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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". 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. 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. 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. • Noncollapsibility of odds/hazard ratios (HRs) has been widely discussed in causal inference literature. Discussion of the impact in randomized controlled trial extrapolations is scarcer. This article explores the importance of understanding the difference between marginal and conditional HRs, specifically in the context of an economic evaluation/health technology assessment using randomized controlled trial data, carrying out an extrapolation assuming treatment effect waning. • If the individual-level treatment effect truly wanes after a period of protective treatment effect, a marginal (eg, unadjusted) HR > 1 from this point is to be expected. This reflects covariate imbalances between arms induced by the treatment's effect and demonstrates the difficulty in interpreting a HR that is dependent on both participant-level hazards and trial-level covariate distributions (and how these shift over time). • Forcing a marginal HR to 1 from the end of trial follow-up is not equivalent to individual-level treatment effect loss (inducing bias in restricted mean survival time difference of up to 0.8 years, increasing with treatment strength and prognostic power of marginal covariates). To most accurately assess sensitivity to treatment effect waning, constraints on the HR should be applied to an estimate that is conditional on all feasible prognostic factors. [ABSTRACT FROM AUTHOR]

There is increasing interest in the use of cure modelling to inform health technology assessment (HTA) due to the development of new treatments that appear to offer the potential for cure in some patients. However, cure models are often not included in evidence dossiers submitted to HTA agencies, and they are relatively rarely relied upon to inform decision-making. This is likely due to a lack of understanding of how cure models work, what they assume, and how reliable they are. In this tutorial we explain why and when cure models may be useful for HTA, describe the key characteristics of mixture and non-mixture cure models, and demonstrate their use in a range of scenarios, providing Stata code. We highlight key issues that must be taken into account by analysts when fitting these models and by reviewers and decision-makers when interpreting their predictions. In particular, we note that flexible parametric non-mixture cure models have not been used in HTA, but they offer advantages that make them well suited to an HTA context when a cure assumption is valid but follow-up is limited. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Background: Royston-Parmar flexible parametric survival models (FPMs) can be fitted on either the cause-specific hazards or cumulative incidence scale in the presence of competing risks. An advantage of modelling within this framework for competing risks data is the ease at which alternative predictions to the (cause-specific or subdistribution) hazard ratio can be obtained. Restricted mean survival time (RMST), or restricted mean failure time (RMFT) on the mortality scale, is one such measure. This has an attractive interpretation, especially when the proportionality assumption is violated. Compared to similar measures, fewer assumptions are required and it does not require extrapolation. Furthermore, one can easily obtain the expected number of life-years lost, or gained, due to a particular cause of death, which is a further useful prognostic measure as introduced by Andersen.Methods: In the presence of competing risks, prediction of RMFT and the expected life-years lost due to a cause of death are presented using Royston-Parmar FPMs. These can be predicted for a specific covariate pattern to facilitate interpretation in observational studies at the individual level, or at the population-level using standardisation to obtain marginal measures. Predictions are illustrated using English colorectal data and are obtained using the Stata post-estimation command, standsurv.Results: Reporting such measures facilitate interpretation of a competing risks analysis, particularly when the proportional hazards assumption is not appropriate. Standardisation provides a useful way to obtain marginal estimates to make absolute comparisons between two covariate groups. Predictions can be made at various time-points and presented visually for each cause of death to better understand the overall impact of different covariate groups.Conclusions: We describe estimation of RMFT, and expected life-years lost partitioned by each competing cause of death after fitting a single FPM on either the log-cumulative subdistribution, or cause-specific hazards scale. These can be used to facilitate interpretation of a competing risks analysis when the proportionality assumption is in doubt. [ABSTRACT FROM AUTHOR]

