in 2012 or 2013, at least 1 year before the observed peak in new diagnoses in 2014. Results indicated a steep decrease in the annual number of new infections among MSM, from 2770 (95% credible interval 2490-3040) in 2013 to 1740 (1500-2010) in 2015, followed by a steadier decrease from 2016, down to 854 (441-1540) infections in 2018. A decline in new infections was consistently estimated in all age groups, and was particularly marked in MSM aged 25-34 years, and slowest in those aged 45 years or older. Similar trends were estimated in the number of undiagnosed infections, with the greatest decrease after 2013 in the 25-34 years age group. Under extrapolation assumptions, we calculated a 40% probability of achieving the defined target elimination threshold by 2030. INTERPRETATION: The sharp decrease in HIV incidence, estimated to have begun before the scale up of PrEP, indicates the success of strengthening treatment as prevention measures among MSM in England. To achieve the 2030 elimination threshold, targeted policies might be required to reach those aged 45 years or older, in whom incidence is decreasing at the slowest rate. FUNDING: UK Medical Research Council, UK National Institute of Health Research Health Protection Unit in Behavioural Science and Evaluation, and Public Health England.

Extending Bayesian back-calculation to estimate age and time specific HIV incidence.

CD4-based multi-state back-calculation methods are key for monitoring the HIV epidemic, providing estimates of HIV incidence and diagnosis rates by disentangling their inter-related contribution to the observed surveillance data. This paper, extends existing approaches to age-specific settings, permitting the joint estimation of age- and time-specific incidence and diagnosis rates and the derivation of other epidemiological quantities of interest. This allows the identification of specific age-groups at higher risk of infection, which is crucial in directing public health interventions. We investigate, through simulation studies, the suitability of various bivariate splines for the non-parametric modelling of the latent age- and time-specific incidence and illustrate our method on routinely collected data from the HIV epidemic among gay and bisexual men in England and Wales.