Making relative survival analysis relatively easy
Section snippets
Motivation
If a person with an incurable disease commits suicide, the cause of death written in the death certificate will be suicide. And if there were many such cases, the mortality statistics would show much lower proportion of deaths due to the disease in question than it really should. And while suicides are just an obvious, more or less hypothetical, example, it is less well known that it is often difficult or even impossible to select among different possible causes of death or assign a certain
Relative survival
The cumulative relative survival function is defined [2] aswhere denotes observed survival and stands for population or expected survival, which is estimated on the basis of population mortality tables. Obviously, can be any non-negative number, although the methods are most often applied to data where is less than 1. Correct calculation of the expected survival is not a straightforward task, and it is now generally accepted that the method of Hakulinen [3]
Estimation
Fitting any model to the transformed data presents no new problems, and as mentioned fitting the multiplicative model is also straightforward. Additive model on the other hand has its own peculiarities. The problem is that the existing methods require baseline excess hazard in (5) to be specified. This is usually done by assuming the baseline excess hazard to be constant in prespecified intervals. Noncritical usage of such an assumption can lead to problems. First, if the assumption is wrong,
Population tables available on the internet
Population tables are an indispensable part of any relative survival analysis. They can be obtained from the national statistical offices, but usually come in quite different formats depending on the national mortality and census data organization. Some work might then be needed for transforming such tables into a format required by R programs. Fortunately, web sites now exist that provide tables for various countries in a uniform format. One such site is the human mortality database (HMD, //www.mortality.org
The R package relsurv
In previous sections, various relative survival methods and their accompanying problems have been presented. The relsurv package, that can be downloaded from CRAN [5], provides a software tool that simplifies their use. While the core functions are described in [13], the package has now been enriched with new methods and several functions that make it more user friendly. Two important additions, the EM-based estimation and the usage of the population tables, available on the Internet, are
Examples
In this section we present three examples of the usage of the package, with emphasis on the usage of population tables. We first explain how to create figures from Section 3.3, and then present two examples of relative survival analysis.
Discussion
Relative survival analysis offers answers to questions that cannot be answered with standard analysis. For now, the methods are used extensively in cancer registries, but are almost unknown to other medical professionals. For example, no textbook on survival analysis has a chapter, or even a section, devoted to the topic. This is partly due to the fact that relative survival analysis is inseparably tied to the population data, which is seen as an obstacle to its usage. With ever greater
Maja Pohar has graduated from mathematics at the University of Ljubljana and is now a final year Ph.D. student of statistics at the same university. She is the author of six SCI papers and has written papers on relative survival in the Journal of the Royal Statistical Society—Series C, Statistics in Medicine, and Computer Methods and Programs in Biomedicine. She is the author of the R package relsurv that is included in CRAN and provides functions for regression in relative survival.
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Ethnic, racial and socioeconomic disparities in breast cancer survival in two Brazilian capitals between 1996 and 2012
2021, Cancer EpidemiologyCitation Excerpt :In these methods, the excess mortality hazard associated with a diagnosis of cancer can be determined through the relation between the survival observed among cancer patients and the survival that would have been expected in the general population, which can be obtained from population life tables of all-cause mortality by age, sex and calendar year. From the excess mortality hazard (EMH), it is possible to estimate relative survival, defined as an estimate of survival from breast cancer after correction for other causes of death (competing hazards), which increase rapidly with age [21,22]. Regional disparities are still among the most relevant public health issues in Brazil and access to screening and treatment are key factors in breast cancer prognosis [23].
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2021, European Journal of Surgical OncologyCitation Excerpt :To analyze relative survival, population tables with the corresponding background mortality data were downloaded from the National Statistical Office (Details: Statistisches Bundesamt (Federal Statistical); 2013). The R package relsurv using the Pohar-Perme estimator was used to analyze relative survival [18]. Population mortality rates were incorporated as time-dependent covariates (multiplicative Cox regression model) [19].
Deprivation gap in colorectal cancer survival attributable to stage at diagnosis: A population-based study in Spain
2020, Cancer EpidemiologyCitation Excerpt :To this end, net survival at 1 and 5 years after diagnosis by patient’s and tumor characteristics were reported. Life-table estimates of net survival were obtained using the Pohar-Perme method [15] as implemented in the R package relsurv [16]. The life tables were provided by the Spanish National Statistics Institute and were stratified by sex, age and calendar year.
Maja Pohar has graduated from mathematics at the University of Ljubljana and is now a final year Ph.D. student of statistics at the same university. She is the author of six SCI papers and has written papers on relative survival in the Journal of the Royal Statistical Society—Series C, Statistics in Medicine, and Computer Methods and Programs in Biomedicine. She is the author of the R package relsurv that is included in CRAN and provides functions for regression in relative survival.
Janez Stare is a full profesor at the Faculty of Medicine at the University of Ljubjana and the head of the Department of Biomedical Informatics.
He is the author of more than 25 SCI papers and has recently written papers on relative survival in the Journal of the Royal Statistical Society—Series C, Statistics in Medicine, and Computer Methods and Programs in Biomedicine.
He has been an invited speaker on the topic of relative survival at the Annual Conference of the International Society for Clinical Biostatistics in Leiden, 2004, and at the ROeS Seminar in Graz, 2005.