Inverse probability weighting and doubly robust standardization in the relative survival framework.

A commonly reported measure when interested in the survival of cancer patients is relative survival. Relative survival circumvents issues with inaccurate cause of death information by incorporating the expected mortality rates of cancer individuals from population lifetables of the general population. A summary of the cancer population prognosis can be obtained using the marginal relative survival. To explore differences between exposure groups, such as socioeconomic groups, the difference in marginal relative survival between exposed and unexposed can be obtained and under assumptions is interpreted as the average causal effect of exposure to survival. In a modeling context, this is usually estimated by applying regression standardization as the average of the individual-specific estimates after fitting a relative survival model. Regression standardization yields an estimator that consistently estimates the causal effect under standard causal inference assumptions and if the relative survival model is correctly specified. We extend inverse probability weighting (IPW) and doubly robust standardization methods in the relative survival framework as additional valuable tools for obtaining average causal effects when correct model specification might not hold for the relative survival model. IPW yields an unbiased estimate of the average causal effect if a correctly specified model has been fitted for the exposure (propensity score) whereas doubly robust standardization requires that at least one of the propensity score model or the relative survival model is correctly specified. An example using data on melanoma is provided and a simulation study is conducted to investigate how sensitive are the methods to model misspecification, including different ways for obtaining standard errors.