Nonparametric Relative Survival Analysis with the R Package relsurv

Relative survival methods are crucial with data in which the cause of death information is either not given or inaccurate, but cause-specific information is nevertheless required. This methodology is standard in cancer registry data analysis and can also be found in other areas. The idea of relative survival is to join the observed data with the general mortality population data and thus extract the information on the disease-specific hazard. While this idea is clear and easy to understand, the practical implementation of the estimators is rather complex since the population hazard for each individual depends on demographic variables and changes in time. A considerable advance in the methodology of this field has been observed in the past decade and while some methods represent only a modification of existing estimators, others require newly programmed functions. The package relsurv covers all the steps of the analysis, from importing the general population tables to estimating and plotting the results. The syntax mimics closely that of the classical survival packages like survival and cmprsk, thus enabling the users to directly use its functions without any further familiarization. In this paper we focus on the nonparametric relative survival analysis, and in particular, on the two key estimators for net survival and crude probability of death. Both estimators were first presented in our package and are still missing in many other software packages, a fact which greatly hampers their frequency of use. The paper offers guidelines for the actual use of the software by means of a detailed nonparametric analysis of the data describing the survival of patients with colon cancer. The data have been provided by the Cancer Registry of Slovenia

Analysing population-based cancer survival - settling the controversies.

BACKGROUND: The relative survival field has seen a lot of development in the last decade, resulting in many different and even opposing suggestions on how to approach the analysis. METHODS: We carefully define and explain the differences between the various measures of survival (overall survival, crude mortality, net survival and relative survival ratio) and study their differences using colon and prostate cancer data extracted from the national population-based cancer registry of Slovenia as well as simulated data. RESULTS: The colon and prostate cancer data demonstrate clearly that when analysing population-based data, it is useful to split the overall mortality in crude probabilities of dying from cancer and from other causes. Complemented by net survival, it provides a complete picture of cancer survival in a given population. But when comparisons of different populations as defined for example by place or time are of interest, our simulated data demonstrate that net survival is the only measure to be used. CONCLUSIONS: The choice of the method should be done in two steps: first, one should determine the measure of interest and second, one should choose among the methods that estimate that measure consistently

Explained variation of excess hazard models.

The availability of longstanding collection of detailed cancer patient information makes multivariable modelling of cancer-specific hazard of death appealing. We propose to report variation in survival explained by each variable that constitutes these models. We adapted the ranks explained (RE) measure to the relative survival data setting, ie, when competing risks of death are accounted for through life tables from the general population. RE is calculated at each event time. We introduce weights for each death reflecting its probability to be a cancer death. RE varies between -1 and +1 and can be reported at given times in the follow-up and as a time-varying measure from diagnosis onward. We present an application for patients diagnosed with colon or lung cancer in England. The RE measure shows reasonable properties and is comparable in both relative and cause-specific settings. One year after diagnosis, RE for the most complex excess hazard models reaches 0.56, 95% CI: 0.54 to 0.58 (0.58 95% CI: 0.56-0.60) and 0.69, 95% CI: 0.68 to 0.70 (0.67, 95% CI: 0.66-0.69) for lung and colon cancer men (women), respectively. Stage at diagnosis accounts for 12.4% (10.8%) of the overall variation in survival among lung cancer patients whereas it carries 61.8% (53.5%) of the survival variation in colon cancer patients. Variables other than performance status for lung cancer (10%) contribute very little to the overall explained variation. The proportion of the variation in survival explained by key prognostic factors is a crucial information toward understanding the mechanisms underpinning cancer survival. The time-varying RE provides insights into patterns of influence for strong predictors

Direct modeling of the crude probability of cancer death and the number of life years lost due to cancer without the need of cause of death: a pseudo-observation approach in the relative survival setting.

In population-based cancer studies, net survival is a crucial measure for population comparison purposes. However, alternative measures, namely the crude probability of death (CPr) and the number of life years lost (LYL) due to death according to different causes, are useful as complementary measures for reflecting different dimensions in terms of prognosis, treatment choice, or development of a control strategy. When the cause of death (COD) information is available, both measures can be estimated in competing risks setting using either cause-specific or subdistribution hazard regression models or with the pseudo-observation approach through direct modeling. We extended the pseudo-observation approach in order to model the CPr and the LYL due to different causes when information on COD is unavailable or unreliable (i.e., in relative survival setting). In a simulation study, we assessed the performance of the proposed approach in estimating regression parameters and examined models with different link functions that can provide an easier interpretation of the parameters. We showed that the pseudo-observation approach performs well for both measures and we illustrated their use on cervical cancer data from the England population-based cancer registry. A tutorial showing how to implement the method in R software is also provided

Analysis of time-to-event for observational studies: Guidance to the use of intensity models

This paper provides guidance for researchers with some mathematical background on the conduct of time-to-event analysis in observational studies based on intensity (hazard) models. Discussions of basic concepts like time axis, event definition and censoring are given. Hazard models are introduced, with special emphasis on the Cox proportional hazards regression model. We provide check lists that may be useful both when fitting the model and assessing its goodness of fit and when interpreting the results. Special attention is paid to how to avoid problems with immortal time bias by introducing time-dependent covariates. We discuss prediction based on hazard models and difficulties when attempting to draw proper causal conclusions from such models. Finally, we present a series of examples where the methods and check lists are exemplified. Computational details and implementation using the freely available R software are documented in Supplementary Material. The paper was prepared as part of the STRATOS initiative.Comment: 28 pages, 12 figures. For associated Supplementary material, see http://publicifsv.sund.ku.dk/~pka/STRATOSTG8