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When analyzing cohort data, we rarely consider potential simultaneous effects of multiple time-scales on estimated survival proportions and hazard ratios. Instead, often, only one time-scale, such as time-on-study or attained age, is taken as the main time-scale and the other time-scale(s) included in the model as time-fixed covariate(s). In this simulation study, we investigate the potential bias in estimated survival proportions and hazard ratios by not modeling multiple time-scales. We simulate data with two time-scales, under various scenarios, and a binary covariate as the exposure of interest. Flexible parametric models with one time-scale were fitted to the simulated data, including the exposure variable of interest and the other time-scale as a fixed covariate. For many of our simulated scenarios, the models with one time-scale showed small bias for the survival proportions. Bias in the log hazard ratios (for the covariate of interest) was observed when there were non-proportional hazards on the second time-scale. If one is modeling only one time-scale it is advisable to include non-proportional hazards and interactions with the time-scale. Exploration of approaches to modeling multiple time-scales is outside the scope of this study. [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]

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. 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. 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. 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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

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. [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]

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]

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

Background: 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: 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]

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: 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]

When patients randomised to the control group of a randomised controlled trial are allowed to switch onto the experimental treatment, intention-to-treat analyses of the treatment effect are confounded because the separation of randomised groups is lost. Previous research has investigated statistical methods that aim to estimate the treatment effect that would have been observed had this treatment switching not occurred and has demonstrated their performance in a limited set of scenarios. Here, we investigate these methods in a new range of realistic scenarios, allowing conclusions to be made based upon a broader evidence base. We simulated randomised controlled trials incorporating prognosis-related treatment switching and investigated the impact of sample size, reduced switching proportions, disease severity, and alternative data-generating models on the performance of adjustment methods, assessed through a comparison of bias, mean squared error, and coverage, related to the estimation of true restricted mean survival in the absence of switching in the control group. Rank preserving structural failure time models, inverse probability of censoring weights, and two-stage methods consistently produced less bias than the intention-to-treat analysis. The switching proportion was confirmed to be a key determinant of bias: sample size and censoring proportion were relatively less important. It is critical to determine the size of the treatment effect in terms of an acceleration factor (rather than a hazard ratio) to provide information on the likely bias associated with rank-preserving structural failure time model adjustments. In general, inverse probability of censoring weight methods are more volatile than other adjustment methods. [ABSTRACT FROM AUTHOR]

Competing risks arise with time-to-event data when individuals are at risk of more than one type of event and the occurrence of one event precludes the occurrence of all other events. A useful measure with competing risks is the cause-specific cumulative incidence function (CIF), which gives the probability of experiencing a particular event as a function of follow-up time, accounting for the fact that some individuals may have a competing event. When modelling the cause-specific CIF, the most common model is a semi-parametric proportional subhazards model. In this paper, we propose the use of flexible parametric survival models to directly model the cause-specific CIF where the effect of follow-up time is modelled using restricted cubic splines. The models provide smooth estimates of the cause-specific CIF with the important advantage that the approach is easily extended to model time-dependent effects. The models can be fitted using standard survival analysis tools by a combination of data expansion and introducing time-dependent weights. Various link functions are available that allow modelling on different scales and have proportional subhazards, proportional odds and relative absolute risks as particular cases. We conduct a simulation study to evaluate how well the spline functions approximate subhazard functions with complex shapes. The methods are illustrated using data from the European Blood and Marrow Transplantation Registry showing excellent agreement between parametric estimates of the cause-specific CIF and those obtained from a semi-parametric model. We also fit models relaxing the proportional subhazards assumption using alternative link functions and/or including time-dependent effects. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Most of the few published models used to obtain small-area estimates of relative survival are based on a generalized linear model with piecewise constant hazards under a Bayesian formulation. Limitations of these models include the need to artificially split the time scale, restricted ability to include continuous covariates, and limited predictive capacity. Here, an alternative Bayesian approach is proposed: a spatial flexible parametric relative survival model. This overcomes previous limitations by combining the benefits of flexible parametric models: the smooth, well-fitting baseline hazard functions and predictive ability, with the Bayesian benefits of robust and reliable small-area estimates. Both spatially structured and unstructured frailty components are included. Spatial smoothing is conducted using the intrinsic conditional autoregressive prior. The model was applied to breast, colorectal, and lung cancer data from the Queensland Cancer Registry across 478 geographical areas. Advantages of this approach include the ease of including more realistic complexity, the feasibility of using individual-level input data, and the capacity to conduct overall, cause-specific, and relative survival analysis within the same framework. Spatial flexible parametric survival models have great potential for exploring small-area survival inequalities, and we hope to stimulate further use of these models within wider contexts. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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

