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In this article, we describe methodology that allows for multiple timescales using flexible parametric survival models without the need for time splitting. When one fits flexible parametric survival models on the log-hazard scale, numerical integration is required in the log likelihood to fit the model. The use of numerical integration allows incorporation of arbitrary functions of time into the model and hence lends itself to the inclusion of multiple timescales in an appealing way. We describe and exemplify these methods and show how to use the command stmt , which implements these methods, alongside its postestimation commands.

Background: Survival of patients with colon and rectal cancer has improved in all Nordic countries during the past decades. The aim of this study was to further assess survival trends in patients with colon and rectal cancer in the Nordic countries by age at diagnosis and to present additional survival measures. Methods: Data on colon and rectal cancer cases diagnosed in the Nordic countries between 1990 and 2016 were obtained from the NORDCAN database. Relative survival was estimated using flexible parametric models. Both age-standardized and age-specific measures for women and men were estimated from the models, as well as reference-adjusted crude probabilities of death and life-years lost. Results: The five-year age-standardized relative survival of colon and rectal cancer patients continued to improve for women and men in all Nordic countries, from around 50% in 1990 to about 70% at the end of the study period. In general, survival was similar across age and sex. The largest improvement was seen for Danish men and women with rectal cancer, from 41% to 69% and from 43% to 71%, respectively. The age-standardized and reference-adjusted five-year crude probability of death in colon cancer ranged from 30% to 36% across countries, and for rectal cancer from 20% to 33%. The average number of age-standardized and reference-adjusted life-years lost ranged between six and nine years. Conclusion: There were substantial improvements in colon and rectal cancer survival in all Nordic countries 1990-2016. Of special note is that the previously observed survival disadvantage in Denmark is no longer present. (C) 2022 The Author(s). Published by Elsevier Ltd.

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.

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.

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.

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.

A commonly reported measure when interested in the survival of cancer patients is relative survival. Relative survival circumvents issues with inaccurate cause of death information by incorporating the expected mortality rates of cancer individuals from population lifetables of the general population. A summary of the cancer population prognosis can be obtained using the marginal relative survival. To explore differences between exposure groups, such as socioeconomic groups, the difference in marginal relative survival between exposed and unexposed can be obtained and under assumptions is interpreted as the average causal effect of exposure to survival. In a modeling context, this is usually estimated by applying regression standardization as the average of the individual-specific estimates after fitting a relative survival model. Regression standardization yields an estimator that consistently estimates the causal effect under standard causal inference assumptions and if the relative survival model is correctly specified. We extend inverse probability weighting (IPW) and doubly robust standardization methods in the relative survival framework as additional valuable tools for obtaining average causal effects when correct model specification might not hold for the relative survival model. IPW yields an unbiased estimate of the average causal effect if a correctly specified model has been fitted for the exposure (propensity score) whereas doubly robust standardization requires that at least one of the propensity score model or the relative survival model is correctly specified. An example using data on melanoma is provided and a simulation study is conducted to investigate how sensitive are the methods to model misspecification, including different ways for obtaining standard errors.

Background: A breast cancer diagnosis is related with psychological distress and possibly with an increased use of antidepressants. Multi-state models can be used to study a number of clinically meaningful research questions related to patterns of medication use such as the total probability of being or total length of stay in an antidepressant medication or discontinuation period over time. Methods: Different multi-state structures may correspond to different research questions and vary from simple ones, such as a single-event survival analysis setting, up to bidirectional and recurrent multi-state structures, with each structure having its own traits, advantages, interpretations, and limitations. There are also a number of factors to consider when applying a multi-state model such as choosing a time-scale for the transition rates, borrowing information across transitions and relaxing the proportional hazards assumption. We explore the use of different multi-state structures when studying antidepressant medication use patterns among women diagnosed with invasive breast cancer (n=18313) and age-matched cancer-free women (n=92454) from the Swedish population, using the information in Breast Cancer Data Base Sweden 2.0 (BCBaSe 2.0). Results: While each structure has its own utility, the more complex structures -bidirectional and recurrent– are able to take into account the intermittent nature of the prescribed medication data and deliver estimates about the total probability and total length of stay of an individual in an antidepressant medication status or discontinuation periods during their follow-up. Sensitivity analyses over different definitions of the medication cycle and different approaches when modelling the transition intensity rates (Markov, semi-Markov or mix of the two) show that the estimates of the complex structures are quite stable. However, even these structures present limitations that should be taken into account during the implementation of the models. Conclusions: In this study we provide insight into the use, interpretation and limitations of different multi-state structures when applied to prescribed medication data. The conclusions drawn provide a better understanding of the application of multi-state models in epidemiology.

