Methods/Statistics
Using Probabilistic Bias Analysis to Adjust for Selection Bias in a Retrospective Case-Control Study Timothy L Lash* Huda Bashir Anke Hüls Richard F MacLehose Thomas P Ahern Lindsay J Collin Timothy L Lash
Retrospective case-control studies are susceptible to selection bias due to differential participation. Most studies present results from analyses on those who agreed to participate with acknowledgement of the potential for selection bias. To better understand the magnitude of bias and impact of bias adjustments, we conducted a simulation study using information about participants’ exposure prevalence to inform non-participants’ exposure prevalence and apply these in probabilistic bias analysis. Using a data-generating mechanism, we simulated 100,000 cohort studies, each with 40,000 subjects, true risk ratio of 2.00, exposure prevalence of 0.20, and baseline risk of 0.01. We then simulated 100,000 case-cohort studies within these cohort studies, sampling two controls per case. We evaluated three scenarios. First, we conducted studies with no selection bias. Second, selection bias was introduced by specifying that exposed cases were less likely to participate than unexposed cases (75 % vs 95%), and exposed controls were slightly more likely to participate than exposed cases (82%), but less likely than unexposed controls (88%). Third, participation rates for cases and controls were switched from the second scenario. In the first scenario with no selection bias, 95% of the 95% confidence intervals (CIs) covered the true odds ratio (OR), as expected. In the second scenario, with no bias adjustment, 77.7% of the CIs covered the true OR with a median estimate of 1.70 (1.29–2.23). In the third scenario, with no bias adjustment, 78% of the CIs covered the true OR with a median estimate of 2.36 (1.79–3.11). Four probability distributions (uniform, triangular, trapezoidal, and beta) for the exposure prevalence in non-participants, informed by participants, were used to obtain bias-adjusted estimates. The trapezoidal distribution provided the best coverage (scenario two: 94.7%, scenario three: 99.8%), and beta distributions provided the worst coverage (both scenarios: 77.3%).