Background: Data from population-based cancer registries are often used to compare cancer survival between countries or regions. The ICBP SURVMARK-2 study is an international partnership aiming to quantify and explore the reasons behind survival differences across high-income countries. However, the magnitude and relevance of differences in cancer survival between countries have been questioned, as it is argued that observed survival variations may be explained, at least in part, by differences in cancer registration practice, completeness and the availability and quality of the respective data sources.Methods: As part of the ICBP SURVMARK-2 study, we used a simulation approach to better understand how differences in completeness, the characteristics of those missed and inclusion of cases found from death certificates can impact on cancer survival estimates.Results: Bias in 1- and 5-year net survival estimates for 216 simulated scenarios is presented. Out of the investigated factors, the proportion of cases not registered through sources other than death certificates, had the largest impact on survival estimates.Conclusion: Our results show that the differences in registration practice between participating countries could in our most extreme scenarios explain only a part of the largest observed differences in cancer survival. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Background: Population-based cancer survival estimates provide valuable insights into the effectiveness of cancer services and can reflect the prospects of cure. As part of the second phase of the International Cancer Benchmarking Partnership (ICBP), the Cancer Survival in High-Income Countries (SURVMARK-2) project aims to provide a comprehensive overview of cancer survival across seven high-income countries and a comparative assessment of corresponding incidence and mortality trends.Methods: In this longitudinal, population-based study, we collected patient-level data on 3·9 million patients with cancer from population-based cancer registries in 21 jurisdictions in seven countries (Australia, Canada, Denmark, Ireland, New Zealand, Norway, and the UK) for seven sites of cancer (oesophagus, stomach, colon, rectum, pancreas, lung, and ovary) diagnosed between 1995 and 2014, and followed up until Dec 31, 2015. We calculated age-standardised net survival at 1 year and 5 years after diagnosis by site, age group, and period of diagnosis. We mapped changes in incidence and mortality to changes in survival to assess progress in cancer control.Findings: In 19 eligible jurisdictions, 3 764 543 cases of cancer were eligible for inclusion in the study. In the 19 included jurisdictions, over 1995-2014, 1-year and 5-year net survival increased in each country across almost all cancer types, with, for example, 5-year rectal cancer survival increasing more than 13 percentage points in Denmark, Ireland, and the UK. For 2010-14, survival was generally higher in Australia, Canada, and Norway than in New Zealand, Denmark, Ireland, and the UK. Over the study period, larger survival improvements were observed for patients younger than 75 years at diagnosis than those aged 75 years and older, and notably for cancers with a poor prognosis (ie, oesophagus, stomach, pancreas, and lung). Progress in cancer control (ie, increased survival, decreased mortality and incidence) over the study period was evident for stomach, colon, lung (in males), and ovarian cancer.Interpretation: The joint evaluation of trends in incidence, mortality, and survival indicated progress in four of the seven studied cancers. Cancer survival continues to increase across high-income countries; however, international disparities persist. While truly valid comparisons require differences in registration practice, classification, and coding to be minimal, stage of disease at diagnosis, timely access to effective treatment, and the extent of comorbidity are likely the main determinants of patient outcomes. Future studies are needed to assess the impact of these factors to further our understanding of international disparities in cancer survival.Funding: Canadian Partnership Against Cancer; Cancer Council Victoria; Cancer Institute New South Wales; Cancer Research UK; Danish Cancer Society; National Cancer Registry Ireland; The Cancer Society of New Zealand; National Health Service England; Norwegian Cancer Society; Public Health Agency Northern Ireland, on behalf of the Northern Ireland Cancer Registry; The Scottish Government; Western Australia Department of Health; and Wales Cancer Network. [ABSTRACT FROM AUTHOR]

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

Relative survival ratios (RSRs) can be useful for evaluating the impact of changes in cancer care on the prognosis of cancer patients or for comparing the prognosis for different subgroups of patients, but their use is problematic for cancer sites where screening has been introduced due to the potential of lead-time bias. Lead-time is survival time that is added to a patient's survival time because of an earlier diagnosis irrespective of a possibly postponed time of death. In the presence of screening it is difficult to disentangle how much of an observed improvement in survival is real and how much is due to lead-time bias. Even so, RSRs are often presented for breast cancer, a site where screening has led to early diagnosis, with the assumption that the lead-time bias is small. We describe a simulation-based framework for studying the lead-time bias due to mammography screening on RSRs of breast cancer based on a natural history model developed in a Swedish setting. We have performed simulations, using this framework, under different assumptions for screening sensitivity and breast cancer survival with the aim of estimating the lead-time bias. Screening every second year among ages 40-75 was introduced assuming that screening had no effect on survival, except for lead-time bias. Relative survival was estimated both with and without screening to enable quantification of the lead-time bias. Scenarios with low, moderate and high breast cancer survival, and low, moderate and high screening sensitivity were simulated, and the lead-time bias assessed in all scenarios. [ABSTRACT FROM AUTHOR]

