Bayesian pairwise meta-analysis of time-to-event outcomes in the presence of non-proportional hazards: A simulation study of flexible parametric, piecewise exponential and fractional polynomial models.

BACKGROUND: Traditionally, meta-analysis of time-to-event outcomes reports a single pooled hazard ratio assuming proportional hazards (PH). For health technology assessment evaluations, hazard ratios are frequently extrapolated across a lifetime horizon. However, when treatment effects vary over time, an assumption of PH is not always valid. The Royston-Parmar (RP), piecewise exponential (PE), and fractional polynomial (FP) models can accommodate non-PH and provide plausible extrapolations of survival curves beyond observed data. METHODS: Simulation study to assess and compare the performance of RP, PE, and FP models in a Bayesian framework estimating restricted mean survival time difference (RMSTD) at 50 years from a pairwise meta-analysis with evidence of non-PH. Individual patient data were generated from a mixture Weibull distribution. Twelve scenarios were considered varying the amount of follow-up data, number of trials in a meta-analysis, non-PH interaction coefficient, and prior distributions. Performance was assessed through bias and mean squared error. Models were applied to a metastatic breast cancer example. RESULTS: FP models performed best when the non-PH interaction coefficient was 0.2. RP models performed best in scenarios with complete follow-up data. PE models performed well on average across all scenarios. In the metastatic breast cancer example, RMSTD at 50-years ranged from -14.6 to 8.48 months. CONCLUSIONS: Synthesis of time-to-event outcomes and estimation of RMSTD in the presence of non-PH can be challenging and computationally intensive. Different approaches make different assumptions regarding extrapolation and sensitivity analyses varying key assumptions are essential to check the robustness of conclusions to different assumptions for the underlying survival function.

Early transfusion patterns improve the Molecular International Prognostic Scoring System (IPSS-M) prediction in myelodysplastic syndromes.

BACKGROUND: The Molecular International Prognostic Scoring System (IPSS-M) is the new gold standard for diagnostic outcome prediction in patients with myelodysplastic syndromes (MDS). This study was designed to assess the additive prognostic impact of dynamic transfusion parameters during early follow-up. METHODS: We retrieved complete transfusion data from 677 adult Swedish MDS patients included in the IPSS-M cohort. Time-dependent erythrocyte transfusion dependency (E-TD) was added to IPSS-M features and analyzed regarding overall survival and leukemic transformation (acute myeloid leukemia). A multistate Markov model was applied to assess the prognostic value of early changes in transfusion patterns. RESULTS: Specific clinical and genetic features were predicted for diagnostic and time-dependent transfusion patterns. Importantly, transfusion state both at diagnosis and within the first year strongly predicts outcomes in both lower (LR) and higher-risk (HR) MDSs. In multivariable analysis, 8-month landmark E-TD predicted shorter survival independently of IPSS-M (p < 0.001). A predictive model based on IPSS-M and 8-month landmark E-TD performed significantly better than a model including only IPSS-M. Similar trends were observed in an independent validation cohort (n = 218). Early transfusion patterns impacted both future transfusion requirements and outcomes in a multistate Markov model. CONCLUSION: The transfusion requirement is a robust and available clinical parameter incorporating the effects of first-line management. In MDS, it provides dynamic risk information independently of diagnostic IPSS-M and, in particular, clinical guidance to LR MDS patients eligible for potentially curative therapeutic intervention.

Multiple imputation strategies for missing event times in a multi-state model analysis.

In clinical studies, multi-state model (MSM) analysis is often used to describe the sequence of events that patients experience, enabling better understanding of disease progression. A complicating factor in many MSM studies is that the exact event times may not be known. Motivated by a real dataset of patients who received stem cell transplants, we considered the setting in which some event times were exactly observed and some were missing. In our setting, there was little information about the time intervals in which the missing event times occurred and missingness depended on the event type, given the analysis model covariates. These additional challenges limited the usefulness of some missing data methods (maximum likelihood, complete case analysis, and inverse probability weighting). We show that multiple imputation (MI) of event times can perform well in this setting. MI is a flexible method that can be used with any complete data analysis model. Through an extensive simulation study, we show that MI by predictive mean matching (PMM), in which sampling is from a set of observed times without reliance on a specific parametric distribution, has little bias when event times are missing at random, conditional on the observed data. Applying PMM separately for each sub-group of patients with a different pathway through the MSM tends to further reduce bias and improve precision. We recommend MI using PMM methods when performing MSM analysis with Markov models and partially observed event times.

