Standardizing Discrete-Time Hazard Ratios With a Disease Risk Score

Confounder Adjustment Using the Disease Risk Score: A Proposal for Weighting Methods

Propensity score analysis is a common approach to addressing confounding in nonrandomized studies. Its implementation, however, requires important assumptions (e.g., positivity). The disease risk score (DRS) is an alternative confounding score that can relax some of these assumptions. Like the propensity score, the DRS summarizes multiple confounders into a single score, on which conditioning by matching allows the estimation of causal effects. However, matching relies on arbitrary choices for pruning out data (e.g., matching ratio, algorithm, and caliper width) and may be computationally demanding. Alternatively, weighting methods, common in propensity score analysis, are easy to implement and may entail fewer choices, yet none have been developed for the DRS. Here we present 2 weighting approaches: One derives directly from inverse probability weighting; the other, named target distribution weighting, relates to importance sampling. We empirically show that inverse probability weighting and target distribution weighting display performance comparable to matching techniques in terms of bias but outperform them in terms of efficiency (mean squared error) and computational speed (up to >870 times faster in an illustrative study). We illustrate implementation of the methods in 2 case studies where we investigate placebo treatments for multiple sclerosis and administration of aspirin in stroke patients.

On Variance of the Treatment Effect in the Treated When Estimated by Inverse Probability Weighting

In the analysis of observational studies, inverse probability weighting (IPW) is commonly used to consistently estimate the average treatment effect (ATE) or the average treatment effect in the treated (ATT). The variance of the IPW ATE estimator is often estimated by assuming that the weights are known and then using the so-called "robust" (Huber-White) sandwich estimator, which results in conservative standard errors (SEs). Here we show that using such an approach when estimating the variance of the IPW ATT estimator does not necessarily result in conservative SE estimates. That is, assuming the weights are known, the robust sandwich estimator may be either conservative or anticonservative. Thus, confidence intervals for the ATT using the robust SE estimate will not be valid, in general. Instead, stacked estimating equations which account for the weight estimation can be used to compute a consistent, closed-form variance estimator for the IPW ATT estimator. The 2 variance estimators are compared via simulation studies and in a data analysis of the association between smoking and gene expression.

Innovations in applied decision theory for health and safety

OBJECTIVES

There are established methods for occupational epidemiological cohort analysis, such as proportional hazards regression, that are well suited to aetiological research and yield parameter estimates that allow for succinct communication among academics. However, these methods are not necessarily well suited for evaluation of health impacts of policy choices and communication to decision makers. An informed decision about a policy that impacts health and safety requires a valid estimate of the policy's potential impact.

METHODS

We propose methods for data summarisation that may facilitate communication with managers, workers and their advocates. We calculate measures of effect in a framework for competing events, graphically display potential impacts on cause-specific mortality under policy alternatives and contrast these results to estimates obtained using standard Poisson regression methods. Methods are illustrated using a cohort mortality study of 28 546 Ontario uranium miners hired between 1950 and 1996 and followed through 2007.

RESULTS

A standard regression analysis yields a positive association between cumulative radon progeny exposure and all-cause mortality (log(RR per 100 WLM)=0.09; SE=0.02). The proposed method yields an estimate of the expected gain in life expectancy (approximately 6 months per worker) and reduction of 261 lung cancer deaths under a policy that eliminated occupational radon progeny exposure.

CONCLUSIONS

The proposed method shifts attention from covariate-adjusted risk ratios or rate ratios to estimates of deaths that are avoided or delayed under a potential policy. The approach may help inform decision-making and strengthen the connection of epidemiological approaches to data analysis with developments in decision theory and systems engineering to improve health and safety.