Leveraging a Bayesian Approach in a Comparative Effectiveness Trial of Major Adverse Cardiovascular Events

Abstract

Purpose: We applied a Bayesian approach to further investigate the association of sodium-glucose cotransporter-2 inhibitors (SGLT2i) with the composite outcome of Major Adverse Cardiovascular Event and Heart Failure hospitalization (MACE+HF) and its individual components leveraging the ability of a Bayesian approach to incorporate prior clinical information and to make probability statements about the parameters.

Methods: We use a Bayesian time-to-event model, where the covariates are directly modeled in the hazard function. Following propensity score matching, we fit three Bayesian models; one with a relatively flat, normal prior on the SGLT2i coefficient (Uninformative) and 2 with informative priors from a meta-analysis (based on a cohort with no history of cardiovascular disease [No CVD] and cohorts with a history of CVD [CVD]). We estimate the posterior distribution for the hazard ratio (HR) using a Hamiltonian Monte Carlo algorithm. It allows us to estimate the probability of a meaningful protective association (HR < 0.90) in addition to point and interval estimates.

Results: The posterior means and 95% credible intervals for the HR suggested a protective association for SGLT2i versus dipeptidyl peptidase 4 inhibitors (DPP4i) for the MACE+HF outcome: No CVD: 0.82 (0.68, 0.96), CVD: 0.82 (0.71, 0.94), and Uninformative: 0.79 (0.65, 0.94). The probability of a meaningful protective association for the No CVD, CVD, and Uninformative priors were 88%, 92%, and 93%, respectively. The probability of a meaningful protective association for the HF hospitalization, CVD hospitalization and CVD death components of MACE+HF were 95%, 67%, and 93%, respectively.

Conclusion: The Bayesian analysis allowed for the incorporation of prior information via an informative prior and further investigation of the association between SGLT2 and the components of the MACE+HF composite outcome. It allowed for the calculation of an easily interpretable summary measure, the probability of a meaningful protective association.

Keywords: bayesian inference; cardiovascular disease; diabetes mellitus; hamiltonian monte carlo; propensity score methods; time-to-event analysis.

Figure 1

Posterior Distributions for the Cause-specific Hazard Ratio. The posterior distributions for the cause-specific hazard ratio for sodium–glucose cotransporter-2 inhibitors (SGLT2i) versus dipeptidyl peptidase 4 inhibitors (DPP4i) for the major adverse cardiovascular events plus heart failure (MACE+HF) outcome from the three different Bayesian models (No CVD: yellow, CVD: blue, Uninformative: black). The vertical dashed lines (No CVD: yellow, CVD: blue, Uninformative: black) denote the posterior means, and the vertical grey line denotes a null association.

Figure 2

Survival Plots. Probability of survival for major adverse cardiovascular events plus heart failure ((A): MACE+HF) and its components ((B): HF, (C): CVD Hospitalization, and (D): CVD Death) among sodium–glucose cotransporter-2 inhibitors (SGLT2i) vs dipeptidyl peptidase 4 inhibitor (DPP4i) users without cardiovascular disease from the cause-specific Bayesian time-to-event analyses using the Uninformative prior. The blue line and blue shading provide the survival function and 95% pointwise prediction interval for SGLT2i users, respectively, and the black line and grey shading provides the survival function and 95% pointwise prediction interval for DPP4i users, respectively.

Figure 3

Hazard Ratio and Probability of Meaningful Association for MACE+HF and Components. The points are the estimated hazard ratios (HR) along with 95% credible intervals (horizonal lines) and the corresponding probability of a meaningful association (HR < 0.90) for the composite outcome of major adverse cardiovascular events plus heart failure (MACE+HF) and its components (HF Hospitalization, CVD Hospitalization, and CVD Death) found using the Bayesian time-to-event models with the Uninformative prior.