Modeling the multi-state natural history of rare diseases with heterogeneous individual patient data: A simulation study.

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

Exploring different research questions via complex multi-state models when using registry-based repeated prescriptions of antidepressants in women with breast cancer and a matched population comparison group.

BACKGROUND: Multi-state models are used to study several clinically meaningful research questions. Depending on the research question of interest and the information contained in the data, different multi-state structures and modelling choices can be applied. We aim to explore different research questions using a series of multi-state models of increasing complexity when studying repeated prescriptions data, while also evaluating different modelling choices. METHODS: We develop a series of research questions regarding the probability of being under antidepressant medication across time using multi-state models, among Swedish women diagnosed with breast cancer (n = 18,313) and an age-matched population comparison group of cancer-free women (n = 92,454) using a register-based database (Breast Cancer Data Base Sweden 2.0). Research questions were formulated ranging from simple to more composite ones. Depending on the research question, multi-state models were built with structures ranging from simpler ones, like single-event survival analysis and competing risks, up to complex bidirectional and recurrent multi-state structures that take into account the recurring start and stop of medication. We also investigate modelling choices, such as choosing a time-scale for the transition rates and borrowing information across transitions. RESULTS: Each structure has its own utility and answers a specific research question. However, the more complex structures (bidirectional, recurrent) enable accounting for the intermittent nature of prescribed medication data. These structures deliver estimates of the probability of being under medication and total time spent under medication over the follow-up period. Sensitivity analyses over different definitions of the medication cycle and different choices of timescale when modelling the transition intensity rates show that the estimates of total probabilities of being in a medication cycle over follow-up derived from the complex structures are quite stable. CONCLUSIONS: Each research question requires the definition of an appropriate multi-state structure, with more composite ones requiring such an increase in the complexity of the multi-state structure. When a research question is related with an outcome of interest that repeatedly changes over time, such as the medication status based on prescribed medication, the use of novel multi-state models of adequate complexity coupled with sensible modelling choices can successfully address composite, more realistic research questions.

Survival by First-line Treatment Type and Timing of Progression Among Follicular Lymphoma Patients: A National Population-based Study in Sweden.

In follicular lymphoma (FL), progression of disease ≤24 months (POD24) has emerged as an important prognostic marker for overall survival (OS). We aimed to investigate survival more broadly by timing of progression and treatment in a national population-based setting. We identified 948 stage II-IV indolent FL patients in the Swedish Lymphoma Register diagnosed 2007-2014 who received first-line systemic therapy, followed through 2020. Hazard ratios (HRs) with 95% confidence intervals (CIs) were estimated by first POD at any time during follow-up using Cox regression. OS was predicted by POD using an illness-death model. During a median follow-up of 6.1 years (IQR: 3.5-8.4), 414 patients experienced POD (44%), of which 270 (65%) occurred ≤24 months. POD was represented by a transformation in 15% of cases. Compared to progression-free patients, POD increased all-cause mortality across treatments, but less so among patients treated with rituximab(R)-single (HR = 4.54, 95% CI: 2.76-7.47) than R-chemotherapy (HR = 8.17, 95% CI: 6.09-10.94). The effect of POD was similar following R-CHOP (HR = 8.97, 95% CI: 6.14-13.10) and BR (HR = 10.29, 95% CI: 5.60-18.91). The negative impact of POD on survival remained for progressions up to 5 years after R-chemotherapy, but was restricted to 2 years after R-single. After R-chemotherapy, the 5-year OS conditional on POD occurring at 12, 24, and 60 months was 34%, 46%, and 57% respectively, versus 78%, 82%, and 83% if progression-free. To conclude, POD before but also beyond 24 months is associated with worse survival, illustrating the need for individualized management for optimal care of FL patients.

A flexible parametric accelerated failure time model and the extension to time-dependent acceleration factors.

