Dose as Instrumental Variable in Exposure–Safety Analysis Using Count Models

A general approach to evaluating the bias of 2-stage instrumental variable estimators

Unmeasured confounding is a common concern when researchers attempt to estimate a treatment effect using observational data or randomized studies with nonperfect compliance. To address this concern, instrumental variable methods, such as 2-stage predictor substitution (2SPS) and 2-stage residual inclusion (2SRI), have been widely adopted. In many clinical studies of binary and survival outcomes, 2SRI has been accepted as the method of choice over 2SPS, but a compelling theoretical rationale has not been postulated. We evaluate the bias and consistency in estimating the conditional treatment effect for both 2SPS and 2SRI when the outcome is binary, count, or time to event. We demonstrate analytically that the bias in 2SPS and 2SRI estimators can be reframed to mirror the problem of omitted variables in nonlinear models and that there is a direct relationship with the collapsibility of effect measures. In contrast to conclusions made by previous studies (Terza et al, 2008), we demonstrate that the consistency of 2SRI estimators only holds under the following conditions: (1) when the null hypothesis is true; (2) when the outcome model is collapsible; or (3) when estimating the nonnull causal effect from Cox or logistic regression models, the strong and unrealistic assumption that the effect of the unmeasured covariates on the treatment is proportional to their effect on the outcome needs to hold. We propose a novel dissimilarity metric to provide an intuitive explanation of the bias of 2SRI estimators in noncollapsible models and demonstrate that with increasing dissimilarity between the effects of the unmeasured covariates on the treatment versus outcome, the bias of 2SRI increases in magnitude.

Determining causal exposure-response relationships with randomized concentration-controlled trials

Determining causal effects in exposure-response relationships is an important but also a challenging task since confounding factors that affect both drug exposure and response often exist and lead to confounding biases in causal effect estimation. Randomized concentration control (RCC) trials are designed to eliminate or to reduce the confounding bias. However, statistical issues in the design and analysis of these trials have not been examined closely in the literature. Analysis of dose-exposure relationship may also be affected by confounding factors if they affect dose adjustments. We examined these issues and suggest methodological and practical solutions. In particular, we proposed using instrumental variables (IV) for the estimation of causal effects in both exposure-response and dose-exposure relationships. We also examined the impacts of confounded treatment heterogeneity on the IV estimate for RCC trials. We illustrated these approaches with a trial design scenario showing the importance of considering multiple practical factors that may alter the performance of the IV estimate. The performance of the IV estimates was examined by simulations for a wide range of scenarios. The results showed clear advantages for the IV estimates over routine estimates. Some situations in which the IV estimates may fail were also identified.

Opportunities for minimization of confounding in observational research

Observational epidemiological studies are increasingly used in pharmaceutical research to evaluate the safety and effectiveness of medicines. Such studies can complement findings from randomized clinical trials by involving larger and more generalizable patient populations by accruing greater durations of follow-up and by representing what happens more typically in the clinical setting. However, the interpretation of exposure effects in observational studies is almost always complicated by non-random exposure allocation, which can result in confounding and potentially lead to misleading conclusions. Confounding occurs when an extraneous factor, related to both the exposure and the outcome of interest, partly or entirely explains the relationship observed between the study exposure and the outcome. Although randomization can eliminate confounding by distributing all such extraneous factors equally across the levels of a given exposure, methods for dealing with confounding in observational studies include a careful choice of study design and the possible use of advanced analytical methods. The aim of this paper is to introduce some of the approaches that can be used to help minimize the impact of confounding in observational research to the reader working in the pharmaceutical industry.