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

Multistate models are increasingly being used to model complex disease profiles. By modelling transitions between disease states, accounting for competing events at each transition, we can gain a much richer understanding of patient trajectories and how risk factors impact over the entire disease pathway. In this article, we concentrate on parametric multistate models, both Markov and semi-Markov, and develop a flexible framework where each transition can be specified by a variety of parametric models including exponential, Weibull, Gompertz, Royston-Parmar proportional hazards models or log-logistic, log-normal, generalised gamma accelerated failure time models, possibly sharing parameters across transitions. We also extend the framework to allow time-dependent effects. We then use an efficient and generalisable simulation method to calculate transition probabilities from any fitted multistate model, and show how it facilitates the simple calculation of clinically useful measures, such as expected length of stay in each state, and differences and ratios of proportion within each state as a function of time, for specific covariate patterns. We illustrate our methods using a dataset of patients with primary breast cancer. User-friendly Stata software is provided. [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]

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]

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. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Simulation studies are conducted to assess the performance of current and novel statistical models in pre-defined scenarios. It is often desirable that chosen simulation scenarios accurately reflect a biologically plausible underlying distribution. This is particularly important in the framework of survival analysis, where simulated distributions are chosen for both the event time and the censoring time. This paper develops methods for using complex distributions when generating survival times to assess methods in practice. We describe a general algorithm involving numerical integration and root-finding techniques to generate survival times from a variety of complex parametric distributions, incorporating any combination of time-dependent effects, time-varying covariates, delayed entry, random effects and covariates measured with error. User-friendly Stata software is provided. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Meta-analysis of individual patient data (IPD) is the gold-standard for synthesizing evidence across clinical studies. However, for some studies IPD may not be available and only aggregate data (AD), such as a treatment effect estimate and its standard error, may be obtained. In this situation, methods for combining IPD and AD are important to utilize all the available evidence. In this paper, we develop and assess a range of statistical methods for combining IPD and AD in meta-analysis of continuous outcomes from randomized controlled trials. The methods take either a one-step or a two-step approach. The latter is simple, with IPD reduced to AD so that standard AD meta-analysis techniques can be employed. The one-step approach is more complex but offers a flexible framework to include both patient-level and trial-level parameters. It uses a dummy variable to distinguish IPD trials from AD trials and to constrain which parameters the AD trials estimate. We show that this is important when assessing how patient-level covariates modify treatment effect, as aggregate-level relationships across trials are subject to ecological bias and confounding. We thus develop models to separate within-trial and across-trials treatment-covariate interactions; this ensures that only IPD trials estimate the former, whilst both IPD and AD trials estimate the latter in addition to the pooled treatment effect and any between-study heterogeneity. Extension to multiple correlated outcomes is also considered. Ten IPD trials in hypertension, with blood pressure the continuous outcome of interest, are used to assess the models and identify the benefits of utilizing AD alongside IPD. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Relative survival is frequently used in population-based studies as a method for estimating disease-related mortality without the need for information on cause of death. We propose an extension to relative survival of a flexible parametric model proposed by Royston and Parmar for censored survival data. The model provides smooth estimates of the relative survival and excess mortality rates by using restricted cubic splines on the log cumulative excess hazard scale. The approach has several advantages over some of the more standard relative survival models, which adopt a piecewise approach, the main being the ability to model time on a continuous scale, the survival and hazard functions are obtained analytically and it does not use split-time data. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Relative survival is used to estimate patient survival excluding causes of death not related to the disease of interest. Rather than using cause of death information from death certificates, which is often poorly recorded, relative survival compares the observed survival to that expected in a matched group from the general population. Models for relative survival can be expressed on the hazard (mortality) rate scale as the sum of two components where the total mortality rate is the sum of the underlying baseline mortality rate and the excess mortality rate due to the disease of interest. Previous models for relative survival have assumed that covariate effects act multiplicatively and have thus provided relative effects of differences between groups using excess mortality rate ratios. In this paper we consider (i) the use of an additive covariate model, which provides estimates of the absolute difference in the excess mortality rate; and (ii) the use of fractional polynomials in relative survival models for the baseline excess mortality rate and time-dependent effects. The approaches are illustrated using data on 115 331 female breast cancer patients diagnosed between 1 January 1986 and 31 December 1990. The use of additive covariate relative survival models can be useful in situations when the excess mortality rate is zero or slightly less than zero and can provide useful information from a public health perspective. The use of fractional polynomials has advantages over the usual piecewise estimation by providing smooth estimates of the baseline excess mortality rate and time-dependent effects for both the multiplicative and additive covariate models. All models presented in this paper can be estimated within a generalized linear models framework and thus can be implemented using standard software. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

