Flexible parametric modelling of cause-specific hazards to estimate cumulative incidence functions.

Background: Competing risks are a common occurrence in survival analysis. They arise when a patient is at risk of more than one mutually exclusive event, such as death from different causes, and the occurrence of one of these may prevent any other event from ever happening. Methods: There are two main approaches to modelling competing risks: the first is to model the cause-specific hazards and transform these to the cumulative incidence function; the second is to model directly on a transformation of the cumulative incidence function. We focus on the first approach in this paper. This paper advocates the use of the flexible parametric survival model in this competing risk framework. Results: An illustrative example on the survival of breast cancer patients has shown that the flexible parametric proportional hazards model has almost perfect agreement with the Cox proportional hazards model. However, the large epidemiological data set used here shows clear evidence of non-proportional hazards. The flexible parametric model is able to adequately account for these through the incorporation of time-dependent effects. Conclusion: A key advantage of using this approach is that smooth estimates of both the cause-specific hazard rates and the cumulative incidence functions can be obtained. It is also relatively easy to incorporate time-dependent effects which are commonly seen in epidemiological studies

Strcs: A command for fitting flexible parametric survival models on the log-hazard scale

In this article, we describe strcs, a user-written command for fitting flexible parametric survival models on the log-hazard scale. strcs is an extension of the user-written stgenreg command (Crowther and Lambert, 2013b, Journal of Statistical Software 53(12): 1-17), which fits general parametric models with user-defined hazard functions using numerical integration. strcs implements a two-step method that incorporates both analytical and numerical integration to estimate the cumulative hazard function required for the log-likelihood function. This method improves the accuracy of the fully numeric estimation implemented in stgenreg. Time-dependent effects can be incorporated, and excess mortality models can be fit by using the available options. We also describe some of the extensive postestimation commands that are easily implemented after fitting an strcs model

A flexible parametric competing-risks model using a direct likelihood approach for the cause-specific cumulative incidence function

In competing-risks analysis, the cause-specific cumulative incidence function (CIF) is usually obtained in a modeling framework by either 1) transforming on all cause-specific hazards or 2) transforming by using a direct relationship with the subdistribution hazard function. We expand on current competing-risks methodology from within the flexible parametric survival modeling framework and focus on the second approach. This approach models all cause-specific CIFs simultaneously and is more useful for answering prognostic-related questions. We propose the direct flexible parametric survival modeling approach for the cause-specific CIF. This approach models the (log cumulative) baseline hazard without requiring numerical integration, which leads to benefits in computational time. It is also easy to make out-of-sample predictions to estimate more useful measures and incorporate alternative link functions, for example, logit links. To implement these methods, we introduce a new estimation command, stpm2cr, and demonstrate useful predictions from the model through an illustrative melanoma dataset

Illustration of different modelling assumptions for estimation of loss in expectation of life due to cancer.

BACKGROUND: The life expectancy of cancer patients, and the loss in expectation of life as compared to the life expectancy without cancer, is a useful measure of cancer patient survival and complement the more commonly reported 5-year survival. The estimation of life expectancy and loss in expectation of life generally requires extrapolation of the survival function, since the follow-up is not long enough for the survival function to reach 0. We have previously shown that the survival of the cancer patients can be extrapolated by breaking down the all-cause survival into two component parts, the expected survival and the relative survival, and make assumptions for extrapolation of these functions independently. When extrapolating survival from a model including covariates such as calendar year, age at diagnosis and deprivation status, care has to be taken regarding the assumptions underlying the extrapolation. There are often different alternative ways for modelling covariate effects or for assumptions regarding the extrapolation. METHODS: In this paper we describe and discuss different alternative approaches for extrapolation of survival when estimating life expectancy and loss in expectation of life for cancer patients. Flexible parametric models within a relative survival setting are used, and examples are presented using data on colon cancer in England. RESULTS: Generally, the different modelling assumptions and approaches give small differences in the estimates of loss in expectation of life, however, the results can differ for younger ages and for conditional estimates. CONCLUSION: Sensitivity analyses should be performed to evaluate the effect of the assumptions made when modelling and extrapolating survival to estimate the loss in expectation of life

Adjusting for measurement error in baseline prognostic biomarkers included in a time-to-event analysis: a joint modelling approach.

