Health outcomes after myocardial infarction: A population study of 56 million people in England.

BACKGROUND: The occurrence of a range of health outcomes following myocardial infarction (MI) is unknown. Therefore, this study aimed to determine the long-term risk of major health outcomes following MI and generate sociodemographic stratified risk charts in order to inform care recommendations in the post-MI period and underpin shared decision making. METHODS AND FINDINGS: This nationwide cohort study includes all individuals aged ≥18 years admitted to one of 229 National Health Service (NHS) Trusts in England between 1 January 2008 and 31 January 2017 (final follow-up 27 March 2017). We analysed 11 non-fatal health outcomes (subsequent MI and first hospitalisation for heart failure, atrial fibrillation, cerebrovascular disease, peripheral arterial disease, severe bleeding, renal failure, diabetes mellitus, dementia, depression, and cancer) and all-cause mortality. Of the 55,619,430 population of England, 34,116,257 individuals contributing to 145,912,852 hospitalisations were included (mean age 41.7 years (standard deviation [SD 26.1]); n = 14,747,198 (44.2%) male). There were 433,361 individuals with MI (mean age 67.4 years [SD 14.4)]; n = 283,742 (65.5%) male). Following MI, all-cause mortality was the most frequent event (adjusted cumulative incidence at 9 years 37.8% (95% confidence interval [CI] [37.6,37.9]), followed by heart failure (29.6%; 95% CI [29.4,29.7]), renal failure (27.2%; 95% CI [27.0,27.4]), atrial fibrillation (22.3%; 95% CI [22.2,22.5]), severe bleeding (19.0%; 95% CI [18.8,19.1]), diabetes (17.0%; 95% CI [16.9,17.1]), cancer (13.5%; 95% CI [13.3,13.6]), cerebrovascular disease (12.5%; 95% CI [12.4,12.7]), depression (8.9%; 95% CI [8.7,9.0]), dementia (7.8%; 95% CI [7.7,7.9]), subsequent MI (7.1%; 95% CI [7.0,7.2]), and peripheral arterial disease (6.5%; 95% CI [6.4,6.6]). Compared with a risk-set matched population of 2,001,310 individuals, first hospitalisation of all non-fatal health outcomes were increased after MI, except for dementia (adjusted hazard ratio [aHR] 1.01; 95% CI [0.99,1.02];p = 0.468) and cancer (aHR 0.56; 95% CI [0.56,0.57];p < 0.001). The study includes data from secondary care only-as such diagnoses made outside of secondary care may have been missed leading to the potential underestimation of the total burden of disease following MI. CONCLUSIONS: In this study, up to a third of patients with MI developed heart failure or renal failure, 7% had another MI, and 38% died within 9 years (compared with 35% deaths among matched individuals). The incidence of all health outcomes, except dementia and cancer, was higher than expected during the normal life course without MI following adjustment for age, sex, year, and socioeconomic deprivation. Efforts targeted to prevent or limit the accrual of chronic, multisystem disease states following MI are needed and should be guided by the demographic-specific risk charts derived in this study.

Evaluation of Flexible Parametric Relative Survival Approaches for Enforcing Long-Term Constraints When Extrapolating All-Cause Survival.

OBJECTIVES: Parametric models are used to estimate the lifetime benefit of an intervention beyond the range of trial follow-up. Recent recommendations have suggested more flexible survival approaches and the use of external data when extrapolating. Both of these can be realized by using flexible parametric relative survival modeling. The overall aim of this article is to introduce and contrast various approaches for applying constraints on the long-term disease-related (excess) mortality including cure models and evaluate the consequent implications for extrapolation. METHODS: We describe flexible parametric relative survival modeling approaches. We then introduce various options for constraining the long-term excess mortality and compare the performance of each method in simulated data. These methods include fitting a standard flexible parametric relative survival model, enforcing statistical cure, and forcing the long-term excess mortality to converge to a constant. We simulate various scenarios, including where statistical cure is reasonable and where the long-term excess mortality persists. RESULTS: The compared approaches showed similar survival fits within the follow-up period. However, when extrapolating the all-cause survival beyond trial follow-up, there is variation depending on the assumption made about the long-term excess mortality. Altering the time point from which the excess mortality is constrained enables further flexibility. CONCLUSIONS: The various constraints can lead to applying explicit assumptions when extrapolating, which could lead to more plausible survival extrapolations. The inclusion of general population mortality directly into the model-building process, which is possible for all considered approaches, should be adopted more widely in survival extrapolation in health technology assessment.