Aims To assess the recording and accuracy of acute myocardial infarction (AMI) hospital admissions between two electronic health record databases within an English cancer population over time and understand the factors that affect case-ascertainment. Methods and results We identified 112 502 hospital admissions for AMI in England 2010–2017 from the Myocardial Ischaemia National Audit Project (MINAP) disease registry and hospital episode statistics (HES) for 95 509 patients with a previous cancer diagnosis up to 15 years prior to admission. Cancer diagnoses were identified from the National Cancer Registration Dataset (NCRD). We calculated the percentage of AMI admissions captured by each source and examined patient characteristics associated with source of ascertainment. Survival analysis assessed whether differences in survival between case-ascertainment sources could be explained by patient characteristics. A total of 57 265 (50.9%) AMI admissions in patients with a prior diagnosis of cancer were captured in both MINAP and HES. Patients captured in both sources were younger, more likely to have ST-segment elevation myocardial infarction and had better prognosis, with lower mortality rates up to 9 years after AMI admission compared with patients captured in only one source. The percentage of admissions captured in both data sources improved over time. Cancer characteristics (site, stage, and grade) had little effect on how AMI was captured. Conclusion MINAP and HES define different populations of patients with AMI. However, cancer characteristics do not substantially impact on case-ascertainment. These findings support a strategy of using multiple linked data sources for observational cardio-oncological research into AMI.

Individual participant data (IPD) from multiple sources allows external validation of a prognostic model across multiple populations. Often this reveals poor calibration, potentially causing poor predictive performance in some populations. However, rather than discarding the model outright, it may be possible to modify the model to improve performance using recalibration techniques. We use IPD meta-analysis to identify the simplest method to achieve good model performance. We examine four options for recalibrating an existing time-to-event model across multiple populations: (i) shifting the baseline hazard by a constant, (ii) re-estimating the shape of the baseline hazard, (iii) adjusting the prognostic index as a whole, and (iv) adjusting individual predictor effects. For each strategy, IPD meta-analysis examines (heterogeneity in) model performance across populations. Additionally, the probability of achieving good performance in a new population can be calculated allowing ranking of recalibration methods. In an applied example, IPD meta-analysis reveals that the existing model had poor calibration in some populations, and large heterogeneity across populations. However, re-estimation of the intercept substantially improved the expected calibration in new populations, and reduced between-population heterogeneity. Comparing recalibration strategies showed that re-estimating both the magnitude and shape of the baseline hazard gave the highest predicted probability of good performance in a new population. In conclusion, IPD meta-analysis allows a prognostic model to be externally validated in multiple settings, and enables recalibration strategies to be compared and ranked to decide on the least aggressive recalibration strategy to achieve acceptable external model performance without discarding existing model information.

As cancer patient survival improves, late effects from treatment are becoming the next clinical challenge. Chemotherapy and radiotherapy, for example, potentially increase the risk of both morbidity and mortality from second malignancies and cardiovascular disease. To provide clinically relevant population-level measures of late effects, it is of importance to (1) simultaneously estimate the risks of both morbidity and mortality, (2) partition these risks into the component expected in the absence of cancer and the component due to the cancer and its treatment, and (3) incorporate the multiple time scales of attained age, calendar time, and time since diagnosis. Multistate models provide a framework for simultaneously studying morbidity and mortality, but do not solve the problem of partitioning the risks. However, this partitioning can be achieved by applying a relative survival framework, allowing us to directly quantify the excess risk. This article proposes a combination of these two frameworks, providing one approach to address (1) to (3). Using recently developed methods in multistate modeling, we incorporate estimation of excess hazards into a multistate model. Both intermediate and absorbing state risks can be partitioned and different transitions are allowed to have different and/or multiple time scales. We illustrate our approach using data on Hodgkin lymphoma patients and excess risk of diseases of the circulatory system, and provide user-friendly Stata software with accompanying example code.