A now common goal in medical research is to investigate the inter-relationships between a repeatedly measured biomarker, measured with error, and the time to an event of interest. This form of question can be tackled with a joint longitudinal-survival model, with the most common approach combining a longitudinal mixed effects model with a proportional hazards survival model, where the models are linked through shared random effects. In this article, we look at incorporating delayed entry (left truncation), which has received relatively little attention. The extension to delayed entry requires a second set of numerical integration, beyond that required in a standard joint model. We therefore implement two sets of fully adaptive Gauss-Hermite quadrature with nested Gauss-Kronrod quadrature (to allow time-dependent association structures), conducted simultaneously, to evaluate the likelihood. We evaluate fully adaptive quadrature compared with previously proposed non-adaptive quadrature through a simulation study, showing substantial improvements, both in terms of minimising bias and reducing computation time. We further investigate, through simulation, the consequences of misspecifying the longitudinal trajectory and its impact on estimates of association. Our scenarios showed the current value association structure to be very robust, compared with the rate of change that we found to be highly sensitive showing that assuming a simpler trend when the truth is more complex can lead to substantial bias. With emphasis on flexible parametric approaches, we generalise previous models by proposing the use of polynomials or splines to capture the longitudinal trend and restricted cubic splines to model the baseline log hazard function. The methods are illustrated on a dataset of breast cancer patients, modelling mammographic density jointly with survival, where we show how to incorporate density measurements prior to the at-risk period, to make use of all the available information. User-friendly Stata software is provided. [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]

Parametric survival models are being increasingly used as an alternative to the Cox model in biomedical research. Through direct modelling of the baseline hazard function, we can gain greater understanding of the risk profile of patients over time, obtaining absolute measures of risk. Commonly used parametric survival models, such as the Weibull, make restrictive assumptions of the baseline hazard function, such as monotonicity, which is often violated in clinical datasets. In this article, we extend the general framework of parametric survival models proposed by Crowther and Lambert (Journal of Statistical Software 53:12, 2013), to incorporate relative survival, and robust and cluster robust standard errors. We describe the general framework through three applications to clinical datasets, in particular, illustrating the use of restricted cubic splines, modelled on the log hazard scale, to provide a highly flexible survival modelling framework. Through the use of restricted cubic splines, we can derive the cumulative hazard function analytically beyond the boundary knots, resulting in a combined analytic/numerical approach, which substantially improves the estimation process compared with only using numerical integration. User-friendly Stata software is provided, which significantly extends parametric survival models available in standard software. [ABSTRACT FROM AUTHOR]

Competing risks are present when the patients within a dataset could experience one or more of several exclusive events and the occurrence of any one of these could impede the event of interest. One of the measures of interest for analyses of this type is the cumulative incidence function. stpm2cif is a postestimation command used to generate predictions of the cumulative incidence function after fitting a flexible parametric survival model using stpm2. There is also the option to generate confidence intervals, cause-specific hazards, and two other measures that will be discussed in further detail. The new command is illustrated through a simple example. [ABSTRACT FROM AUTHOR]

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

The joint modeling of longitudinal and survival data has received remarkable attention in the methodological literature over the past decade; however, the availability of software to implement the methods lags behind. The most common form of joint model assumes that the association between the survival and the longitudinal processes is underlined by shared random effects. As a result, computationally intensive numerical integration techniques such as adaptive Gauss-Hermite quadrature are required to evaluate the likelihood. We describe a new user-written command, stjm, that allows the user to jointly model a continuous longitudinal response and the time to an event of interest. We assume a linear mixed-effects model for the longitudinal submodel, allowing flexibility through the use of fixed or random fractional polynomials of time. Four choices are available for the survival submodel: the exponential, Weibull or Gompertz proportional hazard models, and the flexible parametric model (stpm2). Flexible parametric models are fit on the log cumulative-hazard scale, which has direct computational benefits because it avoids the use of numerical integration to evaluate the cumulative hazard. We describe the features of stjm through application to a dataset investigating the effect of serum bilirubin level on time to death from any cause in 312 patients with primary biliary cirrhosis. [ABSTRACT FROM AUTHOR]

Abstract: Background: Survival from breast cancer is lower in the UK than in some other European countries. We compared survival in England and Norway by age and time from diagnosis. Methods: We included 303,648 English and 24,919 Norwegian cases of breast cancer diagnosed 1996–2004 using flexible parametric relative survival models, enabling improved quantification of differences in survival. Crude probabilities were estimated to partition the probability of death due to all causes into that due to cancer and other causes and to estimate the number of “avoidable” deaths. Results: England had lower relative survival for all ages with the difference increasing with age. Much of the difference was due to higher excess mortality in England in the first few months after diagnosis. Older patients had a higher proportion of deaths due to other causes. At 5 years post diagnosis, a woman aged 85 in England had probabilities of 0.35 of dying of cancer and 0.32 of dying of other causes, whilst in Norway they were 0.26 and 0.35. By eight years the number of “avoidable” all-cause deaths in England was 1020 with the number of “avoidable” breast cancer related deaths 1488. Conclusion: Lower breast cancer survival in England is mainly due to higher mortality in the first year after diagnosis. Crude probabilities aid our understanding of the impact of disease on individual patients and help assess different treatment options. [Copyright &y& Elsevier]