Perils of Randomized Controlled Trial Survival Extrapolation Assuming Treatment Effect Waning: Why the Distinction Between Marginal and Conditional Estimates Matters.

OBJECTIVES: A long-term, constant, protective treatment effect is a strong assumption when extrapolating survival beyond clinical trial follow-up; hence, sensitivity to treatment effect waning is commonly assessed for economic evaluations. Forcing a hazard ratio (HR) to 1 does not necessarily estimate loss of individual-level treatment effect accurately because of HR selection bias. A simulation study was designed to explore the behavior of marginal HRs under a waning conditional (individual-level) treatment effect and demonstrate bias in forcing a marginal HR to 1 when the estimand is "survival difference with individual-level waning". METHODS: Data were simulated under 4 parameter combinations (varying prognostic strength of heterogeneity and treatment effect). Time-varying marginal HRs were estimated in scenarios where the true conditional HR attenuated to 1. Restricted mean survival time differences, estimated having constrained the marginal HR to 1, were compared with true values to assess bias induced by marginal constraints. RESULTS: Under loss of conditional treatment effect, the marginal HR took a value >1 because of covariate imbalances. Constraining this value to 1 lead to restricted mean survival time difference bias of up to 0.8 years (57% increase). Inflation of effect size estimates also increased with the magnitude of initial protective treatment effect. CONCLUSIONS: Important differences exist between survival extrapolations assuming marginal versus conditional treatment effect waning. When a marginal HR is constrained to 1 to assess efficacy under individual-level treatment effect waning, the survival benefits associated with the new treatment will be overestimated, and incremental cost-effectiveness ratios will be underestimated.

Have the recent advancements in cancer therapy and survival benefitted patients of all age groups across the Nordic countries? NORDCAN survival analyses 2002-2021.

BACKGROUND: Since the early 2000s, overall and site-specific cancer survival have improved substantially in the Nordic countries. We evaluated whether the improvements have been similar across countries, major cancer types, and age groups. MATERIAL AND METHODS: Using population-based data from the five Nordic cancer registries recorded in the NORDCAN database, we included a cohort of 1,525,854 men and 1,378,470 women diagnosed with cancer (except non-melanoma skin cancer) during 2002-2021, and followed for death until 2021. We estimated 5-year relative survival (RS) in 5-year calendar periods, and percentage points (pp) differences in 5-year RS from 2002-2006 until 2017-2021. Separate analyses were performed for eight cancer sites (i.e. colorectum, pancreas, lung, breast, cervix uteri, kidney, prostate, and melanoma of skin). RESULTS: Five-year RS improved across nearly all cancer sites in all countries (except Iceland), with absolute differences across age groups ranging from 1 to 21 pp (all cancer sites), 2 to 20 pp (colorectum), -1 to 36 pp (pancreas), 2 to 28 pp (lung), 0 to 9 pp (breast), -11 to 26 pp (cervix uteri), 2 to 44 pp (kidney), -2 to 23 pp (prostate) and -3 to 30 pp (skin melanoma). The oldest patients (80-89 years) exhibited lower survival across all countries and sites, although with varying improvements over time. INTERPRETATION: Nordic cancer patients have generally experienced substantial improvements in cancer survival during the last two decades, including major cancer sites and age groups. Although survival has improved over time, older patients remain at a lower cancer survival compared to younger patients.

Improving communication of cancer survival statistics-feasibility of implementing model-based algorithms in routine publications.

BACKGROUND: Routine reporting of cancer patient survival is important, both to monitor the effectiveness of health care and to inform about prognosis following a cancer diagnosis. A range of different survival measures exist, each serving different purposes and targeting different audiences. It is important that routine publications expand on current practice and provide estimates on a wider range of survival measures. We examine the feasibility of automated production of such statistics. METHODS: We used data on 23 cancer sites obtained from the Cancer Registry of Norway (CRN). We propose an automated way of estimating flexible parametric relative survival models and calculating estimates of net survival, crude probabilities, and loss in life expectancy across many cancer sites and subgroups of patients. RESULTS: For 21 of 23 cancer sites, we were able to estimate survival models without assuming proportional hazards. Reliable estimates of all desired measures were obtained for all cancer sites. DISCUSSION: It may be challenging to implement new survival measures in routine publications as it can require the application of modeling techniques. We propose a way of automating the production of such statistics and show that we can obtain reliable estimates across a range of measures and subgroups of patients.