There has been a recent growth in the use of Bayesian methods in medical research. The main reasons for this are the development of computer intensive simulation based methods such as Markov chain Monte Carlo (MCMC), increases in computing power and the introduction of powerful software such as WinBUGS. This has enabled increasingly complex models to be fitted. The ability to fit these complex models has led to MCMC methods being used as a convenient tool by frequentists, who may have no desire to be fully Bayesian. Often researchers want 'the data to dominate' when there is no prior information and thus attempt to use vague prior distributions. However, with small amounts of data the use of vague priors can be problematic. The results are potentially sensitive to the choice of prior distribution. In general there are fewer problems with location parameters. The main problem is with scale parameters. With scale parameters, not only does one have to decide the distributional form of the prior distribution, but also whether to put the prior distribution on the variance, standard deviation or precision. We have conducted a simulation study comparing the effects of 13 different prior distributions for the scale parameter on simulated random effects meta-analysis data. We varied the number of studies (5, 10 and 30) and compared three different between-study variances to give nine different simulation scenarios. One thousand data sets were generated for each scenario and each data set was analysed using the 13 different prior distributions. The frequentist properties of bias and coverage were investigated for the between-study variance and the effect size. The choice of prior distribution was crucial when there were just five studies. There was a large variation in the estimates of the between-study variance for the 13 different prior distributions. With a large number of studies the choice of prior distribution was less important. The effect size estimated was not biased, but the precision with which it was estimated varied with the choice of prior distribution leading to varying coverage intervals and, potentially, to different statistical inferences. Again there was less of a problem with a larger number of studies. There is a particular problem if the between-study variance is close to the boundary at zero, as MCMC results tend to produce upwardly biased estimates of the between-study variance, particularly if inferences are based on the posterior mean. The choice of 'vague' prior distribution can lead to a marked variation in results, particularly in small studies. Sensitivity to the choice of prior distribution should always be assessed. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Peak expiratory flow (PEF) is a measure commonly used in clinical practice and research for respiratory diseases such as asthma. In research, PEF is usually recorded in a diary for a 2-week period with two or more measurements per day. Interest may lie in whether certain groups of individuals tend to have higher or lower PEF. In addition the variability of PEF may be of interest as, for example, asthmatics tend to have more variable airways. In this paper we develop a three-level hierarchical model that can simultaneously model the mean level and variability of PEF. The variability is broken down into three components, between-subject variability, between-day within-subject variability, and within-day within-subject variability. The latter two components are of specific clinical interest. We fit both classical and Bayesian models. The Bayesian models have the advantage of taking the uncertainty in the variance component estimates into account when estimating the standard errors of the fixed effects. In addition, the Bayesian models provide an intuitive and simple way to investigate the within-subject variance components. Copyright © 2004 John Wiley & Sons, Ltd. [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]

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]

In a competing risks analysis, interest lies in the cause-specific cumulative incidence function (CIF) that can be calculated by either (1) transforming on the cause-specific hazard or (2) through its direct relationship with the subdistribution hazard. We expand on current competing risks methodology from within the flexible parametric survival modelling framework (FPM) and focus on approach (2). This models all cause-specific CIFs simultaneously and is more useful when we look to questions on prognosis. We also extend cure models using a similar approach described by Andersson et al for flexible parametric relative survival models. Using SEER public use colorectal data, we compare and contrast our approach with standard methods such as the Fine & Gray model and show that many useful out-of-sample predictions can be made after modelling the cause-specific CIFs using an FPM approach. Alternative link functions may also be incorporated such as the logit link. Models can also be easily extended for time-dependent effects. [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]

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]

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]

The joint modelling of longitudinal and survival data is a highly active area of biostatistical research. The submodel for the longitudinal biomarker usually takes the form of a linear mixed effects model. We describe a flexible parametric approach for the survival submodel that models the log baseline cumulative hazard using restricted cubic splines. This approach overcomes limitations of standard parametric choices for the survival submodel, which can lack the flexibility to effectively capture the shape of the underlying hazard function. Numerical integration techniques, such as Gauss-Hermite quadrature, are usually required to evaluate both the cumulative hazard and the overall joint likelihood; however, by using a flexible parametric model, the cumulative hazard has an analytically tractable form, providing considerable computational benefits. We conduct an extensive simulation study to assess the proposed model, comparing it with a B-spline formulation, illustrating insensitivity of parameter estimates to the baseline cumulative hazard function specification. Furthermore, we compare non-adaptive and fully adaptive quadrature, showing the superiority of adaptive quadrature in evaluating the joint likelihood. We also describe a useful technique to simulate survival times from complex baseline hazard functions and illustrate the methods using an example data set investigating the association between longitudinal prothrombin index and survival of patients with liver cirrhosis, showing greater flexibility and improved stability with fewer parameters under the proposed model compared with the B-spline approach. We provide user-friendly Stata software. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper considers the quantitative synthesis of published comparative study results when the outcome measures used in the individual studies and the way in which they are reported varies between studies. Whilst the former difficulty may be overcome, at least to a limited extent, by the use of standardized effects, the latter is often more problematic. Two potential solutions to this problem are; sensitivity analyses and a fully Bayesian approach, in which pertinent external information is included. Both approaches are illustrated using the results of two systematic reviews and meta-analyses which consider the difference in mean change in systolic blood pressure and the difference in physical functioning between an intervention and control group. The two examples illustrate that by adopting a fully Bayesian approach, as opposed to undertaking sensitivity analyses assuming fixed values for unknown parameters, the overall intervention effect can be estimated with greater uncertainty, but that assessing the sensitivity of results to choice of prior distributions in such analyses is crucial. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Objectives: To compare the performance of different meta-analysis methods for pooling odds ratios when applied to sparse event data with emphasis on the use of continuity corrections. Background: Meta-analysis of side effects from RCTs or risk factors for rare diseases in epidemiological studies frequently requires the synthesis of data with sparse event rates. Combining such data can be problematic when zero events exist in one or both arms of a study as continuity corrections are often needed, but, these can influence results and conclusions. Methods: A simulation study was undertaken comparing several meta-analysis methods for combining odds ratios (using various classical and Bayesian methods of estimation) on sparse event data. Where required, the routine use of a constant and two alternative continuity corrections; one based on a function of the reciprocal of the opposite group arm size; and the other an empirical estimate of the pooled effect size from the remaining studies in the meta-analysis, were also compared. A number of meta-analysis scenarios were simulated and replicated 1000 times, varying the ratio of the study arm sizes. Results: Mantel-Haenszel summary estimates using the alternative continuity correction factors gave the least biased results for all group size imbalances. Logistic regression was virtually unbiased for all scenarios and gave good coverage properties. The Peto method provided unbiased results for balanced treatment groups but bias increased with the ratio of the study arm sizes. The Bayesian fixed effect model provided good coverage for all group size imbalances. The two alternative continuity corrections outperformed the constant correction factor in nearly all situations. The inverse variance method performed consistently badly, irrespective of the continuity correction used. Conclusions: Many routinely used summary methods provide widely ranging estimates when applied to sparse data with high imbalance between the size of the studies' arms. A sensitivity analysis using several methods and continuity correction factors is advocated for routine practice. Copyright 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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

