Search

Stepped wedge cluster-randomized trial (CRTs) designs randomize clusters of individuals to intervention sequences, ensuring that every cluster eventually transitions from a control period to receive the intervention under study by the end of the study period. The analysis of stepped wedge CRTs is usually more complex than parallel-arm CRTs due to more complex intra-cluster correlation structures. A further challenge in the analysis of closed-cohort stepped wedge CRTs, which follow groups of individuals enrolled in each period longitudinally, is the occurrence of dropout. This is particularly problematic in studies of individuals at high risk for mortality, which causes non-ignorable missing outcomes. If not appropriately addressed, missing outcomes from death will erode statistical power, at best, and bias treatment effect estimates, at worst. Joint longitudinal-survival models can accommodate informative dropout and missingness patterns in longitudinal studies. Specifically, within the joint longitudinal-survival modeling framework, one directly models the dropout process via a time-to-event submodel together with the longitudinal outcome of interest. The two submodels are then linked using a variety of possible association structures. This work extends linear mixed-effects models by jointly modeling the dropout process to accommodate informative missing outcome data in closed-cohort stepped wedge CRTs. We focus on constant intervention and general time-on-treatment effect parametrizations for the longitudinal submodel and study the performance of the proposed methodology using Monte Carlo simulation under several data-generating scenarios. We illustrate the methodology in practice by reanalyzing data from the `Frail Older Adults: Care in Transition' (ACT) trial, a stepped wedge CRT of a multifaceted geriatric care model versus usual care in 35 primary care practices in the Netherlands.

In this paper I describe some substantial extensions to the survsim command for simulating survival data. survsim can now simulate survival data from a parametric distribution, a custom/user-defined distribution, from a fitted merlin model, from a specified cause-specific hazards competing risks model, or from a specified general multi-state model (with multiple timescales). Left truncation (delayed entry) is now also available for all settings. I illustrate the command with some examples, demonstrating the huge flexibility that can be used to better evaluate statistical methods.

Multi-state survival analysis considers several potential events of interest along a disease pathway. Such analyses are crucial to model complex patient trajectories and are increasingly being used in epidemiological and health economic settings. Multi-state models often make the Markov assumption, whereby an individual's future trajectory is dependent only upon their present state, not their past. In reality, there may be transitional dependence upon either previous events and/or more than one timescale, for example time since entry to the current or previous state(s). The aim of this study was to develop an illness-death Weibull model allowing for multiple timescales to impact the future risk of death. Following this, we evaluated the performance of the multiple timescale model against a Markov illness-death model in a set of plausible simulation scenarios when the Markov assumption was violated. Guided by a study in breast cancer, data were simulated from Weibull baseline distributions, with hazard functions dependent on single and multiple timescales. Markov and non-Markov models were fitted to account for/ignore the underlying data structure. Ignoring the presence of multiple timescales led to bias in underlying transition rates between states and associated covariate effects, while transition probabilities and lengths of stay were fairly robustly estimated. Further work may be needed to evaluate different estimands or more complex multi-state models. Software implementations in Stata are also described for simulating and estimating multiple timescale multi-state models.

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. Multi-state 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, by allowing is to directly quantify the excess risk. This paper proposes a combination of these two frameworks, providing one approach to address (1)-(3). Using recently developed methods in multi-state modeling, we incorporate estimation of excess hazards into a multi-state 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.

The R package merlin performs flexible joint modelling of hierarchical multi-outcome data. Increasingly, multiple longitudinal biomarker measurements, possibly censored time-to-event outcomes and baseline characteristics are available. However, there is limited software that allows all of this information to be incorporated into one model. In this paper, we present merlin which allows for the estimation of models with unlimited numbers of continuous, binary, count and time-to-event outcomes, with unlimited levels of nested random effects. A wide variety of link functions, including the expected value, the gradient and shared random effects, are available in order to link the different outcomes in a biologically plausible way. The accompanying predict.merlin function allows for individual and population level predictions to be made from even the most complex models. There is the option to specify user-defined families, making merlin ideal for methodological research. The flexibility of merlin is illustrated using an example in patients followed up after heart valve replacement, beginning with a linear model, and finishing with a joint multiple longitudinal and competing risks survival model.