Using temporal recalibration to improve the calibration of risk prediction models in competing risk settings when there are trends in survival over time.

We have previously proposed temporal recalibration to account for trends in survival over time to improve the calibration of predictions from prognostic models for new patients. This involves first estimating the predictor effects using data from all individuals (full dataset) and then re-estimating the baseline using a subset of the most recent data whilst constraining the predictor effects to remain the same. In this article, we demonstrate how temporal recalibration can be applied in competing risk settings by recalibrating each cause-specific (or subdistribution) hazard model separately. We illustrate this using an example of colon cancer survival with data from the Surveillance Epidemiology and End Results (SEER) program. Data from patients diagnosed in 1995-2004 were used to fit two models for deaths due to colon cancer and other causes respectively. We discuss considerations that need to be made in order to apply temporal recalibration such as the choice of data used in the recalibration step. We also demonstrate how to assess the calibration of these models in new data for patients diagnosed subsequently in 2005. Comparison was made to a standard analysis (when improvements over time are not taken into account) and a period analysis which is similar to temporal recalibration but differs in the data used to estimate the predictor effects. The 10-year calibration plots demonstrated that using the standard approach over-estimated the risk of death due to colon cancer and the total risk of death and that calibration was improved using temporal recalibration or period analysis.

Including uncertainty of the expected mortality rates in the prediction of loss in life expectancy.

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.

Exploring different research questions via complex multi-state models when using registry-based repeated prescriptions of antidepressants in women with breast cancer and a matched population comparison group.

BACKGROUND: Multi-state models are used to study several clinically meaningful research questions. Depending on the research question of interest and the information contained in the data, different multi-state structures and modelling choices can be applied. We aim to explore different research questions using a series of multi-state models of increasing complexity when studying repeated prescriptions data, while also evaluating different modelling choices. METHODS: We develop a series of research questions regarding the probability of being under antidepressant medication across time using multi-state models, among Swedish women diagnosed with breast cancer (n = 18,313) and an age-matched population comparison group of cancer-free women (n = 92,454) using a register-based database (Breast Cancer Data Base Sweden 2.0). Research questions were formulated ranging from simple to more composite ones. Depending on the research question, multi-state models were built with structures ranging from simpler ones, like single-event survival analysis and competing risks, up to complex bidirectional and recurrent multi-state structures that take into account the recurring start and stop of medication. We also investigate modelling choices, such as choosing a time-scale for the transition rates and borrowing information across transitions. RESULTS: Each structure has its own utility and answers a specific research question. However, the more complex structures (bidirectional, recurrent) enable accounting for the intermittent nature of prescribed medication data. These structures deliver estimates of the probability of being under medication and total time spent under medication over the follow-up period. Sensitivity analyses over different definitions of the medication cycle and different choices of timescale when modelling the transition intensity rates show that the estimates of total probabilities of being in a medication cycle over follow-up derived from the complex structures are quite stable. CONCLUSIONS: Each research question requires the definition of an appropriate multi-state structure, with more composite ones requiring such an increase in the complexity of the multi-state structure. When a research question is related with an outcome of interest that repeatedly changes over time, such as the medication status based on prescribed medication, the use of novel multi-state models of adequate complexity coupled with sensible modelling choices can successfully address composite, more realistic research questions.

Flexible parametric methods for calculating life expectancy in small populations.

BACKGROUND: Life expectancy is a simple measure of assessing health differences between two or more populations but current life expectancy calculations are not reliable for small populations. A potential solution to this is to borrow strength from larger populations from the same source, but this has not formally been investigated. METHODS: Using data on 451,222 individuals from the Clinical Practice Research Datalink on the presence/absence of intellectual disability and type 2 diabetes mellitus, we compared stratified and combined flexible parametric models, and Chiang's methods, for calculating life expectancy. Confidence intervals were calculated using the Delta method, Chiang's adjusted life table approach and bootstrapping. RESULTS: The flexible parametric models allowed calculation of life expectancy by exact age and beyond traditional life expectancy age thresholds. The combined model that fit age interaction effects as a spline term provided less bias and greater statistical precision for small covariate subgroups by borrowing strength from the larger subgroups. However, careful consideration of the distribution of events in the smallest group was needed. CONCLUSIONS: Life expectancy is a simple measure to compare health differences between populations. The use of combined flexible parametric methods to calculate life expectancy in small samples has shown promising results by allowing life expectancy to be modelled by exact age, greater statistical precision, less bias and prediction of different covariate patterns without stratification. We recommend further investigation of their application for both policymakers and researchers.

