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Background: When quantifying the probability of survival in cancer patients using cancer registration data, it is common to estimate marginal relative survival, which under assumptions can be interpreted as marginal net survival. Net survival is a hypothetical construct giving the probability of being alive if it was only possible to die of the cancer under study, enabling comparisons between populations with differential mortality rates due to causes other the cancer under study. Marginal relative survival can be estimated non-parametrically (Pohar Perme estimator) or in a modeling framework. In a modeling framework, even when just interested in marginal relative survival it is necessary to model covariates that affect the expected mortality rates (e.g. age, sex and calendar year). The marginal relative survival function is then obtained through regression standardization. Given that these covariates will generally have non-proportional effects, the model can become complex before other exposure variables are even considered.Methods: We propose a flexible parametric model incorporating restricted cubic splines that directly estimates marginal relative survival and thus removes the need to model covariates that affect the expected mortality rates. In order to do this the likelihood needs to incorporate the marginal expected mortality rates at each event time taking account of informative censoring. In addition time-dependent weights are incorporated into the likelihood. An approximation is proposed through splitting the time scale into intervals, which enables the marginal relative survival model to be fitted using standard software. Additional weights can be incorporated when standardizing to an external reference population.Results: The methods are illustrated using national cancer registry data. In addition, a simulation study is performed to compare different estimators; a non-parametric approach, regression-standardization and the new marginal relative model. The simulations study shows the new approach is unbiased and has good relative precision compared to the non-parametric estimator.Conclusion: The approach enables estimation of standardized marginal relative survival without the need to model covariates that affect expected mortality rates and thus reduces the chance of model misspecification. [ABSTRACT FROM AUTHOR]

Background: Age-standardized net survival provides an important population-based summary of cancer survival that appropriately accounts for differences in other-cause mortality rates and standardizes the population age distribution to allow fair comparisons. Recently, there has been debate over the most appropriate method for estimating this quantity, with the traditional Ederer II approach being shown to have potential bias. Methods: We compare lifetable-based estimates (Ederer II), a new unbiased method based on inverse probability of censoring weights (Pohar Perme) and model-based estimates. We make the comparison in a simulation setting; generating scenarios where we would expect to see a large theoretical bias. Results: Our simulations demonstrate that even in relatively extreme scenarios there is negligible bias in age-standardized net survival when using the age-standardized Ederer II method, modelling with continuous age or using the Pohar Perme method. However, both the Ederer II and modelling approaches have some advantages over the Pohar Perme method in terms of greater precision, particularly for longer-term follow-up (10 and 15 years). Conclusions: Our results show that, when age-standardizing, concern over bias with the traditional methods is unfounded. We have also shown advantages in using the more traditional and modelling methods. [ABSTRACT FROM AUTHOR]

Background: Relative survival is commonly used for studying survival of cancer patients as it captures both the direct and indirect contribution of a cancer diagnosis on mortality by comparing the observed survival of the patients to the expected survival in a comparable cancer-free population. However, existing methods do not allow estimation of the impact of isolated conditions (e.g., excess cardiovascular mortality) on the total excess mortality. For this purpose we extend flexible parametric survival models for relative survival, which use restricted cubic splines for the baseline cumulative excess hazard and for any time-dependent effects. Methods: In the extended model we partition the excess mortality associated with a diagnosis of cancer through estimating a separate baseline excess hazard function for the outcomes under investigation. This is done by incorporating mutually exclusive background mortality rates, stratified by the underlying causes of death reported in the Swedish population, and by introducing cause of death as a time-dependent effect in the extended model. This approach thereby enables modeling of temporal trends in e.g., excess cardiovascular mortality and remaining cancer excess mortality simultaneously. Furthermore, we illustrate how the results from the proposed model can be used to derive crude probabilities of death due to the component parts, i.e., probabilities estimated in the presence of competing causes of death. Results: The method is illustrated with examples where the total excess mortality experienced by patients diagnosed with breast cancer is partitioned into excess cardiovascular mortality and remaining cancer excess mortality. Conclusions: The proposed method can be used to simultaneously study disease patterns and temporal trends for various causes of cancer-consequent deaths. Such information should be of interest for patients and clinicians as one way of improving prognosis after cancer is through adapting treatment strategies and follow-up of patients towards reducing the excess mortality caused by side effects of the treatment. [ABSTRACT FROM AUTHOR]

Purpose: This study introduces a novel method for estimating the variance of life expectancy since diagnosis (LEC) and loss in life expectancy (LLE) for cancer patients within a relative survival framework in situations where life tables based on the entire general population are not accessible. LEC and LLE are useful summary measures of survival in population-based cancer studies, but require information on the mortality in the general population. Our method addresses the challenge of incorporating the uncertainty of expected mortality rates when using a sample from the general population. Methods: To illustrate the approach, we estimated LEC and LLE for patients diagnosed with colon and breast cancer in Sweden. General population mortality rates were based on a random sample drawn from comparators of a matched cohort. Flexible parametric survival models were used to model the mortality among cancer patients and the mortality in the random sample from the general population. Based on the models, LEC and LLE together with their variances were estimated. The results were compared with those obtained using fixed expected mortality rates. Results: By accounting for the uncertainty of expected mortality rates, the proposed method ensures more accurate estimates of variances and, therefore, confidence intervals of LEC and LLE for cancer patients. This is particularly valuable for older patients and some cancer types, where underestimation of the variance can be substantial when the entire general population data are not accessible. Conclusion: The method can be implemented using existing software, making it accessible for use in various cancer studies. The provided example of Stata code further facilitates its adoption. [ABSTRACT FROM AUTHOR]

Background: A relative survival approach is often used in population-based cancer studies, where other cause (or expected) mortality is assumed to be the same as the mortality in the general population, given a specific covariate pattern. The population mortality is assumed to be known (fixed), i.e. measured without uncertainty. This could have implications for the estimated standard errors (SE) of any measures obtained within a relative survival framework, such as relative survival (RS) ratios and the loss in life expectancy (LLE). We evaluated the existing approach to estimate SE of RS and the LLE in comparison to if uncertainty in the population mortality was taken into account.Methods: The uncertainty from the population mortality was incorporated using parametric bootstrap approach. The analysis was performed with different levels of stratification and sizes of the general population used for creating expected mortality rates. Using these expected mortality rates, SEs of 5-year RS and the LLE for colon cancer patients in Sweden were estimated.Results: Ignoring uncertainty in the general population mortality rates had negligible (less than 1%) impact on the SEs of 5-year RS and LLE, when the expected mortality rates were based on the whole general population, i.e. all people living in a country or region. However, the smaller population used for creating the expected mortality rates, the larger impact. For a general population reduced to 0.05% of the original size and stratified by age, sex, year and region, the relative precision for 5-year RS was 41% for males diagnosed at age 85. For the LLE the impact was more substantial with a relative precision of 1286%. The relative precision for marginal estimates of 5-year RS was 3% and 30% and for the LLE 22% and 313% when the general population was reduced to 0.5% and 0.05% of the original size, respectively.Conclusions: When the general population mortality rates are based on the whole population, the uncertainty in the estimates of the expected measures can be ignored. However, when based on a smaller population, this uncertainty should be taken into account, otherwise SEs may be too small, particularly for marginal values, and, therefore, confidence intervals too narrow. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]