Using Super Learner Prediction Modeling to Improve High-dimensional Propensity Score Estimation :

Adjusting for large numbers of covariates ascertained from patients' health care claims data may improve control of confounding, as these variables may collectively be proxies for unobserved factors. Here, we develop and test an algorithm that empirically identifies candidate covariates, prioritizes covariates, and integrates them into a propensity-score-based confounder adjustment model. We developed a multistep algorithm to implement high-dimensional proxy adjustment in claims data. Steps include (1) identifying data dimensions, eg, diagnoses, procedures, and medications; (2) empirically identifying candidate covariates; (3) assessing recurrence of codes; (4) prioritizing covariates; (5) selecting covariates for adjustment; (6) estimating the exposure propensity score; and (7) estimating an outcome model. This algorithm was tested in Medicare claims data, including a study on the effect of Cox-2 inhibitors on reduced gastric toxicity compared with nonselective nonsteroidal anti-inflammatory drugs (NSAIDs). In a population of 49,653 new users of Cox-2 inhibitors or nonselective NSAIDs, a crude relative risk (RR) for upper GI toxicity (RR = 1.09 [95% confidence interval = 0.91-1.30]) was initially observed. Adjusting for 15 predefined covariates resulted in a possible gastroprotective effect (0.94 [0.78-1.12]). A gastroprotective effect became stronger when adjusting for an additional 500 algorithm-derived covariates (0.88 [0.73-1.06]). Results of a study on the effect of statin on reduced mortality were similar. Using the algorithm adjustment confirmed a null finding between influenza vaccination and hip fracture (1.02 [0.85-1.21]). In typical pharmacoepidemiologic studies, the proposed high-dimensional propensity score resulted in improved effect estimates compared with adjustment limited to predefined covariates, when benchmarked against results expected from randomized trials.

Inferring causation from non-randomized studies of exposure requires that exposure groups can be balanced with respect to prognostic factors for the outcome. Although there is broad agreement in the literature that balance should be checked, there is confusion regarding the appropriate metric. We present a simulation study that compares several balance metrics with respect to the strength of their association with bias in estimation of the effect of a binary exposure on a binary, count, or continuous outcome. The simulations utilize matching on the propensity score with successively decreasing calipers to produce datasets with varying covariate balance. We propose the post-matching C-statistic as a balance metric and found that it had consistently strong associations with estimation bias, even when the propensity score model was misspecified, as long as the propensity score was estimated with sufficient study size. This metric, along with the average standardized difference and the general weighted difference, outperformed all other metrics considered in association with bias, including the unstandardized absolute difference, Kolmogorov-Smirnov and Lévy distances, overlapping coefficient, Mahalanobis balance, and L1 metrics. Of the best-performing metrics, the C-statistic and general weighted difference also have the advantage that they automatically evaluate balance on all covariates simultaneously and can easily incorporate balance on interactions among covariates. Therefore, when combined with the usual practice of comparing individual covariate means and standard deviations across exposure groups, these metrics may provide useful summaries of the observed covariate imbalance.

Recent theoretical studies have shown that conditioning on an instrumental variable (IV), a variable that is associated with exposure but not associated with outcome except through exposure, can increase both bias and variance of exposure effect estimates. Although these findings have obvious implications in cases of known IVs, their meaning remains unclear in the more common scenario where investigators are uncertain whether a measured covariate meets the criteria for an IV or rather a confounder. The authors present results from two simulation studies designed to provide insight into the problem of conditioning on potential IVs in routine epidemiologic practice. The simulations explored the effects of conditioning on IVs, near-IVs (predictors of exposure that are weakly associated with outcome), and confounders on the bias and variance of a binary exposure effect estimate. The results indicate that effect estimates which are conditional on a perfect IV or near-IV may have larger bias and variance than the unconditional estimate. However, in most scenarios considered, the increases in error due to conditioning were small compared with the total estimation error. In these cases, minimizing unmeasured confounding should be the priority when selecting variables for adjustment, even at the risk of conditioning on IVs.