Estimation of HbA1c after weight loss using a beta-regression for an economic evaluation of a behavioural weight management programme from the GLoW trial: a methodological study

Abstract

Background: In economic evaluations, average intervention effects are usually applied to a population. However, this fails to reflect the change in the distribution of HbA_1c due to heterogeneous responses to weight loss. We aimed to investigate whether allowing heterogeneous treatment effects using a beta regression better represented the distribution of HbA_1c after a weight-loss intervention, and how this affected cost effectiveness.

Methods: The Glucose Lowering through Weight Management (GLoW) trial evaluated the effectiveness of a diabetes education and weight-loss intervention against a standard diabetes education programme. Adults diagnosed with type 2 diabetes within 3 years were recruited from Clinical Commissioning Groups across 159 sites in England from July 20, 2018, to July 22, 2018. Ethics approval (18/ES/0048) and participant informed consent were obtained. Considering the between-treatment-arm difference in HbA_1c after 12 months, we compared a mean-effect estimated from a mixed-effects regression to a heterogeneous effect estimated from a beta regression performed on 12-month HbA_1c conditional on baseline HbA_1c, gender, diabetes duration and intervention group. We used the School of Public Health Research (SPHR) Diabetes Treatment model to apply these treatment effects and evaluate the lifetime NHS costs and quality-adjusted life-years (QALYs), discounted at 3·5%. The microsimulation model estimated diabetes-related health outcomes using the UK Prospective Diabetes Study Outcomes Model 2 risk equations and risk factor trajectory equations, alongside estimating diabetes remission, osteoarthritis, and cancer. We calculated the incremental net benefit (INB) of the intervention using a £20 000 per QALY valuation, by deterministic analysis. The GLoW trial is registered with the ISRCTN Registry, ISRCTN18399564.

Findings: The trial recruited 577 participants (mean age 60 years; 278 [53%] female, 247 [47%] male; 474 [91%] white ethnic background). Applying heterogeneous HbA_1c changes better reproduced the skewness in post-intervention HbA_1c than applying a mean-effect (Kolmogorov-Smirnov test p=0·02 compared with p=0·0000007). The beta-regression method suggested the intervention was more cost-effective, estimating an INB of £736 per person, compared with £584 when applying the mean-effect.

Interpretation: Alternative regression specification methods should be considered when evaluating the cost-effectiveness of interventions if the key intervention outcomes are not normally distributed. However, this alternative method requires further investigation to conclude its appropriateness in evaluating cost-effectiveness in different contexts.

Funding: National Institute for Health and Care Research (NIHR) Programme Grants for Applied Research Programme (Reference Number RP-PG0216-20010).