A useful summary measure for survival data is the expectation of life, which is calculated by obtaining the area under a survival curve. The loss in expectation of life due to a certain type of cancer is the difference between the expectation of life in the general population and the expectation of life among the cancer patients. This measure is used little in practice as its estimation generally requires extrapolation of both the expected and observed survival. A parametric distribution can be used for extrapolation of the observed survival, but it is difficult to find a distribution that captures the underlying shape of the survival function after the end of follow-up. In this paper, we base our extrapolation on relative survival, because it is more stable and reliable. Relative survival is defined as the observed survival divided by the expected survival, and the mortality analogue is excess mortality. Approaches have been suggested for extrapolation of relative survival within life-table data, by assuming that the excess mortality has reached zero (statistical cure) or has stabilized to a constant. We propose the use of flexible parametric survival models for relative survival, which enables estimating the loss in expectation of life on individual level data by making these assumptions or by extrapolating the estimated linear trend at the end of follow-up. We have evaluated the extrapolation from this model using data on four types of cancer, and the results agree well with observed data. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Meta-analyses of randomized controlled trials (RCTs) provide the highest level of evidence regarding the effectiveness of interventions and as such underpin much of evidence-based medicine. Despite this, meta-analyses are usually produced as observational by-products of the existing literature, with no formal consideration of future meta-analyses when individual trials are being designed. Basing the sample size of a new trial on the results of an updated meta-analysis which will include it, may sometimes make more sense than powering the trial in isolation. A framework for sample size calculation for a future RCT based on the results of a meta-analysis of the existing evidence is presented. Both fixed and random effect approaches are explored through an example. Bayesian Markov Chain Monte Carlo simulation modelling is used for the random effects model since it has computational advantages over the classical approach. Several criteria on which to base inference and hence power are considered. The prior expectation of the power is averaged over the prior distribution for the unknown true treatment effect. An extension to the framework allowing for consideration of the design for a series of new trials is also presented. Results suggest that power can be highly dependent on the statistical model used to meta-analyse the data and even very large studies may have little impact on a meta-analysis when there is considerable between study heterogeneity. This raises issues regarding the appropriateness of the use of random effect models when designing and drawing inferences across a series of studies. [ABSTRACT FROM AUTHOR]

A genetic model-free method for the meta-analysis of genetic association studies is described that estimates the mode of inheritance from the data rather than assuming that it is known. For a bi-allelic polymorphism, with G as risk allele and g as wild-type, the genetic model depends on the ratio of the two log odds ratios, lambda = log OR(Gg)/log OR(GG), where OR(GG) compares GG with gg and OR(Gg) compares Gg with gg. Modelling log OR(GG) as a random effect creates a hierarchical model that can be implemented within a Bayesian framework. In Bayesian modelling, vague prior distributions have to be specified for all unknown parameters when no external information is available. When the data are sparse even supposedly vague prior distributions may have an influence on the posterior estimates. We investigate the impact of different vague prior distributions for the between-study standard deviation of log OR(GG) and for lambda, by considering three published meta-analyses and associated simulations. Our results show that depending on the characteristics of the meta-analysis the results may indeed be sensitive to the choice of vague prior distribution for either parameter. Genetic association studies usually use a case-control design that should be analysed by the corresponding retrospective likelihood. However, under some circumstances the prospective likelihood has been shown to produce identical results and it is usually preferred for its simplicity. In our meta-analyses the two likelihoods give very similar results. [ABSTRACT FROM AUTHOR]