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.

Health status of prevalent cancer cases as measured by mortality dynamics (cancer vs. noncancer): Application to five major cancers sites.

BACKGROUND: Cancer prevalence is heterogeneous because it includes individuals who are undergoing initial treatment and those who are in remission, experiencing relapse, or cured. The proposed statistical approach describes the health status of this group by estimating the probabilities of death among prevalent cases. The application concerns colorectal, lung, breast, and prostate cancers and melanoma in France in 2017. METHODS: Excess mortality was used to estimate the probabilities of death from cancer and other causes. RESULTS: For the studied cancers, most deaths from cancer occurred during the first 5 years after diagnosis. The probability of death from cancer decreased with increasing time since diagnosis except for breast cancer, for which it remained relatively stable. The time beyond which the probability of death from cancer became lower than that from other causes depended on age and cancer site: for colorectal cancer, it was 6 years after diagnosis for women (7 years for men) aged 75-84 and 20 years for women (18 years for men) aged 45-54 years, whereas cancer was the major cause of death for women younger than 75 years whatever the time since diagnosis for breast and for all patients younger than 75 years for lung cancer. In contrast, deaths from other causes were more frequent in all the patients older than 75 years. Apart from breast cancer in women younger than 55 years and lung cancer in women older than 55 years and men older than 65 years, the probability of death from cancer among prevalent cases fell below 1%, with varying times since diagnosis. CONCLUSIONS: The authors' approach can be used to better describe the burden of cancer by estimating outcomes in prevalent cases.

Non-parametric estimation of reference adjusted, standardised probabilities of all-cause death and death due to cancer for population group comparisons.

BACKGROUND: Ensuring fair comparisons of cancer survival statistics across population groups requires careful consideration of differential competing mortality due to other causes, and adjusting for imbalances over groups in other prognostic covariates (e.g. age). This has typically been achieved using comparisons of age-standardised net survival, with age standardisation addressing covariate imbalance, and the net estimates removing differences in competing mortality from other causes. However, these estimates lack ease of interpretability. In this paper, we motivate an alternative non-parametric approach that uses a common rate of other cause mortality across groups to give reference-adjusted estimates of the all-cause and cause-specific crude probability of death in contrast to solely reporting net survival estimates. METHODS: We develop the methodology for a non-parametric equivalent of standardised and reference adjusted crude probabilities of death, building on the estimation of non-parametric crude probabilities of death. We illustrate the approach using regional comparisons of survival following a diagnosis of rectal cancer for men in England. We standardise to the covariate distribution and other cause mortality of England as a whole to offer comparability, but with close approximation to the observed all-cause region-specific mortality. RESULTS: The approach gives comparable estimates to observed crude probabilities of death, but allows direct comparison across population groups with different covariate profiles and competing mortality patterns. In our illustrative example, we show that regional variations in survival following a diagnosis of rectal cancer persist even after accounting for the variation in deprivation, age at diagnosis and other cause mortality. CONCLUSIONS: The methodological approach of using standardised and reference adjusted metrics offers an appealing approach for future cancer survival comparison studies and routinely published cancer statistics. Our non-parametric estimation approach through the use of weighting offers the ability to estimate comparable survival estimates without the need for statistical modelling.

Different survival analysis methods for measuring long-term outcomes of Indigenous and non-Indigenous Australian cancer patients in the presence and absence of competing risks.

