Bayesian modeling of cost-effectiveness studies with unmeasured confounding: a simulation study

unmconf : an R package for Bayesian regression with unmeasured confounders

The inability to correctly account for unmeasured confounding can lead to bias in parameter estimates, invalid uncertainty assessments, and erroneous conclusions. Sensitivity analysis is an approach to investigate the impact of unmeasured confounding in observational studies. However, the adoption of this approach has been slow given the lack of accessible software. An extensive review of available R packages to account for unmeasured confounding list deterministic sensitivity analysis methods, but no R packages were listed for probabilistic sensitivity analysis. The R package unmconf implements the first available package for probabilistic sensitivity analysis through a Bayesian unmeasured confounding model. The package allows for normal, binary, Poisson, or gamma responses, accounting for one or two unmeasured confounders from the normal or binomial distribution. The goal of unmconf is to implement a user friendly package that performs Bayesian modeling in the presence of unmeasured confounders, with simple commands on the front end while performing more intensive computation on the back end. We investigate the applicability of this package through novel simulation studies. The results indicate that credible intervals will have near nominal coverage probability and smaller bias when modeling the unmeasured confounder(s) for varying levels of internal/external validation data across various combinations of response-unmeasured confounder distributional families.

On the censored cost-effectiveness analysis using copula information

Background

Information and theory beyond copula concepts are essential to understand the dependence relationship between several marginal covariates distributions. In a therapeutic trial data scheme, most of the time, censoring occurs. That could lead to a biased interpretation of the dependence relationship between marginal distributions. Furthermore, it could result in a biased inference of the joint probability distribution function. A particular case is the cost-effectiveness analysis (CEA), which has shown its utility in many medico-economic studies and where censoring often occurs.

Methods

This paper discusses a copula-based modeling of the joint density and an estimation method of the costs, and quality adjusted life years (QALY) in a cost-effectiveness analysis in case of censoring. This method is not based on any linearity assumption on the inferred variables, but on a punctual estimation obtained from the marginal distributions together with their dependence link.

Results

Our results show that the proposed methodology keeps only the bias resulting statistical inference and don’t have anymore a bias based on a unverified linearity assumption. An acupuncture study for chronic headache in primary care was used to show the applicability of the method and the obtained ICER keeps in the confidence interval of the standard regression methodology.

Conclusion

For the cost-effectiveness literature, such a technique without any linearity assumption is a progress since it does not need the specification of a global linear regression model. Hence, the estimation of the a marginal distributions for each therapeutic arm, the concordance measures between these populations and the right copulas families is now sufficient to process to the whole CEA.

Illustration of the Impact of Unmeasured Confounding Within an Economic Evaluation Based on Nonrandomized Data

Background: Propensity score (PS) methods are frequently used within economic evaluations based on nonrandomized data to adjust for measured confounders, but many researchers omit the fact that they cannot adjust for unmeasured confounders. Objective: To illustrate how confounding due to unmeasured confounders can bias an economic evaluation despite PS matching. Methods: We used data from a previously published nonrandomized study to select a prematched population consisting of 121 patients (46.5%) who received endovascular aneurysm repair (EVAR) and 139 patients (53.5%) who received open surgical repair (OSR), in which sufficient data regarding eight measured confounders were available. One-to-one PS matching was used within this population to select two PS-matched subpopulations. The Matched PS-Smoking Excluded Subpopulation was selected by matching patients using a PS model that omitted patients’ smoking status (one of the measured confounders), whereas the Matched PS-Smoking Included Subpopulation was selected by matching patients using a PS model that included all eight measured confounders. Incremental cost-effectiveness ratios (ICERs) were assessed within both subpopulations. Results: Both subpopulations were composed of two different sets of 164 patients. Balance within the Matched PS-Smoking Excluded Subpopulation was achieved on all confounders except for patients’ smoking status, whereas balance within the Matched PS-Smoking Included Subpopulation was achieved on all confounders. Results indicated that the ICER of EVAR over OSR differed between both subpopulations; the ICER was estimated at $157,909 per life-year gained (LYG) within the Matched PS-Smoking Excluded Subpopulation, while it was estimated at $235,074 per LYG within the Matched PS-Smoking Included Subpopulation. Discussion: Although effective in controlling for measured confounding, PS matching may not adjust for unmeasured confounders that may bias the results of an economic evaluation based on nonrandomized data.

Bias Analysis for Uncontrolled Confounding in the Health Sciences

Uncontrolled confounding due to unmeasured confounders biases causal inference in health science studies using observational and imperfect experimental designs. The adoption of methods for analysis of bias due to uncontrolled confounding has been slow, despite the increasing availability of such methods. Bias analysis for such uncontrolled confounding is most useful in big data studies and systematic reviews to gauge the extent to which extraneous preexposure variables that affect the exposure and the outcome can explain some or all of the reported exposure-outcome associations. We review methods that can be applied during or after data analysis to adjust for uncontrolled confounding for different outcomes, confounders, and study settings. We discuss relevant bias formulas and how to obtain the required information for applying them. Finally, we develop a new intuitive generalized bias analysis framework for simulating and adjusting for the amount of uncontrolled confounding due to not measuring and adjusting for one or more confounders.

Pre-study feasibility and identifying sensitivity analyses for protocol pre-specification in comparative effectiveness research

The use of healthcare databases for comparative effectiveness research (CER) is increasing exponentially despite its challenges. Researchers must understand their data source and whether outcomes, exposures and confounding factors are captured sufficiently to address the research question. They must also assess whether bias and confounding can be adequately minimized. Many study design characteristics may impact on the results; however, minimal if any sensitivity analyses are typically conducted, and those performed are post hoc. We propose pre-study steps for CER feasibility assessment and to identify sensitivity analyses that might be most important to pre-specify to help ensure that CER produces valid interpretable results.