Background: Methodological development of joint models of longitudinal and survival data has been rapid in recent years; however, their full potential in applied settings are yet to be fully explored. We describe a novel use of a specific association structure, linking the two component models through the subject specific intercept, and thus extend joint models to account for measurement error in a biomarker, even when only the baseline value of the biomarker is of interest. This is a common occurrence in registry data sources, where often repeated measurements exist but are simply ignored. Methods: The proposed specification is evaluated through simulation and applied to data from the General Practice Research Database, investigating the association between baseline Systolic Blood Pressure (SBP) and the time-to-stroke in a cohort of obese patients with type 2 diabetes mellitus. Results: By directly modelling the longitudinal component we reduce bias in the hazard ratio for the effect of baseline SBP on the time-to-stroke, showing the large potential to improve on previous prognostic models which use only observed baseline biomarker values. Conclusions: The joint modelling of longitudinal and survival data is a valid approach to account for measurement error in the analysis of a repeatedly measured biomarker and a time-to-event. User friendly Stata software is provided

Relative Survival – What Can Cardiovascular Disease Learn from Cancer?

Aims: To illustrate the application of relative survival to observational studies in coronary heart disease and potential advantages compared to all-cause survival methods. Survival after myocardial infarction is generally assessed using all-cause or cause-specific methods. Neither method is able to assess the impact of the disease or condition of interest in comparison to expected survival in a similar population. Relative survival, the ratio of the observed and the expected survival rates, is applied routinely in cancer studies and may improve on current methods for assessment of survival in coronary heart disease. Methods and results: Using a cohort of subjects after a first recorded acute myocardial infarction, we discuss the application of relative survival in coronary heart disease and illustrate a number of the key issues. We compare the findings from relative survival with those obtained using Cox proportional and non-proportional hazards models in standard all-cause survival. Estimated survival rates are higher using relative survival models compared to all-cause methods. Conclusion: Estimates obtained from all-cause mortality fail to disentangle mortality associated with the condition of interest from that due to all other causes. Relative survival gives an estimate of survival due to the disease of interest without the need for cause of death information

Flexible parametric models for relative survival, with application in coronary heart disease

Relative survival is frequently used in population-based studies as a method for estimating disease-related mortality without the need for information on cause of death. We propose an extension to relative survival of a flexible parametric model proposed by Royston and Parmar for censored survival data. The model provides smooth estimates of the relative survival and excess mortality rates by using restricted cubic splines on the log cumulative excess hazard scale. The approach has several advantages over some of the more standard relative survival models, which adopt a piecewise approach, the main being the ability to model time on a continuous scale, the survival and hazard functions are obtained analytically and it does not use split-time data

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

Loss in life expectancy and gain in life years as measures of cancer impact.

There are a broad range of survival-based metrics that are available to report from cancer survival studies, with varying advantages and disadvantages. A combination of metrics should be considered to improve comprehensibility and give a fuller understanding of the impact of cancer. In this article, we discuss the utility of loss in life expectancy and gain in life years as measures of cancer impact, and to quantify differences across population groups. These measures are simple to interpret, have a real-world meaning, and evaluate impact over a life-time horizon. We illustrate the use of the loss in life expectancy measures through a range of examples using data on women diagnosed with cancer in England. We use four different examples across a number of tumour types to illustrate different uses of the metrics, and highlight how they can be interpreted and used in practice in population-based oncology studies. Extensions of the measures conditional on survival to specific times after diagnosis can be used to give updated prognosis for cancer patients. Furthermore, we show how the measures can be used to understand the impact of population differences seen across patient groups. We believe that these under-used, and relatively easy to calculate, measures of overall impact can supplement reporting of cancer survival metrics and improve the comprehensibility compared to the metrics typically reported

Life Expectancy of Patients With Chronic Myeloid Leukemia Approaches the Life Expectancy of the General Population.

PURPOSE: A dramatic improvement in the survival of patients with chronic myeloid leukemia (CML) occurred after the introduction of imatinib mesylate, the first tyrosine kinase inhibitor (TKI). We assessed how these changes affected the life expectancy of patients with CML and life-years lost as a result of CML between 1973 and 2013 in Sweden. MATERIALS AND METHODS: Patients recorded as having CML in the Swedish Cancer Registry from 1973 to 2013 were included in the study and followed until death, censorship, or end of follow-up. The life expectancy and loss in expectation of life were predicted from a flexible parametric relative survival model. RESULTS: A total of 2,662 patients with CML were diagnosed between 1973 and 2013. Vast improvements in the life expectancy of these patients were seen over the study period; larger improvements were seen in the youngest ages. The great improvements in life expectancy translated into great reductions in the loss in expectation of life. Patients of all ages diagnosed in 2013 will, on average, lose < 3 life-years as a result of CML. CONCLUSION: Imatinib mesylate and new TKIs along with allogeneic stem cell transplantation and other factors have contributed to the life expectancy in patients with CML approaching that of the general population today. This will be an important message to convey to patients to understand the impact of a CML diagnosis on their life. In addition, the increasing prevalence of patients with CML will have a great effect on future health care costs as long as continuous TKI treatment is required