If interest lies in reporting absolute measures of risk from time-to-event data then obtaining an appropriate approximation to the shape of the underlying hazard function is vital. It has previously been shown that restricted cubic splines can be used to approximate complex hazard functions in the context of time-to-event data. The degree of complexity for the spline functions is dictated by the number of knots that are defined. We highlight through the use of a motivating example that complex hazard function shapes are often required when analysing time-to-event data. Through the use of simulation, we show that provided a sufficient number of knots are used, the approximated hazard functions given by restricted cubic splines fit closely to the true function for a range of complex hazard shapes. The simulation results also highlight the insensitivity of the estimated relative effects (hazard ratios) to the correct specification of the baseline hazard. [ABSTRACT FROM AUTHOR]

Abstract: Background: It is vital that unbiased estimates of relative survival are estimated and reported by cancer registries. A single figure of relative survival is often required to make reporting simpler. This can be obtained by pooling all ages or, more commonly, by using age-standardisation. The various methods for providing a single figure estimate of relative survival can give very different estimates. Methods: The problem is illustrated through an example using Finnish thyroid cancer data. The differences are further explored through a simulation study that investigates the effect of age on the estimates of relative survival. Results: The example highlights that in practice the all-age estimates from the various methods can be substantially different (up to 6 percentage units at 15 years of follow-up). The simulation study confirms the finding that differing estimates for the all-age estimates of relative survival are obtained. Performing age-standardisation makes the methods more comparable and results in better estimation of the true net survival. Conclusions: The all-age estimates of relative survival rarely give an appropriate estimate of net survival. We feel that modelling or stratifying by age when calculating relative survival is vitally important as the lack of homogeneity in the cohort of patients leads to potentially biased estimates. We feel that the methods using modelling provide a greater flexibility than life-table based approaches. The flexible parametric approach does not require an arbitrary splitting of the time-scale, which makes it more computationally efficient. It also has the advantage of easily being extended to incorporate time-dependent effects. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Background: Immortal time bias is common in observational studies but is typically described for pharmacoepidemiology studies where there is a delay between cohort entry and treatment initiation.Methods: This study used the Clinical Practice Research Datalink (CPRD) and linked national mortality data in England from 2000 to 2019 to investigate immortal time bias for a specific life-long condition, intellectual disability. Life expectancy (Chiang's abridged life table approach) was compared for 33,867 exposed and 980,586 unexposed individuals aged 10+ years using five methods: (1) treating immortal time as observation time; (2) excluding time before date of first exposure diagnosis; (3) matching cohort entry to first exposure diagnosis; (4) excluding time before proxy date of inputting first exposure diagnosis (by the physician); and (5) treating exposure as a time-dependent measure.Results: When not considered in the design or analysis (Method 1), immortal time bias led to disproportionately high life expectancy for the exposed population during the first calendar period (additional years expected to live: 2000-2004: 65.6 [95% CI: 63.6,67.6]) compared to the later calendar periods (2005-2009: 59.9 [58.8,60.9]; 2010-2014: 58.0 [57.1,58.9]; 2015-2019: 58.2 [56.8,59.7]). Date of entry of diagnosis (Method 4) was unreliable in this CPRD cohort. The final methods (Method 2, 3 and 5) appeared to solve the main theoretical problem but residual bias may have remained.Conclusions: We conclude that immortal time bias is a significant issue for studies of life-long conditions that use electronic health record data and requires careful consideration of how clinical diagnoses are entered onto electronic health record systems. [ABSTRACT FROM AUTHOR]

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 these models in capturing non-proportional hazards, and the ability of the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) in selecting degrees of freedom. The simulation results for scenarios with differing complexities showed little bias in the survival and hazard functions for simple scenarios; bias increased in complex scenarios when fewer degrees of freedom were modeled. Neither AIC nor BIC consistently performed better and both generally selected models with little bias. [ABSTRACT FROM AUTHOR]

There is a need to systematically compare and contrast mortality predictors and disparities in people with intellectual disabilities (ID) for global prevention strategy development. Bibliographic databases and grey literature were searched using systematic review methodology and the machine learning tool "Abstrackr." Fifty-four relevant articles and reports published from 2010 to 2019 were identified. Nearly all (n = 53) were from high-income countries. Mortality disparities were apparent and consistent across countries and publication years, with no evidence of a decrease over time. People with ID can still expect to live 12–23 years less than the general population and are particularly vulnerable to deaths from respiratory infections and epilepsy. Both population and individual-level approaches to prevention are indicated to tackle the continuing mortality disparities in people with ID, including consideration of reasonable adjustments in general population efforts to reduce health inequalities. [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]

