Subgroup analysis for secondary outcomes 1 and 2
REGRESSION, SECONDARY
To estimate possible treatment effect heterogeneity for the primary outcome, we will use a Bayesian hierarchical model with main effects and interaction term between intervention group and type of narcotic (morphine or methadone). This approach allows us to specify a priori how likely (or unlikely) it is for subgroup differences to be present and to shrink the subgroup estimates to the overall mean treatment effect. We will specify a model that allows different standard deviations of the outcome for the two subgroups (as observed in Davis et al.). Prior distributions for main effects will be the same as for the primary outcome. Neutral and skeptical priors will be used for the interaction terms. Point estimates of treatment effect and 95% credible intervals will be reported for each subgroup along with probability of subgroup treatment differences.We will analyze secondary binary outcomes with Bayesian logistic regression models, including treatment group, maternal treatment, and stratification dose as covariates, and we will include hospital as a random effect. We will use a neutral prior centered at 1.0 with 95% CrI of 0.33–3.0 (to allow for large range of ORs) for the treatment effect. In the log OR scale, this prior will be normal (0, SD=0.57), and all other priors will be the same as above.We will analyze secondary outcomes of the total opioid exposure and assessments of maternal well-being, maternal-infant attachment, infant neurobehavioral functioning, infant development, and growth with a similar linear regression model used for the primary outcome.We will analyze secondary outcome of length of stay with a linear regression model similar to the one used to analyze the primary outcome; however, we will also fit survival analysis models to study the effects of skewness.We will implement all Bayesian models via Markov chain Monte Carlo methods (MCMC) by using R or SAS software. For SAS, the procedure will be PROC MCMC. For R, possible software is “RJAGS” which is an interface to JAGS MCMC software, “rstan,” “rstanarm,” and “brms,” which are packages that interface with the Stan language. For each analysis, we will run three MCMC chains with randomly drawn starting values. We will use a burn-in of 3000 iterations, with sampling from a further 30,000 iterations for each chain. Thinning will be used as necessary to reduce autocorrelation among the samples to improve posterior sampling. To monitor convergence, we will use trace plots and the Gelman-Rubin convergence diagnostic (Rhat < 1.1 indicating convergence) for all parameters.