Standardised survival probabilities: a useful and informative tool for reporting regression models for survival data.

BACKGROUND: When interested in studying the effect of a treatment (or other exposure) on a time-to-event outcome, the most popular approach is to estimate survival probabilities using the Kaplan-Meier estimator. In the presence of confounding, regression models are fitted, and results are often summarised as hazard ratios. However, despite their broad use, hazard ratios are frequently misinterpreted as relative risks instead of relative rates. METHODS: We discuss measures for summarising the analysis from a regression model that overcome some of the limitations associated with hazard ratios. Such measures are the standardised survival probabilities for treated and untreated: survival probabilities if everyone in the population received treatment and if everyone did not. The difference between treatment arms can be calculated to provide a measure for the treatment effect. RESULTS: Using publicly available data on breast cancer, we demonstrated the usefulness of standardised survival probabilities for comparing the experience between treated and untreated after adjusting for confounding. We also showed that additional important research questions can be addressed by standardising among subgroups of the total population. DISCUSSION: Standardised survival probabilities are a useful way to report the treatment effect while adjusting for confounding and have an informative interpretation in terms of risk.

Obtaining long-term stage-specific relative survival estimates in the presence of incomplete historical stage information.

BACKGROUND: Completeness of recording for cancer stage at diagnosis is often historically poor in cancer registries, making it challenging to provide long-term stage-specific survival estimates. Stage-specific survival differences are driven by differences in short-term prognosis, meaning estimated survival metrics using period analysis are unlikely to be sensitive to imputed historical stage data. METHODS: We used data from the Surveillance, Epidemiology, and End Results (SEER) Program for lung, colon and breast cancer. To represent missing data patterns in less complete registry data, we artificially inflated the proportion of missing stage information conditional on stage at diagnosis and calendar year of diagnosis. Period analysis was applied and missing stage at diagnosis information was imputed under four different conditions to emulate extreme imputed stage distributions. RESULTS: We fit a flexible parametric model for each cancer stage on the excess hazard scale and the differences in stage-specific marginal relative survival were assessed. Estimates were also obtained from non-parametric approaches for validation. There was little difference between the 10-year stage-specific marginal relative survival estimates, regardless of the assumed historical stage distribution. CONCLUSIONS: When conducting a period analysis, multiple imputation can be used to obtain stage-specific long-term estimates of relative survival, even when the historical stage information is largely incomplete.

Five ways to improve international comparisons of cancer survival: lessons learned from ICBP SURVMARK-2.

BACKGROUND: Comparisons of population-based cancer survival between countries are important to benchmark the overall effectiveness of cancer management. The International Cancer Benchmarking Partnership (ICBP) Survmark-2 study aims to compare survival in seven high-income countries across eight cancer sites and explore reasons for the observed differences. A critical aspect in ensuring comparability in the reported survival estimates are similarities in practice across cancer registries. While ICBP Survmark-2 has shown these differences are unlikely to explain the observed differences in cancer-specific survival between countries, it is important to keep in mind potential biases linked to registry practice and understand their likely impact. METHODS: Based on experiences gained within ICBP Survmark-2, we have developed a set of recommendations that seek to optimally harmonise cancer registry datasets to improve future benchmarking exercises. RESULTS: Our recommendations stem from considering the impact on cancer survival estimates in five key areas: (1) the completeness of the registry and the availability of registration sources; (2) the inclusion of death certification as a source of identifying cases; (3) the specification of the date of incidence; (4) the approach to handling multiple primary tumours and (5) the quality of linkage of cases to the deaths register. CONCLUSION: These recommendations seek to improve comparability whilst maintaining the opportunity to understand and act upon international variations in outcomes among cancer patients.

Minimum sample size calculations for external validation of a clinical prediction model with a time-to-event outcome.

