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 performed numerical analyses to study the bias and efficiency of these estimators. Furthermore, we compared two different model selection strategies based on 1) the Akaike and Bayesian Information Criteria and 2) machine-learning algorithms, and illustrated double-robust estimators’ performance in a real setting. In simulations with correctly specified models and near-positivity violations, all but the naïve estimators presented relatively good performance. However, the augmented inverse-probability 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 one-year mortality risk differences in 183,426 lung cancer patients diagnosed after admittance to an emergency department versus non-emergency 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.