Background Multi-state models are being increasingly used to capture complex disease pathways. The convenient formula of the exponential multi-state model can facilitate a quick and accessible understanding of the data. However, assuming time constant transition rates is not always plausible. On the other hand, obtaining predictions from a fitted model with time-dependent transitions can be challenging. One proposed solution is to utilise a general simulation algorithm to calculate predictions from a fitted multi-state model. Methods Predictions obtained from an exponential multi-state model were compared to those obtained from two different parametric models and to non-parametric Aalen-Johansen estimates. The first comparative approach fitted a multi-state model with transition-specific distributions, chosen separately based on the Akaike Information Criterion. The second approach was a Royston-Parmar multi-state model with 4 degrees of freedom, which was chosen as a reference model flexible enough to capture complex hazard shapes. All quantities were obtained analytically for the exponential and Aalen-Johansen approaches. The transition rates for the two comparative approaches were also obtained analytically, while all other quantities were obtained from the fitted models via a general simulation algorithm. Metrics investigated were: transition probabilities, attributable mortality (AM), population attributable fraction (PAF) and expected length of stay. This work was performed on previously analysed hospital acquired infection (HAI) data. By definition, a HAI takes three days to develop and therefore selected metrics were also predicted from time 3 (delayed entry). Results Despite clear deviations from the constant transition rates assumption, the empirical estimates of the transition probabilities were approximated reasonably well by the exponential model. However, functions of the transition probabilities, e.g. AM and PAF, were not well approximated and the comparative models offered considerable improvements for these metrics. They also provided consistent predictions with the empirical estimates in the case of delayed entry time, unlike the exponential model. Conclusion We conclude that methods and software are readily available for obtaining predictions from multi-state models that do not assume constant transition rates. The package in facilitates a range of predictions with confidence intervals, which can provide a more comprehensive understanding of the data. User-friendly code is provided.

Mediation analysis can be applied to investigate the effect of a third variable on the pathway between an exposure and the outcome. Such applications include investigating the determinants that drive differences in cancer survival across subgroups. However, cancer disparities may be the result of complex mechanisms that involve both cancer‐related and other‐cause mortality differences making it difficult to identify the causing factors. Relative survival, a commonly used measure in cancer epidemiology, can be used to focus on cancer‐related differences. We extended mediation analysis to the relative survival framework for exploring cancer inequalities. The marginal effects were obtained using regression standardization, after fitting a relative survival model. Contrasts of interests included both marginal relative survival and marginal all‐cause survival differences between exposure groups. Such contrasts include the indirect effect due to a mediator that is identifiable under certain assumptions. A separate model was fitted for the mediator and uncertainty was estimated using parametric bootstrapping. The avoidable deaths under interventions can also be estimated to quantify the impact of eliminating differences. The methods are illustrated using data for individuals diagnosed with colon cancer. Mediation analysis within relative survival allows focus on factors that account for cancer‐related differences instead of all‐cause differences and helps improve our understanding on cancer inequalities.

Background This paper investigates the difference in survival of melanoma patients across stage and sex by utilising net survival measures. Metrics are presented at both the individual and population level. Methods Flexible parametric models were fitted to estimate life-expectancy metrics to be applied to a group of 104,938 subjects with a melanoma skin cancer diagnosis from 2000 to 2017. Period analysis was used for better predictions for newly diagnosed patients, and missing-stage information was imputed for 9918 patients. Female relative survival was assigned to male subjects to demonstrate the survival discrepancies experienced between sexes. Results At the age of 60, males diagnosed at the regional stage lose an average of 4.99 years of life compared to the general population, and females lose 4.79 years, demonstrating the sex variation in expected mortality. In 2017, males contributed 3545 more life years lost than females, and a potential 1931 life years could be preserved if sex differences in survival were eliminated. Conclusions This study demonstrates the survival differences across population subgroups as a result of a melanoma cancer diagnosis. Females experience better prognosis across age and stage at diagnosis; however, further investigation is necessary to better understand the mechanisms behind this difference.