Accelerated failure time (AFT) models are used widely in medical research, though to a much lesser extent than proportional hazards models. In an AFT model, the effect of covariates act to accelerate or decelerate the time to event of interest, i.e. shorten or extend the time to event. Commonly used parametric AFT models are limited in the underlying shapes that they can capture. In this article, we propose a general parametric AFT model, and in particular concentrate on using restricted cubic splines to model the baseline to provide substantial flexibility. We then extend the model to accommodate time-dependent acceleration factors. Delayed entry is also allowed, and hence, time-dependent covariates. We evaluate the proposed model through simulation, showing substantial improvements compared to standard parametric AFT models. We also show analytically and through simulations that the AFT models are collapsible, suggesting that this model class will be well suited to causal inference. We illustrate the methods with a dataset of patients with breast cancer. User friendly Stata and R software packages are provided.

Simulation studies allow us to explore the properties of statistical methods. They provide a powerful tool with a multiplicity of aims; among others: evaluating and comparing new or existing statistical methods, assessing violations of modelling assumptions, helping with the understanding of statistical concepts, and supporting the design of clinical trials. The increased availability of powerful computational tools and usable software has contributed to the rise of simulation studies in the current literature. However, simulation studies involve increasingly complex designs, making it difficult to provide all relevant results clearly. Dissemination of results plays a focal role in simulation studies: it can drive applied analysts to use methods that have been shown to perform well in their settings, guide researchers to develop new methods in a promising direction, and provide insights into less established methods. It is crucial that we can digest relevant results of simulation studies. Therefore, we developed INTEREST: an INteractive Tool for Exploring REsults from Simulation sTudies. The tool has been developed using the Shiny framework in R and is available as a web app or as a standalone package. It requires uploading a tidy format dataset with the results of a simulation study in R, Stata, SAS, SPSS, or comma-separated format. A variety of performance measures are estimated automatically along with Monte Carlo standard errors; results and performance summaries are displayed both in tabular and graphical fashion, with a wide variety of available plots. Consequently, the reader can focus on simulation parameters and estimands of most interest. In conclusion, INTEREST can facilitate the investigation of results from simulation studies and supplement the reporting of results, allowing researchers to share detailed results from their simulations and readers to explore them freely.

Survival models incorporating random effects to account for unmeasured heterogeneity are being increasingly used in biostatistical and applied research. Specifically, unmeasured covariates whose lack of inclusion in the model would lead to biased, inefficient results are commonly modelled by including a subject-specific (or cluster-specific) frailty term that follows a given distribution (e.g. Gamma or log-Normal). Despite that, in the context of parametric frailty models little is known about the impact of misspecifying the baseline hazard, the frailty distribution, or both. Therefore, our aim is to quantify the impact of such misspecification in a wide variety of clinically plausible scenarios via Monte Carlo simulation, using open source software readily available to applied researchers. We generate clustered survival data assuming various baseline hazard functions, including mixture distributions with turning points, and assess the impact of sample size, variance of the frailty, baseline hazard function, and frailty distribution. Models compared include standard parametric distributions and more flexible spline-based approaches; we also included semiparametric Cox models. The resulting bias can be clinically relevant. In conclusion, we highlight the importance of fitting models that are flexible enough and the importance of assessing model fit. We illustrate our conclusions with two applications using data on diabetic retinopathy and bladder cancer. Our results show the importance of assessing model fit with respect to the baseline hazard function and the distribution of the frailty: misspecifying the former leads to biased relative and absolute risk estimates while misspecifying the latter affects absolute risk estimates and measures of heterogeneity.

Electronic health records are being increasingly used in medical research to answer more relevant and detailed clinical questions; however, they pose new and significant methodological challenges. For instance, observation times are likely correlated with the underlying disease severity: patients with worse conditions utilise health care more and may have worse biomarker values recorded. Traditional methods for analysing longitudinal data assume independence between observation times and disease severity; yet, with healthcare data such assumptions unlikely holds. Through Monte Carlo simulation, we compare different analytical approaches proposed to account for an informative visiting process to assess whether they lead to unbiased results. Furthermore, we formalise a joint model for the observation process and the longitudinal outcome within an extended joint modelling framework. We illustrate our results using data from a pragmatic trial on enhanced care for individuals with chronic kidney disease, and we introduce user-friendly software that can be used to fit the joint model for the observation process and a longitudinal outcome.

