Bayesian approaches for comparative effectiveness research

Abstract

Background: A hallmark of comparative effectiveness research is the analysis of all the available evidence from different studies addressing a given question of medical risk versus benefit. The Bayesian statistical approach is ideally suited for such investigations because it is inherently synthetic and because it is philosophically uninhibited regarding the ability to analyze all the available evidence.

Purpose: To consider a variety of comparative effectiveness research settings and show how the Bayesian approach applies.

Methods: The Bayesian approach is described as it has been applied to the comparative analysis of implantable cardioverter defibrillators and mammographic screening, in the Cancer Intervention and Surveillance Modeling Network, in comparisons of patient outcomes data from different sources, and in designing adaptive clinical trials to support the development of 'personalized medicine.'

Results: Bayesian methods allow for continued learning as data accrue and for cumulating meta-analyses and the comparison of heterogeneous studies. Bayesian methods enable predictive probability distributions of the results of future studies.

Limitations: Bayesian posterior distributions are subject to potential bias - in the selection of 'available' evidence and in the choice of a likelihood model. Sensitivity analyses help to control this bias.

Conclusions: The Bayesian approach has much to offer comparative effectiveness research. It provides a mechanism for synthesizing various sources of information and for updating knowledge in an online fashion as evidence accumulates.

Figure 1

Base model in blue (blue triangles, control; blue diamonds, implantable cardioverter defibrillators [ICD]). Variant of base model in red (red squares, control; red x’s, ICD). Panel A shows the posterior means of annual hazard rates. Control hazards are modeled separately in each of the 5 years post follow-up. For the base model, ICD is assumed to have the same relative risk in each of the 5 years. Therefore, the ratios of the blue diamonds to the blue triangles are the same in each year. For the model variant, the control and ICD hazards are modeled separately in each year of follow-up. So, in the variant there is no constraint to have the same (or otherwise related) hazard ratios in different years. Panel B shows the survival version of Panel A, the posterior means of survival for the base model in blue and the variant model in red.

Figure 2

Predictive distribution of hazard ratio (HR; implantable cardioverter defibrillators [ICD] to control) of mortality for the next trial over time, compared with observed HR from the trial. The names of the 12 trials are abbreviated in red lettering. Red dots are the point estimates of HR for each trial. The black bars show the 95% probability interval of the predictive distribution under the base model for each trial based on data available before that trial’s results became known, at the time of the trial’s publication. The predictive distributions depend on the information available about the ICD effect from previous trials, but also on the total number of events in the new trial as a measure of information to be contained in that trial.

Figure 3

Plots of mortality rates in the eight randomized screening trials. Points are labeled with the first letter of the trial name. (a) Breast cancer mortality rates per 100,000 life years by randomization group. (b) Estimated reduction in breast cancer mortality, screening over control. Positive reductions indicate a benefit for the screening group. Labels in upper case are the observed reductions in the trials and those in lower case are the Bayesian estimates. The overall mean reductions are 18% in both cases. The updates and the UK Study are described in the text. a. Adapted from Berry DA. Benefits and risks of screening mammography for women in their forties: a statistical appraisal. J Natl Cancer Inst 1998; 90: 1431–9 (by permission of Oxford University Press).

Figure 4

Example of a Bayesian Cancer Intervention and Surveillance Modeling Network (CISNET) model simulation that is within the ‘acceptance window’ around actual US breast cancer mortality.

Figure 5

Prior and posterior distributions for the reduction in breast cancer mortality for primary breast cancers that are estrogen-receptor positive. The posterior distribution corresponds to the information available via modeling regarding the effectiveness of 5 years of tamoxifen in ordinary clinical practice in the United States between 1975 and 2000. The posterior mean effect of tamoxifen is 0.37, corresponding to a 37% reduction in the hazard of breast cancer mortality.

Figure 6

Dot-plot of the accepted simulations for Bayesian Model M, showing how the information available in the various sources used translates via modeling into reductions in breast cancer mortality due to screening and due to adjuvant treatment.