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 (mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:semanticsmml:mrowmml:miC/mml:mimml:miI/mml:mimml:miF/mml:mi/mml:mrowmml:annotation$CIF$/mml:annotation/mml:semantics/mml:maths) 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 estimatedmml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:semanticsmml:mrowmml:miC/mml:mimml:miI/mml:mimml:miF/mml:mimml:mis/mml:mi/mml:mrowmml:annotation$CIFs$/mml:annotation/mml:semantics/mml:mathand how different factors may influence the bias. We also use regression standardization methods in order to obtain marginalmml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:semanticsmml:mrowmml:miC/mml:mimml:miI/mml:mimml:miF/mml:mi/mml:mrowmml:annotation$CIF$/mml:annotation/mml:semantics/mml:mathestimates. Using time since diagnosis as the timescale for all competing events leads to a low degree of bias inmml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:semanticsmml:mrowmml:miC/mml:mimml:miI/mml:mimml:miF/mml:mi/mml:mrowmml:annotation$CIF$/mml:annotation/mml:semantics/mml:mathfor cancer mortality (mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:semanticsmml:mrowmml:miC/mml:mimml:miI/mml:mimml:msubmml:miF/mml:mimml:mn1/mml:mn/mml:msub/mml:mrowmml:annotation$CIF_{1}$/mml:annotation/mml:semantics/mml:math) under all approaches. It also leads to a low degree of bias inmml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:semanticsmml:mrowmml:miC/mml:mimml:miI/mml:mimml:miF/mml:mi/mml:mrowmml:annotation$CIF$/mml:annotation/mml:semantics/mml:mathfor other cause mortality (mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:semanticsmml:mrowmml:miC/mml:mimml:miI/mml:mimml:msubmml:miF/mml:mimml:mn2/mml:mn/mml:msub/mml:mrowmml:annotation$CIF_{2}$/mml:annotation/mml:semantics/mml:math), 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.

BACKGROUND: The loss in life expectancy, LLE, is defined as the difference in life expectancy between cancer patients and that of the general population. It is a useful measure for summarising the impact of a cancer diagnosis on an individual’s life expectancy. However, it is less useful for making comparisons of cancer survival across groups or over time, since the LLE is influenced by both mortality due to cancer and other causes and the life expectancy in the general population. METHODS: We present an approach for making LLE estimates comparable across groups and over time by using reference expected mortality rates with flexible parametric relative survival models. The approach is illustrated by estimating temporal trends in LLE of colon cancer patients in Sweden. RESULTS: The life expectancy of Swedish colon cancer patients has improved, but the LLE has not decreased to the same extent since the life expectancy in the general population has also increased. When using a fixed population and other-cause mortality, i.e. a reference-adjusted approach, the LLE decreases over time. For example, using 2010 mortality rates as the reference, the LLE for females diagnosed at age 65 decreased from 11.3 if diagnosed in 1976 to 7.2 if diagnosed in 2010, and from 3.9 to 1.9 years for women 85 years old at diagnosis. CONCLUSION: The reference-adjusted LLE is useful for making comparisons across calendar time, or groups, since differences in other cause mortality are removed. IMPACT: The reference-adjusted approach enhances the use of LLE as a comparative measure.

Background The impact of cardiovascular disease (CVD) comorbidity on resection rates and survival for patients with early-stage non-small-cell lung cancer (NSCLC) is unclear. We explored if CVD comorbidity explained surgical resection rate variation and the impact on survival if resection rates increased. Methods Cancer registry data consisted of English patients diagnosed with NSCLC from 2012 to 2016. Linked hospital records identified CVD comorbidities. We investigated resection rate variation by geographical region using funnel plots; resection and death rates using time-to-event analysis. We modelled an increased propensity for resection in regions with the lowest resection rates and estimated survival change. Results Among 57,373 patients with Stage 1−3A NSCLC, resection rates varied considerably between regions. Patients with CVD comorbidity had lower resection rates and higher mortality rates. CVD comorbidity explained only 1.9% of the variation in resection rates. For every 100 CVD comorbid patients, increasing resection in regions with the lowest rates from 24 to 44% would result in 16 more patients resected and alive after 1 year and two fewer deaths overall. Conclusions Variation in regional resection rate is not explained by CVD comorbidities. Increasing resection in patients with CVD comorbidity to the levels of the highest resecting region would increase 1-year survival.