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. [ABSTRACT FROM AUTHOR]

Multi‐state survival models are used to represent the natural history of a disease, forming the basis of a health technology assessment comparing a novel treatment to current practice. Constructing such models for rare diseases is problematic, since evidence sources are typically much sparser and more heterogeneous. This simulation study investigated different one‐stage and two‐stage approaches to meta‐analyzing individual patient data (IPD) in a multi‐state survival setting when the number and size of studies being meta‐analyzed are small. The objective was to assess methods of different complexity to see when they are accurate, when they are inaccurate and when they struggle to converge due to the sparsity of data. Biologically plausible multi‐state IPD were simulated from study‐ and transition‐specific hazard functions. One‐stage frailty and two‐stage stratified models were estimated, and compared to a base case model that did not account for study heterogeneity. Convergence and the bias/coverage of population‐level transition probabilities to, and lengths of stay in, each state were used to assess model performance. A real‐world application to Duchenne Muscular Dystrophy, a neuromuscular rare disease, was conducted, and a software demonstration is provided. Models not accounting for study heterogeneity were consistently out‐performed by two‐stage models. Frailty models struggled to converge, particularly in scenarios of low heterogeneity, and predictions from models that did converge were also subject to bias. Stratified models may be better suited to meta‐analyzing disparate sources of IPD in rare disease natural history/economic modeling, as they converge more consistently and produce less biased predictions of lengths of stay. [ABSTRACT FROM AUTHOR]

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. 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. 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. 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. • Extrapolation of all-cause survival from randomized controlled trial data is often required in the context of economic evaluation of novel interventions. External information can be used to guide long-term survival trends when extrapolating all-cause survival. This article investigates relative survival modeling approaches to incorporate general population mortality rates into long-term extrapolation. In doing so, we expand on existing approaches by clearly detailing how to apply various constraints on the long-term disease-specific mortality in this modeling framework. • Flexible parametric survival models can apply various extrapolation approaches in the framework. We compare models by imposing constraints on parameter estimation and applying those constraints at specific points of follow-up, including beyond the range of the data. We compare these methods in scenarios where cure is simulated to be reasonable and in cases where it is not. The result shows that different assumptions on the excess hazards can result in different extrapolations of all-cause survival. The various constraints can lead to more plausible survival extrapolation depending on the disease or treatment characteristics. • The approaches for all-cause survival extrapolation outlined offer a suite of possibilities to clearly describe an approach to extrapolation that automatically incorporates general population mortality rates while making explicit choices on how long disease-related mortality will affect the cohort. The choice of approach can be dictated by the clinical context in the decision-making process. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Background: In population-based cancer survival studies, the most common measure to compare population groups is age-standardized marginal relative survival, which under assumptions can be interpreted as marginal net survival; the probability of surviving if it was not possible to die of causes other than the cancer under study (if the age distribution was that of a common reference population). The hypothetical nature of this definition has led to confusion and incorrect interpretation. For any measure to be fair in terms of comparing cancer survival, then differences between population groups should depend only on differences in excess mortality rates due to the cancer and not differences in other-cause mortality rates or differences in the age distribution.Methods: We propose using crude probabilities of death and all-cause survival which incorporate reference expected mortality rates. This makes it possible to obtain marginal crude probabilities and all-cause probability of death that only differ between population groups due to excess mortality rate differences. Choices have to be made regarding what reference mortality rates to use and what age distribution to standardize to.Results: We illustrate the method and some potential choices using data from England for men diagnosed with melanoma. Various marginal measures are presented and compared.Conclusions: The new measures help enhance understanding of cancer survival and are a complement to the more commonly used measures. [ABSTRACT FROM AUTHOR]

The article focuses on effect of patient care in cancer patient survival. Topics discussed include contribution of health-care officials, health policy makers, and charities in development of treatment and diagnostic techniques in cancer control, creation of survival index for improving survival of cancer patients and epidemiological measure in quantification of cancer survival.