Objective: To examine differences in the relative survival and excess death rates of patients with colorectal cancer in Norway, Sweden and England. Methods: All individuals diagnosed with colorectal cancer (ICD10 (International Classification of Diseases, 10th revision) C18-C20) between 1996 and 2004 in England, Norway and Sweden were included in this population-based study of patients with colorectal cancer. The main outcome measures were 5-year cumulative relative period of survival and excess death rates stratified by age and period of follow-up. Results: The survival of English patients with colorectal cancer was significantly lower than was observed in both Norway and Sweden. Five-year age-standardised colon cancer relative survival was 51.1% (95% CI 50.1% to 52.0%) in England compared with 57.9% (95% CI 55.2% to 60.5%) in Norway and 59.9% (95% CI 57.7% to 62.0%) in Sweden. Five-year rectal cancer survival was 52.3% (95% CI 51.1% to 53.5%) in England compared with 60.7% (95% CI 57.0% to 64.2%) and 59.8% (95% CI 56.9% to 62.6%) in Norway and Sweden, respectively. The lower survival for colon cancer in England was primarily due to a high number of excess deaths among older patients in the first 3 months after diagnosis. In patients with rectal cancer, excess deaths remained elevated until 2 years of follow-up. If the lower excess death rate in Norway applied in the English population, then 890 (13.6%) and 654 (16.8%) of the excess deaths in the colon and rectal cancer populations, respectively, could have been prevented at 5 years follow-up. Most of these avoidable deaths occurred shortly after diagnosis. Conclusions: There was significant variation in survival between the countries, with the English population experiencing a poorer outcome, primarily due to a relatively higher number of excess deaths in older patients in the short term after diagnosis. It seems likely, therefore, that in England a greater proportion of the population present with more rapidly fatal disease (especially in the older age groups) than in Norway or Sweden. [ABSTRACT FROM AUTHOR]

: ObjectiveStandard survival methods can yield out-of-date estimates of long-term survival. Period analysis, based on life-table methodology, provides more up-to-date survival estimates by exploring survival during a restricted recent period of interest. It excludes the short-term survival of patients recruited at the start of the study. We use statistical models to further develop the method of period analysis, providing more up-to-date estimates of survival and the ability to explore differences in survival by covariates and adjust for case mix.: MethodsWe use cancer registry data for colorectal cancer in Leicestershire, UK, to illustrate the use of Cox proportional hazards (CPH) models to estimate period and standard survival. We compare these estimates with those obtained using life-table methodology.: ResultsPeriod estimates were slightly higher than the standard estimates as they reflect recent improvements in short-term survival. The results for period analysis using the life-table approach and using CPH models were similar. However, CPH models allowed further investigation of other risk factors and the ability to control for potential confounding variables.: ConclusionUsing period survival estimates, more up-to-date information is available to clinicians and others with an interest in monitoring survival. Period CHP models offer all the advantages of statistical modeling, and are straightforward to fit in standard statistical packages. [Copyright &y& Elsevier]

Background: Breast cancer can negatively influence working life, but it is unclear how many working years women with breast cancer can expect to lose.Methods: Women diagnosed with breast cancer between 1997 and 2012 were identified in the Breast Cancer Data Base Sweden (N=19 661), together with breast cancer-free comparison women (N=81 303). Using flexible parametric survival modelling, the loss in working years was calculated as the difference in the remaining years in the work force between women with and without breast cancer.Results: Women aged 50 years at diagnosis with stage I disease lost on average 0.5 years (95% CI, 0.2-0.7) of their remaining working time; the corresponding estimates were 0.9 years (0.5-1.2) in stage II, 2.5 years (1.9-3.1) in stage III and 8.1 years (6.5-9.7) in stage IV. Women with in situ breast cancer did not lose any working years. The strongest treatment determinant was axillary lymph node dissection.Conclusions: We found a loss in working years not only in late but also in early-stage breast cancer. Although it is reassuring that some groups had no or only a modest work loss, the economic consequences for society are considerable given the large number of women annually diagnosed with breast cancer. [ABSTRACT FROM AUTHOR]

The survival in patients diagnosed with cutaneous malignant melanoma (CMM) has improved in the Nordic countries in the last decades. It is of interest to know if these improvements are observed in all ages and for both women and men. Patients diagnosed with CMM in the Nordic countries in 1990–2016 were identified in the NORDCAN database. Flexible parametric relative survival models were fitted, except for Iceland where a non-parametric Pohar-Perme approach was used. A range of survival metrics were estimated by sex, both age-standardised and age-specific. The 5-year relative survival improved in all countries, in both women and men and across age. While the improvement was more pronounced in men, women still had a higher survival at the end of the study period. The survival was generally high, with age-standardised estimates of 5-year relative survival towards the end of the study period ranging from 85% in Icelandic men to 95% in Danish women. The age-standardised and reference-adjusted 5-year crude probability of death due to CMM ranged from 5% in Danish and Swedish women to 13% in Icelandic men. Although survival following CMM was relatively high in the Nordic countries in 1990, continued improvements in survival were observed throughout the study period in both women and men and across age. • Survival following cutaneous malignant melanoma is high in the Nordic countries. • The survival has continuously improved between 1990 and 2016. • Survival improvements were observed across age and in both men and women. [ABSTRACT FROM AUTHOR]