merlin can do a lot of things. From simple stuff, like fitting a linear regression or a Weibull survival model, to a three-level logistic mixed effects model, or a multivariate joint model of multiple longitudinal outcomes (of different types) and a recurrent event and survival with non-linear effects...the list is rather endless. merlin can do things I haven't even thought of yet. I'll take a single dataset, and attempt to show you the full range of capabilities of merlin, and discuss some future directions for the implementation in Stata., Comment: Submitted to the Stata Journal

Joint modelling of longitudinal and time-to-event data has received much attention recently. Increasingly, extensions to standard joint modelling approaches are being proposed to handle complex data structures commonly encountered in applied research. In this paper we propose a joint model for hierarchical longitudinal and time-to-event data. Our motivating application explores the association between tumor burden and progression-free survival in non-small cell lung cancer patients. We define tumor burden as a function of the sizes of target lesions clustered within a patient. Since a patient may have more than one lesion, and each lesion is tracked over time, the data have a three-level hierarchical structure: repeated measurements taken at time points (level 1) clustered within lesions (level 2) within patients (level 3). We jointly model the lesion-specific longitudinal trajectories and patient-specific risk of death or disease progression by specifying novel association structures that combine information across lower level clusters (e.g. lesions) into patient-level summaries (e.g. tumor burden). We provide user-friendly software for fitting the model under a Bayesian framework. Lastly, we discuss alternative situations in which additional clustering factor(s) occur at a level higher in the hierarchy than the patient-level, since this has implications for the model formulation., Comment: 35 pages, 3 figures, 2 tables

Simulation studies are computer experiments that involve creating data by pseudorandom sampling. The key strength of simulation studies is the ability to understand the behaviour of statistical methods because some 'truth' (usually some parameter/s of interest) is known from the process of generating the data. This allows us to consider properties of methods, such as bias. While widely used, simulation studies are often poorly designed, analysed and reported. This tutorial outlines the rationale for using simulation studies and offers guidance for design, execution, analysis, reporting and presentation. In particular, this tutorial provides: a structured approach for planning and reporting simulation studies, which involves defining aims, data-generating mechanisms, estimands, methods and performance measures ('ADEMP'); coherent terminology for simulation studies; guidance on coding simulation studies; a critical discussion of key performance measures and their estimation; guidance on structuring tabular and graphical presentation of results; and new graphical presentations. With a view to describing recent practice, we review 100 articles taken from Volume 34 of Statistics in Medicine that included at least one simulation study and identify areas for improvement., Comment: 31 pages, 9 figures (2 in appendix), 8 tables (1 in appendix)

Multivariate data occurs in a wide range of fields, with ever more flexible model specifications being proposed, often within a multivariate generalised linear mixed effects (MGLME) framework. In this article, we describe an extended framework, encompassing multiple outcomes of any type, each of which could be repeatedly measured (longitudinal), with any number of levels, and with any number of random effects at each level. Many standard distributions are described, as well as non-standard user-defined non-linear models. The extension focuses on a complex linear predictor for each outcome model, allowing sharing and linking between outcome models in an extremely flexible way, either by linking random effects directly, or the expected value of one outcome (or function of it) within the linear predictor of another. Non-linear and time-dependent effects are also seamlessly incorporated to the linear predictor through the use of splines or fractional polynomials. We further propose level-specific random effect distributions and numerical integration techniques to improve usability, relaxing the normally distributed random effects assumption to allow multivariate $t$-distributed random effects. We consider some special cases of the general framework, describing some new models in the fields of clustered survival data, joint longitudinal-survival models, and discuss various potential uses of the implementation. User friendly, and easily extendable, software is provided.

In this article, I present the user written stmixed command for the fitting of multilevel survival models, which serves as both an alternative to Stata's official mestreg, and a complimentary program with substantial extensions. stmixed can fit multilevel survival models with any number of levels and random effects at each level, including flexible spline-based approaches (such as Royston-Parmar and the log hazard equivalent) or user-defined hazard models. Simple or complex time-dependent effects can be included, as well as the addition of expected mortality for a relative survival model. Left-truncation/delayed entry can be used and t-distributed random effects are provided as an alternative to Gaussian random effects. The methods are illustrated with a commonly used dataset of patients with kidney disease suffering recurrent infections, and a simulated example, illustrating a simple approach to simulating clustered survival data using survsim (Crowther and Lambert 2012, 2013). stmixed is part of the merlin family (Crowther 2017, 2018).