Data-Adaptive Estimation for Double-Robust Methods in Population-Based Cancer Epidemiology: Risk Differences for Lung Cancer Mortality by Emergency Presentation

Abstract

In this paper, we propose a structural framework for population-based cancer epidemiology and evaluate the performance of double-robust estimators for a binary exposure in cancer mortality. We conduct numerical analyses to study the bias and efficiency of these estimators. Furthermore, we compare 2 different model selection strategies based on 1) Akaike's Information Criterion and the Bayesian Information Criterion and 2) machine learning algorithms, and we illustrate double-robust estimators' performance in a real-world setting. In simulations with correctly specified models and near-positivity violations, all but the naive estimators had relatively good performance. However, the augmented inverse-probability-of-treatment weighting estimator showed the largest relative bias. Under dual model misspecification and near-positivity violations, all double-robust estimators were biased. Nevertheless, the targeted maximum likelihood estimator showed the best bias-variance trade-off, more precise estimates, and appropriate 95% confidence interval coverage, supporting the use of the data-adaptive model selection strategies based on machine learning algorithms. We applied these methods to estimate adjusted 1-year mortality risk differences in 183,426 lung cancer patients diagnosed after admittance to an emergency department versus persons with a nonemergency cancer diagnosis in England (2006-2013). The adjusted mortality risk (for patients diagnosed with lung cancer after admittance to an emergency department) was 16% higher in men and 18% higher in women, suggesting the importance of interventions targeting early detection of lung cancer signs and symptoms.

Figure 1.

Directed acyclic graph for a proposed structural causal framework in population-based cancer research. Conditional exchangeability of the treatment effect or exposure (A) on 1-year cancer mortality (Y) is obtained through conditioning on a set of available covariates (Y₁,Y₀ ⊥ A|W). The minimum sufficient set, based on the backdoor criterion, is obtained through conditioning on only W₁, W₃, and W₄. The average treatment effect for the structural framework is estimated as the average risk difference between the expected effect of the treatment conditional on W among treated persons (E(Y|A = 1; W)) and the expected effect of the treatment conditional on W among the untreated (E(Y|A = 0; W)). W₁, socioeconomic status; W₂, age; W₃, cancer stage; W₄, comorbidity.

Figure 2.

Overlap of the propensity scores for correctly specified (first scenario (A)) and misspecified (second scenario (B)) models for the probabilities of treatment status P(A = 1|W) and P(A = 0|W) in 1 random sample from 1,000 Monte Carlo simulations.

Figure 3.

Sex-specific adjusted risk difference for 1-year lung cancer mortality according to different double-robust estimators among 183,426 lung cancer patients diagnosed after admittance to an emergency department versus persons with a nonemergency cancer diagnosis, England, 2006–2013. A) women; B) men. Bars, 95% confidence intervals. AIPTW, augmented inverse-probability-of-treatment weighting; BF-AIPTW, best-fit augmented inverse-probability-of-treatment weighting (data-adaptive estimation based on Akaike’s Information Criterion (AIC) and the Bayesian Information Criterion (BIC)); BF-IPTW-RA, best-fit inverse-probability-of-treatment-weighted regression adjustment (data-adaptive estimation based on AIC-BIC); IPTW-RA, inverse-probability-of-treatment-weighted regression adjustment; TMLE, targeted maximum likelihood estimation (data-adaptive estimation based on ensemble learning and k-fold cross-validation).