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, that is, 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 data set of patients with breast cancer. Finally, we provide highly efficient, user-friendly Stata, and R software packages.

A scoping methodological review of simulation studies comparing statistical and machine learning approaches to risk prediction for time-to-event data.

BACKGROUND: There is substantial interest in the adaptation and application of so-called machine learning approaches to prognostic modelling of censored time-to-event data. These methods must be compared and evaluated against existing methods in a variety of scenarios to determine their predictive performance. A scoping review of how machine learning methods have been compared to traditional survival models is important to identify the comparisons that have been made and issues where they are lacking, biased towards one approach or misleading. METHODS: We conducted a scoping review of research articles published between 1 January 2000 and 2 December 2020 using PubMed. Eligible articles were those that used simulation studies to compare statistical and machine learning methods for risk prediction with a time-to-event outcome in a medical/healthcare setting. We focus on data-generating mechanisms (DGMs), the methods that have been compared, the estimands of the simulation studies, and the performance measures used to evaluate them. RESULTS: A total of ten articles were identified as eligible for the review. Six of the articles evaluated a method that was developed by the authors, four of which were machine learning methods, and the results almost always stated that this developed method's performance was equivalent to or better than the other methods compared. Comparisons were often biased towards the novel approach, with the majority only comparing against a basic Cox proportional hazards model, and in scenarios where it is clear it would not perform well. In many of the articles reviewed, key information was unclear, such as the number of simulation repetitions and how performance measures were calculated. CONCLUSION: It is vital that method comparisons are unbiased and comprehensive, and this should be the goal even if realising it is difficult. Fully assessing how newly developed methods perform and how they compare to a variety of traditional statistical methods for prognostic modelling is imperative as these methods are already being applied in clinical contexts. Evaluations of the performance and usefulness of recently developed methods for risk prediction should be continued and reporting standards improved as these methods become increasingly popular.

On the choice of timescale for other cause mortality in a competing risk setting using flexible parametric survival models.

In competing risks settings where the events are death due to cancer and death due to other causes, it is common practice to use time since diagnosis as the timescale for all competing events. However, attained age has been proposed as a more natural choice of timescale for modeling other cause mortality. We examine the choice of using time since diagnosis versus attained age as the timescale when modeling other cause mortality, assuming that the hazard rate is a function of attained age, and how this choice can influence the cumulative incidence functions ( C I F $CIF$ s) derived using flexible parametric survival models. An initial analysis on the colon cancer data from the population-based Swedish Cancer Register indicates such an influence. A simulation study is conducted in order to assess the impact of the choice of timescale for other cause mortality on the bias of the estimated C I F s $CIFs$ and how different factors may influence the bias. We also use regression standardization methods in order to obtain marginal C I F $CIF$ estimates. Using time since diagnosis as the timescale for all competing events leads to a low degree of bias in C I F $CIF$ for cancer mortality ( C I F 1 $CIF_{1}$ ) under all approaches. It also leads to a low degree of bias in C I F $CIF$ for other cause mortality ( C I F 2 $CIF_{2}$ ), provided that the effect of age at diagnosis is included in the model with sufficient flexibility, with higher bias under scenarios where a covariate has a time-varying effect on the hazard rate for other cause mortality on the attained age scale.

Challenges of modelling approaches for network meta-analysis of time-to-event outcomes in the presence of non-proportional hazards to aid decision making: Application to a melanoma network.

BACKGROUND: Synthesis of clinical effectiveness from multiple trials is a well-established component of decision-making. Time-to-event outcomes are often synthesised using the Cox proportional hazards model assuming a constant hazard ratio over time. However, with an increasing proportion of trials reporting treatment effects where hazard ratios vary over time and with differing lengths of follow-up across trials, alternative synthesis methods are needed. OBJECTIVES: To compare and contrast five modelling approaches for synthesis of time-to-event outcomes and provide guidance on key considerations for choosing between the modelling approaches. METHODS: The Cox proportional hazards model and five other methods of estimating treatment effects from time-to-event outcomes, which relax the proportional hazards assumption, were applied to a network of melanoma trials reporting overall survival: restricted mean survival time, generalised gamma, piecewise exponential, fractional polynomial and Royston-Parmar models. RESULTS: All models fitted the melanoma network acceptably well. However, there were important differences in extrapolations of the survival curve and interpretability of the modelling constraints demonstrating the potential for different conclusions from different modelling approaches. CONCLUSION: The restricted mean survival time, generalised gamma, piecewise exponential, fractional polynomial and Royston-Parmar models can accommodate non-proportional hazards and differing lengths of trial follow-up within a network meta-analysis of time-to-event outcomes. We recommend that model choice is informed using available and relevant prior knowledge, model transparency, graphically comparing survival curves alongside observed data to aid consideration of the reliability of the survival estimates, and consideration of how the treatment effect estimates can be incorporated within a decision model.

