A Bayesian factor analysis model for non-randomised staggered designs

Abstract

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.

Figures (5)

• Figure 1: Graphical summaries of data. Abbreviations: Jan: January; #: Number. (a) Number of peers working in each Operation Delivery Network during each month between June 2016 and May 2021. (b) Number of individuals living with Hepatitis C infection and eligible for treatment with direct-acting antiviral drugs identified each month between June 2016 and May 2021.
• Figure 2: Directed acyclic graph representing causal relationships between variables. The unit subscript $i$ is omitted to simplify the notation.
• Figure 3: Estimated cumulative number of treatment eligible Hepatitis-C-virus-infected individuals identified due to the peers intervention. Abbreviations: 95%-CrI: 95% credible interval; PPos: Posterior probability of a positive intervention effect. The cumulative effects were taken across the whole study period and all Operation Delivery Networks. $\rho$ is the assumed correlation between the potential outcomes using the Gaussian copula approach. The full model uses all available data (pre- and post-intervention outcomes and intervention assignment), the outcome model discards intervention assignment, and the pre-intervention outcome model discards post-intervention outcomes and assignment mechanism.
• Figure 4: Additional results graphs. (a) Point estimates (posterior mean) of $\tau_{it}$ for $\rho=0$ (394 in total). Red dots signal that the 95% credible interval did not include 0, while blue dots signal that it did. (b) Point estimates and 95% CrIs for $\exp\left(s\left(\sum_{j=1}^{t}a_{j}\right)\right)$. (c) Posterior distribution of $\exp(\theta_1)$. The dark blue indicates the 80% CrI and the light blue indicates the 95% CrI. (d) Posterior distribution of the share of additional Hepatitis-C-virus-infected individuals identified during the COVID-19 lockdown relative to the overall number of additional Hepatitis-C-virus-infected individuals identified ($\tau_c/\tau$).
• Figure 5: Estimated individual intervention effects across time for the Operation Delivery Networks ‘Kent’, ‘Merseyside & Cheshire’, and ‘South Yorkshire’. Abbreviations: Merseys. & Che.: Merseyside & Cheshire. $\rho$ is the assumed correlation between the potential outcomes using the Gaussian copula approach.