A Bayesian factor analysis model for non-randomised staggered designs

The employment of peer supporter workers starting in 2018 was one of the interventions deployed by National Health Service England as part of its Hepatitis C virus (HCV) elimination plan. Peers are individuals with relevant lived experience who educate their communities about the virus and promote testing and treatment. In this paper, we assess the causal effect of the peers intervention on HCV patient case-finding, using data on 22 administrative regions from January 2016 to May 2021. To do this, we develop a Bayesian causal factor analysis model for count outcomes and ordinal interventions. Our method provides uncertainty quantification for all causal estimands of interest, gains efficiency by jointly modelling the intervention assignment process, pre- and post-intervention outcomes, and provides estimates of both conditional average and individual treatment effects (ITEs). For ITEs, we propose a copula-based approach that allows practitioners to perform sensitivity analysis to assumptions made regarding the joint distribution of potential outcomes, that are necessary to estimate these quantities. Our analysis suggests that the introduction of peers led to an increase in HCV patient case-finding. Further, we found that the effect of the intervention increased with intervention intensity, and was stronger during the national COVID-19 lockdown.