Previous articles in Statistics in Medicine describe how to calculate the sample size required for external validation of prediction models with continuous and binary outcomes. The minimum sample size criteria aim to ensure precise estimation of key measures of a model's predictive performance, including measures of calibration, discrimination, and net benefit. Here, we extend the sample size guidance to prediction models with a time-to-event (survival) outcome, to cover external validation in datasets containing censoring. A simulation-based framework is proposed, which calculates the sample size required to target a particular confidence interval width for the calibration slope measuring the agreement between predicted risks (from the model) and observed risks (derived using pseudo-observations to account for censoring) on the log cumulative hazard scale. Precise estimation of calibration curves, discrimination, and net-benefit can also be checked in this framework. The process requires assumptions about the validation population in terms of the (i) distribution of the model's linear predictor and (ii) event and censoring distributions. Existing information can inform this; in particular, the linear predictor distribution can be approximated using the C-index or Royston's D statistic from the model development article, together with the overall event risk. We demonstrate how the approach can be used to calculate the sample size required to validate a prediction model for recurrent venous thromboembolism. Ideally the sample size should ensure precise calibration across the entire range of predicted risks, but must at least ensure adequate precision in regions important for clinical decision-making. Stata and R code are provided.

Generating high-fidelity synthetic time-to-event datasets to improve data transparency and accessibility.

BACKGROUND: A lack of available data and statistical code being published alongside journal articles provides a significant barrier to open scientific discourse, and reproducibility of research. Information governance restrictions inhibit the active dissemination of individual level data to accompany published manuscripts. Realistic, high-fidelity time-to-event synthetic data can aid in the acceleration of methodological developments in survival analysis and beyond by enabling researchers to access and test published methods using data similar to that which they were developed on. METHODS: We present methods to accurately emulate the covariate patterns and survival times found in real-world datasets using synthetic data techniques, without compromising patient privacy. We model the joint covariate distribution of the original data using covariate specific sequential conditional regression models, then fit a complex flexible parametric survival model from which to generate survival times conditional on individual covariate patterns. We recreate the administrative censoring mechanism using the last observed follow-up date information from the initial dataset. Metrics for evaluating the accuracy of the synthetic data, and the non-identifiability of individuals from the original dataset, are presented. RESULTS: We successfully create a synthetic version of an example colon cancer dataset consisting of 9064 patients which aims to show good similarity to both covariate distributions and survival times from the original data, without containing any exact information from the original data, therefore allowing them to be published openly alongside research. CONCLUSIONS: We evaluate the effectiveness of the methods for constructing synthetic data, as well as providing evidence that there is minimal risk that a given patient from the original data could be identified from their individual unique patient information. Synthetic datasets using this methodology could be made available alongside published research without breaching data privacy protocols, and allow for data and code to be made available alongside methodological or applied manuscripts to greatly improve the transparency and accessibility of medical research.

Estimating causal effects in the presence of competing events using regression standardisation with the Stata command standsurv.

BACKGROUND: When interested in a time-to-event outcome, competing events that prevent the occurrence of the event of interest may be present. In the presence of competing events, various estimands have been suggested for defining the causal effect of treatment on the event of interest. Depending on the estimand, the competing events are either accommodated or eliminated, resulting in causal effects with different interpretations. The former approach captures the total effect of treatment on the event of interest while the latter approach captures the direct effect of treatment on the event of interest that is not mediated by the competing event. Separable effects have also been defined for settings where the treatment can be partitioned into two components that affect the event of interest and the competing event through different causal pathways. METHODS: We outline various causal effects that may be of interest in the presence of competing events, including total, direct and separable effects, and describe how to obtain estimates using regression standardisation with the Stata command standsurv. Regression standardisation is applied by obtaining the average of individual estimates across all individuals in a study population after fitting a survival model. RESULTS: With standsurv several contrasts of interest can be calculated including differences, ratios and other user-defined functions. Confidence intervals can also be obtained using the delta method. Throughout we use an example analysing a publicly available dataset on prostate cancer to allow the reader to replicate the analysis and further explore the different effects of interest. CONCLUSIONS: Several causal effects can be defined in the presence of competing events and, under assumptions, estimates of those can be obtained using regression standardisation with the Stata command standsurv. The choice of which causal effect to define should be given careful consideration based on the research question and the audience to which the findings will be communicated.

Assessing the impact of including variation in general population mortality on standard errors of relative survival and loss in life expectancy.

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.

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.