Development of a dynamic interactive web tool to enhance understanding of multi-state model analyses: MSMplus.

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

Unmarried or less-educated patients with mantle cell lymphoma are less likely to undergo a transplant, leading to lower survival.

It is unknown how many mantle cell lymphoma (MCL) patients undergo consolidation with autologous hematopoietic cell transplantation (AHCT), and the reasons governing the decision, are also unknown. The prognostic impact of omitting AHCT is also understudied. We identified all MCL patients diagnosed from 2000 to 2014, aged 18 to 65 years, in the Swedish Lymphoma Register. Odds ratios (ORs) and 95% confidence intervals (CIs) from logistic regression models were used to compare the likelihood of AHCT within 18 months of diagnosis. All-cause mortality was compared between patients treated with/without AHCT using hazard ratios (HRs) and 95% CIs estimated from Cox regression models. Probabilities of being in each of the following states: alive without AHCT, alive with AHCT, dead before AHCT, and dead after AHCT, were estimated over time from an illness-death model. Among 369 patients, 148 (40%) were not treated with AHCT within 18 months. Compared with married patients, never married and divorced patients had lower likelihood of undergoing AHCT, as had patients with lower educational level, and comorbid patients. Receiving AHCT was associated with reduced all-cause mortality (HR = 0.58, 95% CI: 0.40-0.85). Transplantation-related mortality was low (2%). MCL patients not receiving an AHCT had an increased mortality rate, and furthermore, an undue concern about performing an AHCT in certain societal groups was seen. Improvements in supportive functions potentially increasing the likelihood of tolerating an AHCT and introduction of more tolerable treatments for these groups are needed.

A multistate model incorporating estimation of excess hazards and multiple time scales.

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.

Multiple imputation strategies for a bounded outcome variable in a competing risks analysis.

In patient follow-up studies, events of interest may take place between periodic clinical assessments and so the exact time of onset is not observed. Such events are known as "bounded" or "interval-censored." Methods for handling such events can be categorized as either (i) applying multiple imputation (MI) strategies or (ii) taking a full likelihood-based (LB) approach. We focused on MI strategies, rather than LB methods, because of their flexibility. We evaluated MI strategies for bounded event times in a competing risks analysis, examining the extent to which interval boundaries, features of the data distribution and substantive analysis model are accounted for in the imputation model. Candidate imputation models were predictive mean matching (PMM); log-normal regression with postimputation back-transformation; normal regression with and without restrictions on the imputed values and Delord and Genin's method based on sampling from the cumulative incidence function. We used a simulation study to compare MI methods and one LB method when data were missing at random and missing not at random, also varying the proportion of missing data, and then applied the methods to a hematopoietic stem cell transplantation dataset. We found that cumulative incidence and median event time estimation were sensitive to model misspecification. In a competing risks analysis, we found that it is more important to account for features of the data distribution than to restrict imputed values based on interval boundaries or to ensure compatibility with the substantive analysis by sampling from the cumulative incidence function. We recommend MI by type 1 PMM.

Relaxing the assumption of constant transition rates in a multi-state model in hospital epidemiology.

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

INTEREST: INteractive Tool for Exploring REsults from Simulation sTudies.

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, readers to explore them freely.

Assessing the Course of Organ Dysfunction Using Joint Longitudinal and Time-to-Event Modeling in the Vasopressin and Septic Shock Trial.