BACKGROUND: Net survival is the most common measure of cancer prognosis and has been used to study differentials in cancer survival between ethnic or racial population subgroups. However, net survival ignores competing risks of deaths and so provides incomplete prognostic information for cancer patients, and when comparing survival between populations with different all-cause mortality. Another prognosis measure, "crude probability of death", which takes competing risk of death into account, overcomes this limitation. Similar to net survival, it can be calculated using either life tables (using Cronin-Feuer method) or cause of death data (using Fine-Gray method). The aim of this study is two-fold: (1) to compare the multivariable results produced by different survival analysis methods; and (2) to compare the Cronin-Feuer with the Fine-Gray methods, in estimating the cancer and non-cancer death probability of both Indigenous and non-Indigenous cancer patients and the Indigenous cancer disparities. METHODS: Cancer survival was investigated for 9,595 people (18.5% Indigenous) diagnosed with cancer in the Northern Territory of Australia between 1991 and 2009. The Cox proportional hazard model along with Poisson and Fine-Gray regression were used in the multivariable analysis. The crude probabilities of cancer and non-cancer methods were estimated in two ways: first, using cause of death data with the Fine-Gray method, and second, using life tables with the Cronin-Feuer method. RESULTS: Multivariable regression using the relative survival, cause-specific survival, and competing risk analysis produced similar results. In the presence of competing risks, the Cronin-Feuer method produced similar results to Fine-Gray in the estimation of cancer death probability (higher Indigenous cancer death probabilities for all cancers) and non-cancer death probabilities (higher Indigenous non-cancer death probabilities for all cancers except lung cancer and head and neck cancers). Cronin-Feuer estimated much lower non-cancer death probabilities than Fine-Gray for non-Indigenous patients with head and neck cancers and lung cancers (both smoking-related cancers). CONCLUSION: Despite the limitations of the Cronin-Feuer method, it is a reasonable alternative to the Fine-Gray method for assessing the Indigenous survival differential in the presence of competing risks when valid and reliable subgroup-specific life tables are available and cause of death data are unavailable or unreliable.

Summarizing and communicating on survival data according to the audience: a tutorial on different measures illustrated with population-based cancer registry data.

Survival data analysis results are usually communicated through the overall survival probability. Alternative measures provide additional insights and may help in communicating the results to a wider audience. We describe these alternative measures in two data settings, the overall survival setting and the relative survival setting, the latter corresponding to the particular competing risk setting in which the cause of death is unavailable or unreliable. In the overall survival setting, we describe the overall survival probability, the conditional survival probability and the restricted mean survival time (restricted to a prespecified time window). In the relative survival setting, we describe the net survival probability, the conditional net survival probability, the restricted mean net survival time, the crude probability of death due to each cause and the number of life years lost due to each cause over a prespecified time window. These measures describe survival data either on a probability scale or on a timescale. The clinical or population health purpose of each measure is detailed, and their advantages and drawbacks are discussed. We then illustrate their use analyzing England population-based registry data of men 15-80 years old diagnosed with colon cancer in 2001-2003, aiming to describe the deprivation disparities in survival. We believe that both the provision of a detailed example of the interpretation of each measure and the software implementation will help in generalizing their use.

InterPreT cancer survival: A dynamic web interactive prediction cancer survival tool for health-care professionals and cancer epidemiologists.

BACKGROUND: There are a variety of ways for quantifying cancer survival with each measure having advantages and disadvantages. Distinguishing these measures and how they should be interpreted has led to confusion among scientists, the media, health care professionals and patients. This motivates the development of tools to facilitate communication and interpretation of these statistics. METHODS: "InterPreT Cancer Survival" is a newly developed, publicly available, online interactive cancer survival tool targeted towards health-care professionals and epidemiologists (http://interpret.le.ac.uk). It focuses on the correct interpretation of commonly reported cancer survival measures facilitated through the use of dynamic interactive graphics. Statistics presented are based on parameter estimates obtained from flexible parametric relative survival models using large population-based English registry data containing information on survival across 6 cancer sites; Breast, Colon, Rectum, Stomach, Melanoma and Lung. RESULTS: Through interactivity, the tool improves understanding of various measures and how survival or mortality may vary by age and sex. Routine measures of cancer survival are reported, however, individualised estimates using crude probabilities are advocated, which is more appropriate for patients or health care professionals. The results are presented in various interactive formats facilitating understanding of individual risk and differences between various measures. CONCLUSIONS: "InterPreT Cancer Survival" is presented as an educational tool which engages the user through interactive features to improve the understanding of commonly reported cancer survival statistics. The tool has received positive feedback from a Cancer Research UK patient sounding board and there are further plans to incorporate more disease characteristics, e.g. stage.