Modelling multiple time-scales with flexible parametric survival models.

BACKGROUND: There are situations when we need to model multiple time-scales in survival analysis. A usual approach in this setting would involve fitting Cox or Poisson models to a time-split dataset. However, this leads to large datasets and can be computationally intensive when model fitting, especially if interest lies in displaying how the estimated hazard rate or survival change along multiple time-scales continuously. METHODS: We propose to use flexible parametric survival models on the log hazard scale as an alternative method when modelling data with multiple time-scales. By choosing one of the time-scales as reference, and rewriting other time-scales as a function of this reference time-scale, users can avoid time-splitting of the data. RESULT: Through case-studies we demonstrate the usefulness of this method and provide examples of graphical representations of estimated hazard rates and survival proportions. The model gives nearly identical results to using a Poisson model, without requiring time-splitting. CONCLUSION: Flexible parametric survival models are a powerful tool for modelling multiple time-scales. This method does not require splitting the data into small time-intervals, and therefore saves time, helps avoid technological limitations and reduces room for error.

Age-specific survival trends and life-years lost in women with breast cancer 1990-2016: the NORDCAN survival studies.

BACKGROUND: A recent overview of cancer survival trends 1990-2016 in the Nordic countries reported continued improvements in age-standardized breast cancer survival among women. The aim was to estimate age-specific survival trends over calendar time, including life-years lost, to evaluate if improvements have benefited patients across all ages in the Nordic countries. METHODS: Data on breast cancers diagnosed 1990-2016 in Denmark, Finland, Iceland, Norway, and Sweden were obtained from the NORDCAN database. Age-standardized and age-specific relative survival (RS) was estimated using flexible parametric models, as was reference-adjusted crude probabilities of death and life-years lost. RESULTS: Age-standardized period estimates of 5-year RS in women diagnosed with breast cancer ranged from 87% to 90% and 10-year RS from 74% to 85%. Ten-year RS increased with 15-18 percentage points from 1990 to 2016, except in Sweden (+9 percentage points) which had the highest survival in 1990. The largest improvements were observed in Denmark, where a previous survival disadvantage diminished. Most recent 5-year crude probabilities of cancer death ranged from 9% (Finland, Sweden) to 12% (Denmark, Iceland), and life-years lost from 3.3 years (Finland) to 4.6 years (Denmark). Although survival improvements were consistent across different ages, women aged ≥70 years had the lowest RS in all countries. Period estimates of 5-year RS were 94-95% in age 55 years and 84-89% in age 75 years, while 10-year RS were 88-91% in age 55 years and 69-84% in age 75 years. Women aged 40 years lost on average 11.0-13.8 years, while women lost 3.8-6.0 years if aged 55 and 1.9-3.5 years if aged 75 years. CONCLUSIONS: Survival for Nordic women with breast cancer improved from 1990 to 2016 in all age groups, albeit with larger country variation among older women where survival was also lower. Women over 70 years of age have not had the same survival improvement as women of younger age.

On the choice of timescale for other cause mortality in a competing risk setting using flexible parametric survival models.

In competing risks settings where the events are death due to cancer and death due to other causes, it is common practice to use time since diagnosis as the timescale for all competing events. However, attained age has been proposed as a more natural choice of timescale for modeling other cause mortality. We examine the choice of using time since diagnosis versus attained age as the timescale when modeling other cause mortality, assuming that the hazard rate is a function of attained age, and how this choice can influence the cumulative incidence functions ( C I F $CIF$ s) derived using flexible parametric survival models. An initial analysis on the colon cancer data from the population-based Swedish Cancer Register indicates such an influence. A simulation study is conducted in order to assess the impact of the choice of timescale for other cause mortality on the bias of the estimated C I F s $CIFs$ and how different factors may influence the bias. We also use regression standardization methods in order to obtain marginal C I F $CIF$ estimates. Using time since diagnosis as the timescale for all competing events leads to a low degree of bias in C I F $CIF$ for cancer mortality ( C I F 1 $CIF_{1}$ ) under all approaches. It also leads to a low degree of bias in C I F $CIF$ for other cause mortality ( C I F 2 $CIF_{2}$ ), provided that the effect of age at diagnosis is included in the model with sufficient flexibility, with higher bias under scenarios where a covariate has a time-varying effect on the hazard rate for other cause mortality on the attained age scale.