Interpreting Net Survival: What We Estimate Versus What We Think We Estimate

TL;DR

Empirical evidence is presented showing relative risk of other-cause deaths ranging from 1.0 (colorectal cancer) to 4.0+ (head and neck cancers), and calculations demonstrating that net survival can substantially underestimate cancer-specific survival probability when relative risk exceeds 1.0.

Abstract

Net survival is conventionally defined as ``survival if cancer were the only possible cause of death'', an estimand corresponding to cancer-specific mortality alone. The Pohar Perme estimator targets this by removing general population other-cause mortality from observed total mortality, but achieves it only when cancer patients experience the same other-cause mortality as the general population. However, cancer patients often experience elevated other-cause mortality due to baseline health differences and treatment-induced effects. Using recent theoretical work decomposing total mortality into four components (cancer deaths, baseline health differences, treatment-induced other-cause deaths, and general population other-cause mortality), we show that the Pohar Perme estimator delivers the sum of cancer deaths, baseline differences, and treatment-induced deaths, falling short of its intended estimand whenever either source of excess is present. From Botta \textit{et al}, we present empirical evidence showing relative risk of other-cause deaths ranging from 1.0 (colorectal cancer) to 4.0+ (head and neck cancers), and calculations demonstrating that net survival can substantially underestimate cancer-specific survival probability when relative risk exceeds 1.0. Critically, treatment-induced other-cause deaths represent irreducible causal pathways from cancer to death that cannot be eliminated through better stratification. We recommend interpreting net survival as ``survival where general population other-cause mortality is removed'' rather than as a causal counterfactual, and call for more precise language in cancer epidemiology.

Figures (4)

• Figure 1: Directed acyclic graph of the four-component mortality hazard decomposition. Solid arrows represent direct causal effects; dashed arrows represent paths involving unmeasured confounding ($U$). The four main nodes lie on a common horizontal axis. Component A ($h_A$, red): cancer-specific deaths from tumour progression or metastasis (Cancer diagnosis $\rightarrow$ Cancer-specific death). Component B ($h_B$): excess other-cause mortality from unmeasured factors $U$ (smoking, comorbidity, frailty, deprivation) shared by cancer patients and the general population; a backdoor path in principle addressable by conditioning on proxies of $U$ through improved life table stratification. Component C ($h_C$): treatment-induced other-cause deaths along the causal chain Cancer diagnosis $\rightarrow$ Treatment $\rightarrow$ Other-cause death; irreducible because no stratification can remove a node on a causal path. Treatment may also influence cancer-specific death directly. Component D ($h_D$): background other-cause mortality determined by age, sex, and calendar time. The arrow from Other-cause death to Cancer-specific death reflects the competing risks structure: a patient who dies from another cause is no longer at risk of cancer-specific death, so other-cause death forecloses it. The lower brace indicates these two outcomes are competing events. The Pohar Perme estimator removes Component D via matched life tables but retains A, B, and C. Net survival therefore equals cancer-specific survival only when $h_B = h_C = 0$.
• Figure 2: Decision tree for selecting the appropriate survival estimand. Starting from observed total mortality, the researcher answers four sequential questions to identify which estimand their analysis produces. Component letters correspond to the hazard decomposition in Equation 2.
• Figure 3: Five-year survival probability by relative risk of other-cause mortality under three component allocation scenarios. Each panel shows disease-specific survival (Component A; black solid), disease-attributable survival (Components A + C; orange dashed), and estimated net survival (Components A + B + C; blue dotted) at five-year follow-up across relative risk values of 1.0, 1.5, 2.0, 3.0, and 4.0. Panel A: all excess other-cause mortality allocated to Component B (pure baseline differences). Panel B: all excess allocated to Component C (pure treatment effects). Panel C: equal split between B and C (mixed). Cancer-specific hazard: Weibull (shape 1.5, scale 5.3), yielding 40% five-year cancer-specific survival. General population other-cause hazard: $h_D = 0.025$ per year (UK life tables, age 70). At RR = 1.0, all three estimands coincide.
• Figure 4: Survival curves over 10 years by relative risk value and component allocation scenario. Panels are arranged in a $3 \times 3$ grid: rows correspond to relative risk values (RR = 1.0, 2.0, 4.0); columns correspond to component allocation scenarios (pure baseline differences, pure treatment effects, mixed). Within each panel, three lines show disease-specific survival (Component A; black solid), disease-attributable survival (Components A + C; orange dashed), and estimated net survival (Components A + B + C; blue dotted). Brackets at five years indicate the absolute gap (percentage points) between net survival and disease-specific survival. Cancer-specific hazard: Weibull (shape 1.5, scale 5.3). General population other-cause hazard: $h_D = 0.025$ per year. In RR = 1.0 panels, all three lines are coincident. The gap between net survival and cancer-specific survival widens from diagnosis and reaches a maximum around four to five years before narrowing as survival probabilities converge toward zero.