A Pseudo-Value Approach to Causal Deep Learning of Semi-Competing Risks

While mortality is often the main focus of cancer studies, non-fatal events, such as disease progression, can vitally impact patient outcomes. For example, recurrence after curative treatment is a crucial endpoint in lung cancer, affecting available second-line treatments and personalized care. Estimating the de-confounded effect of interventions on disease recurrence is a key aspect of assessing cancer treatments. However, semi-competing risks complicate causal inference when death prevents disease recurrence. Existing approaches for estimating causal quantities in semi-competing survival functions rely on complex objective functions with strong assumptions and are challenging to estimate accurately. To address these challenges, we propose a deep learning approach for estimating the causal effect of treatment on non-fatal outcomes in the presence of dependent censoring and complex covariate relationships. Our three-stage approach involves estimating the marginal survival function using an Archimedean copula representation, and a jackknife pseudo-value approach that estimates pseudo-survival probabilities at fixed time points. These pseudo-survival probabilities serve as target values for developing causal estimators that are consistent and do not rely on assumptions like proportional hazards across all time points. In the final stage, we employ a deep neural network to link pseudo-outcomes, the causal variable, and additional confounders. This enables us to estimate survival average causal effects through direct standardization. We evaluate our approach through numerical studies and apply it to the Boston Lung Cancer Study, specifically examining the effect of surgical tumor resection in patients with early-stage non-small cell lung cancer.