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. [ABSTRACT FROM AUTHOR]

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. [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]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Aims To compare ST-segment elevation myocardial infarction (STEMI) and non-STEMI (NSTEMI) mortality between Sweden and the UK, adjusting for background population rates of expected death, case mix, and treatments. Methods and results National data were collected from hospitals in Sweden [ n  = 73 hospitals, 180 368 patients, Swedish Web-system for Enhancement and Development of Evidence-based care in Heart disease Evaluated According to Recommended Therapies (SWEDEHEART)] and the UK [ n  = 247, 662 529 patients, Myocardial Ischaemia National Audit Project (MINAP)] between 2003 and 2013. There were lower rates of revascularization [STEMI (43.8% vs. 74.9%); NSTEMI (27.5% vs. 43.6%)] and pharmacotherapies at time of hospital discharge including [aspirin (82.9% vs. 90.2%) and (79.9% vs. 88.0%), β-blockers (73.4% vs. 86.4%) and (65.3% vs. 85.1%)] in the UK compared with Sweden, respectively. Standardized net probability of death (NPD) between admission and 1 month was higher in the UK for STEMI [8.0 (95% confidence interval 7.4–8.5) vs. 6.7 (6.5–6.9)] and NSTEMI [6.8 (6.4–7.2) vs. 4.9 (4.7–5.0)]. Between 6 months and 1 year and more than 1 year, NPD remained higher in the UK for NSTEMI [2.9 (2.5–3.3) vs. 2.3 (2.2–2.5)] and [21.4 (20.0–22.8) vs. 18.3 (17.6–19.0)], but was similar for STEMI [0.7 (0.4–1.0) vs. 0.9 (0.7–1.0)] and [8.4 (6.7–10.1) vs. 8.3 (7.5–9.1)]. Conclusion Short-term mortality following STEMI and NSTEMI was higher in the UK compared with Sweden. Mid- and longer-term mortality remained higher in the UK for NSTEMI but was similar for STEMI. Differences in mortality may be due to differential use of guideline-indicated treatments. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Background: Colorectal cancer prognosis varies substantially with socioeconomic status. We investigated differences in life expectancy between socioeconomic groups and estimated the potential gain in life-years if cancer-related survival differences could be eliminated.Methods: This population-based study included 470,000 individuals diagnosed with colon and rectal cancers between 1998 and 2013 in England. Using flexible parametric survival models, we obtained a range of life expectancy measures by deprivation status. The number of life-years that could be gained if differences in cancer-related survival between the least and most deprived groups were removed was also estimated.Results: We observed up to 10% points differences in 5-year relative survival between the least and most deprived. If these differences had been eliminated for colon and rectal cancers diagnosed in 2013 then almost 8231 and 7295 life-years would have been gained respectively. This results for instance in more than 1-year gain for each colon cancer male patient in the most deprived group on average. Cancer-related differences are more profound earlier on, as conditioning on 1-year survival the main reason for socioeconomic differences were factors other than cancer.Conclusion: This study highlights the importance of policies to eliminate socioeconomic differences in cancer survival as in this way many life-years could be gained. [ABSTRACT FROM AUTHOR]

Background: Differences in cancer survival exist across socio-economic groups for many cancer types. Standard metrics fail to show the overall impact for patients and the population.Methods: The available data consist of a population of ∼2.5 million patients and include all patients recorded as being diagnosed with melanoma, prostate, bladder, breast, colon, rectum, lung, ovarian and stomach cancers in England between 1998 and 2013. We estimated the average loss in expectation of life per patient in years and the proportion of life lost for a range of cancer types, separately by deprivation group. In addition, estimates for the total number of years lost due to each cancer were also obtained.Results: Lung and stomach cancers result in the highest overall loss for males and females in all deprivation groups in terms of both absolute life years lost and loss as a proportion of expected life remaining. Female lung cancer patients in the least- and most-deprived group lose 14.4 and 13.8 years on average, respectively, that is translated as 86.1% and 87.3% of their average expected life years remaining. Melanoma, prostate and breast cancers have the lowest overall loss. On the basis of the number of patients diagnosed in 2013, lung cancer results in the most life years lost in total followed by breast cancer. Melanoma and bladder cancer account for the lowest total life years lost.Conclusions: There are wide differences in the impact of cancer on life expectancy across deprivation groups, and for most cancers the most affluent lose less years. [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]