Background Prognostic models are typically developed in studies covering long time periods. However, if more recent years have seen improvements in survival, then using the full dataset may lead to out-of-date survival predictions. Period analysis addresses this by developing the model in a subset of the data from a recent time window, but results in a reduction of sample size. Methods We propose a new approach, called temporal recalibration, to combine the advantages of period analysis and full cohort analysis. This approach develops a model in the entire dataset and then recalibrates the baseline survival using a period analysis sample. The approaches are demonstrated utilizing a prognostic model in colon cancer built using both Cox proportional hazards and flexible parametric survival models with data from 1996–2005 from the Surveillance, Epidemiology, and End Results (SEER) Program database. Comparison of model predictions with observed survival estimates were made for new patients subsequently diagnosed in 2006 and followed-up until 2015. Results Period analysis and temporal recalibration provided more up-to-date survival predictions that more closely matched observed survival in subsequent data than the standard full cohort models. In addition, temporal recalibration provided more precise estimates of predictor effects. Conclusion Prognostic models are typically developed using a full cohort analysis that can result in out-of-date long-term survival estimates when survival has improved in recent years. Temporal recalibration is a simple method to address this, which can be used when developing and updating prognostic models to ensure survival predictions are more closely calibrated with the observed survival of individuals diagnosed subsequently.

Background In population-based cancer survival studies, the event of interest is usually death due to cancer. However, other competing events may be present. Relative survival is a commonly used measure in cancer studies that circumvents problems caused by the inaccuracy of the cause of death information. A summary of the prognosis of the cancer population and potential differences between subgroups can be obtained using marginal estimates of relative survival. Methods We utilize regression standardization to obtain marginal estimates of interest in a relative survival framework. Such measures include the standardized relative survival, standardized all-cause survival and standardized crude probabilities of death. Contrasts of these can be formed to explore differences between exposure groups and under certain assumptions are interpreted as causal effects. The difference in standardized all-cause survival can also provide an estimate for the impact of eliminating cancer-related differences between exposure groups. The potential avoidable deaths after such hypothetical scenarios can also be estimated. To illustrate the methods we use the example of survival differences across socio-economic groups for colon cancer. Results Using relative survival, a range of marginal measures and contrasts were estimated. For these measures we either focused on cancer-related differences only or chose to incorporate both cancer and other cause differences. The impact of eliminating differences between groups was also estimated. Another useful way for quantifying that impact is the avoidable deaths under hypothetical scenarios. Conclusions Marginal estimates within the relative survival framework provide useful summary measures and can be applied to better understand differences across exposure groups.

Background Multi-state models are used in complex disease pathways to describe a process where an individual moves from one state to the next, taking into account competing states during each transition. In a multi-state setting, there are various measures to be estimated that are of great epidemiological importance. However, increased complexity of the multi-state setting and predictions over time for individuals with different covariate patterns may lead to increased difficulty in communicating the estimated measures. The need for easy and meaningful communication of the analysis results motivated the development of a web tool to address these issues. Results MSMplus is a publicly available web tool, developed via the Shiny R package, with the aim of enhancing the understanding of multi-state model analyses results. The results from any multi-state model analysis are uploaded to the application in a pre-specified format. Through a variety of user-tailored interactive graphs, the application contributes to an improvement in communication, reporting and interpretation of multi-state analysis results as well as comparison between different approaches. The predicted measures that can be supported by MSMplus include, among others, the transition probabilities, the transition intensity rates, the length of stay in each state, the probability of ever visiting a state and user defined measures. Representation of differences, ratios and confidence intervals of the aforementioned measures are also supported. MSMplus is a useful tool that enhances communication and understanding of multi-state model analyses results. Conclusions Further use and development of web tools should be encouraged in the future as a means to communicate scientific research.

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.

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.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.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.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.

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.

Accurately recorded vital status of individuals is essential when estimating cancer patient survival. When deaths are ascertained by linkage with vital statistics registers, some may be missed, and such individuals will wrongly appear to be long-term survivors, and survival will be overestimated. Interval-specific relative survival that levels off above one indicates that the survival among the cancer patients is better than expected, which could be due to the presence of immortals.We included colon cancer cases diagnosed in 1995-1999 within the 19 jurisdictions in seven countries participating in ICBP SURVMARK-2, with follow-up information available until end-2015. Interval-specific relative survival was estimated for each year following diagnosis, by country and age group at diagnosis.The interval-specific relative survival levels off at 1 for all countries and age groups, with two exceptions: for the age group diagnosed at age 75 years and above in Ireland, and, to a lesser extent, in New Zealand.Overall, a subset of immortals are not apparent in the early years within the ICBP SURVMARK-2 study, except for possibly in Ireland. We suggest this approach as one strategy of exploring the existence of immortals, and to be part of routine checks of cancer registry data.

