; CENSUR working survival group. Challenges in the estimation of Net SURvival: The CENSUR working survival group

A permutation test based on the restricted mean survival time for comparison of net survival distributions in non-proportional excess hazard settings

Net survival is used in epidemiological studies to assess excess mortality due to a given disease when causes of death are unreliable. By correcting for the general population mortality, it allows comparisons between regions or periods and thus evaluation of health policies. The Pohar-Perme non-parametric estimator of net survival has been recently proposed, soon followed by an appropriate log-rank-type test. However, log-rank tests are known to be under-optimal in non-proportional settings (e.g. crossing of the hazard functions). In classical survival analysis, one solution is to compare the restricted mean survival times. A difference in restricted mean survival time represents a life benefit or loss over the studied period. In the present article the restricted mean net survival time was used to derive a specific test statistic to compare net survivals in proportional and non-proportional hazards settings. The new test was generalized to more than two groups and to stratified analysis. The test performance was assessed on simulation study, compared to the log-rank-type test, and its use illustrated on a population-based colorectal cancer registry. The new test for net survival comparisons proved robust to non-proportionality and well-performing in proportional hazards situations. Furthermore, it is also suited to the classical survival framework.

Correcting for misclassification and selection effects in estimating net survival in clinical trials

BACKGROUND

Net survival, a measure of the survival where the patients would only die from the cancer under study, may be compared between treatment groups using either "cause-specific methods", when the causes of death are known and accurate, or "population-based methods", when the causes are missing or inaccurate. The latter methods rely on the assumption that mortality due to other causes than cancer is the same as the expected mortality in the general population with same demographic characteristics derived from population life tables. This assumption may not hold in clinical trials where patients are likely to be quite different from the general population due to some criteria for patient selection.

METHODS

In this work, we propose and assess the performance of a new flexible population-based model to estimate long-term net survival in clinical trials and that allows for cause-of-death misclassification and for effects of selection. Comparisons were made with cause-specific and other population-based methods in a simulation study and in an application to prostate cancer clinical trial data.

RESULTS

In estimating net survival, cause-specific methods seemed to introduce important biases associated with the degree of misclassification of cancer deaths. The usual population-based method provides also biased estimates, depending on the strength of the selection effect. Compared to these methods, the new model was able to provide more accurate estimates of net survival in long-term clinical trials.

CONCLUSION

Finally, the new model paves the way for new methodological developments in the field of net survival methods in multicenter clinical trials.

More accurate cancer-related excess mortality through correcting background mortality for extra variables

Relative survival methods used to estimate the excess mortality of cancer patients rely on the background (or expected) mortality derived from general population life tables. These methods are based on splitting the observed mortality into the excess mortality and the background mortality. By assuming a regression model for the excess mortality, usually a Cox-type model, one may investigate the effects of certain covariates on the excess mortality. Some covariates are cancer-specific whereas others are variables that may influence the background mortality as well. The latter should be taken into account in the background mortality to avoid biases in estimating their effects on the excess mortality. Unfortunately, the available life table might not include such variables and, consequently, might provide inaccurate values of the background mortality. We propose a model that uses multiplicative parameters to correct potentially inaccurate background mortality. The model can be seen as an extension of the frequently used Estève model because we assume a Cox-type model for the excess mortality with a piecewise constant baseline function and introduce additional parameters that multiply the background mortality. The original and the extended model are compared, first in a simulation study, then in an application to colon cancer registry data.