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.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.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.These recommendations seek to improve comparability whilst maintaining the opportunity to understand and act upon international variations in outcomes among cancer patients.

In population-based cancer survival studies, the event of interest is usually death due to cancer. However, other competing events may be present. Relative survival is a commonly used measure in cancer studies that circumvents problems caused by the inaccuracy of the cause of death information. A summary of the prognosis of the cancer population and potential differences between subgroups can be obtained using marginal estimates of relative survival.We utilize regression standardization to obtain marginal estimates of interest in a relative survival framework. Such measures include the standardized relative survival, standardized all-cause survival and standardized crude probabilities of death. Contrasts of these can be formed to explore differences between exposure groups and under certain assumptions are interpreted as causal effects. The difference in standardized all-cause survival can also provide an estimate for the impact of eliminating cancer-related differences between exposure groups. The potential avoidable deaths after such hypothetical scenarios can also be estimated. To illustrate the methods we use the example of survival differences across socio-economic groups for colon cancer.Using relative survival, a range of marginal measures and contrasts were estimated. For these measures we either focused on cancer-related differences only or chose to incorporate both cancer and other cause differences. The impact of eliminating differences between groups was also estimated. Another useful way for quantifying that impact is the avoidable deaths under hypothetical scenarios.Marginal estimates within the relative survival framework provide useful summary measures and can be applied to better understand differences across exposure groups.

Background Cancer survival statistics are typically reported by using measures discounting the impact of other-cause mortality, such as net survival. This is a hypothetical measure and is interpreted as excluding the possibility of cancer patients dying from other causes. Crude probability of death partitions the all-cause probability of death into deaths from cancer and other causes. Methods The National Cancer Registration and Analysis Service is the single cancer registry for England. In 2006–2015, 1,590,477 malignant tumours were diagnosed for breast, colorectal, lung, melanoma and prostate cancer in adults. We used a relative survival framework, with a period approach, providing estimates for up to 10-year survival. Mortality was partitioned into deaths due to cancer or other causes. Unconditional and conditional (on surviving 1-years and 5-years) crude probability of death were estimated for the five cancers. Results Elderly patients who survived for a longer period before dying were more likely to die from other causes of death (except for lung cancer). For younger patients, deaths were almost entirely due to the cancer. Conclusion There are different measures of survival, each with their own strengths and limitations. Careful choices of survival measures are needed for specific scenarios to maximise the understanding of the data.

Non-proportional hazards are common within time-to-event data and can be modeled using restricted cubic splines in flexible parametric survival models. This simulation study assesses the ability of...

Many studies have found evidence of socioeconomic differences in breast cancer survival. This study aimed to quantify the impact of removing differences in stage distribution and stage-specific relative survival between education groups in Swedish women with breast cancer. Using information from a breast cancer research database, the study population contained 62 121 women diagnosed with breast cancer in three healthcare regions of Sweden from 1992 to 2012. The loss in expectation of life and life years lost due to breast cancer were estimated using flexible parametric relative survival models by education group and age at diagnosis. The potential gain in life years and postponable deaths were calculated by applying the 1) stage distribution, 2) stage-specific relative survival, and 3) both stage distribution and stage-specific relative survival of the high education group to the low and medium education groups. For a cohort of around 3500 women diagnosed with breast cancer residing in three Swedish healthcare regions in a typical calendar year, we estimated that removing stage differences would postpone an additional 25 deaths at five years after diagnosis, and result in a gain of approximately 573 life years. Alternatively, if stage-specific breast cancer survival could be equated, approximately 692 life years could be saved and an additional 26 deaths could be postponed five years after diagnosis. Results such as these can help guide decisions on interventions intended to minimise socioeconomic differences in breast cancer outcomes.

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 . 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 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 . 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.