Non-mortality septic shock outcomes (e.g., Sequential Organ Failure Assessment score) are important clinical endpoints in pivotal sepsis trials. However, comparisons of observed longitudinal non-mortality outcomes between study groups can be biased if death is unequal between study groups or is associated with an intervention (i.e., informative censoring). We compared the effects of vasopressin versus norepinephrine on the Sequential Organ Failure Assessment score in the Vasopressin and Septic Shock Trial to illustrate the use of joint modeling to help minimize potential bias from informative censoring. DESIGN: Secondary analysis of the Vasopressin and Septic Shock Trial data. SETTING: Twenty-seven ICUs in Canada, Australia, and United States. SUBJECTS: Seven hundred sixty-three participants with septic shock who received blinded vasopressin (n = 389) or norepinephrine infusions (n = 374). MEASUREMENTS AND MAIN RESULTS: Sequential Organ Failure Assessment scores were calculated daily until discharge, death, or day 28 after randomization. Mortality was numerically higher in the norepinephrine arm (28 d mortality of 39% vs 35%; p = 0.25), and there was a positive association between higher Sequential Organ Failure Assessment scores and patient mortality, characteristics that suggest a potential for bias from informative censoring of Sequential Organ Failure Assessment scores by death. The best-fitting joint longitudinal (i.e., linear mixed-effects model) and survival (i.e., Cox proportional hazards model for the time-to-death) model showed that norepinephrine was associated with a more rapid improvement in the total Sequential Organ Failure Assessment score through day 4, and then the daily Sequential Organ Failure Assessment scores converged and overlapped for the remainder of the study period. CONCLUSIONS: Short-term reversal of organ dysfunction occurred more rapidly with norepinephrine compared with vasopressin, although differences between study arms did not persist after day 4. Joint models are an accessible methodology that could be used in critical care trials to assess the effects of interventions on the longitudinal progression of key outcomes (e.g., organ dysfunction, biomarkers, or quality of life) that may be informatively truncated by death or other censoring events.

Dynamic assessment of venous thromboembolism risk in patients with cancer by longitudinal D-Dimer analysis: A prospective study.

BACKGROUND: Venous thromboembolism (VTE) is a frequent complication of cancer. Elevated D-dimer is associated with an increased risk of cancer-associated VTE. Whether changes in D-dimer over time harbor additional prognostic information that may be exploited clinically for dynamic prediction of VTE is unclear. OBJECTIVES: To explore the potential role of longitudinal D-dimer trajectories for personalized prediction of cancer-associated VTE. PATIENTS/METHODS: A total of 167 patients with active malignancy were prospectively enrolled (gastrointestinal: n = 59 [35%], lung: n = 56 [34%], brain: n = 50 [30%], others: n = 2 [1%]; metastatic disease: n = 74 [44%]). D-dimer (median = 0.8 µg/mL [25th-75th percentile: 0.4-2.0]) was measured at baseline and during 602 monthly follow-up visits. Joint models of longitudinal and time-to-event data were implemented to quantify the association between D-dimer trajectories and prospective risk of VTE. RESULTS: VTE occurred in 20 patients (250-day VTE risk = 12.1%, 95% confidence interval [CI], 7.8-18.5). D-dimer increased by 34%/month (0.47 µg/mL/month, 95% CI, 0.22-0.72, P < .0001) in patients who developed VTE, but remained constant in patients who did not develop VTE (change/month = -0.06 µg/mL, 95% CI, -0.15 to 0.02, P = .121). In joint modeling, a doubling of the D-dimer trajectory was associated with a 2.8-fold increase in the risk of VTE (hazard ratio = 2.78, 95% CI, 1.69-4.58, P < .0001). This finding was independent of established VTE risk factors. Highly personalized, dynamic predictions of VTE conditional on individual patients' D-dimer trajectories could be obtained. CONCLUSIONS: D-dimer increases before the onset of cancer-associated VTE, but remains constant over time in patients without VTE. This study represents proof-of-concept that longitudinal trajectories of D-Dimer may advance the personalized assessment of VTE risk in the oncologic setting.

Mixed-effects models for health care longitudinal data with an informative visiting process: A Monte Carlo simulation study.

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 health care data, such assumptions unlikely hold. 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.

Impact of model misspecification in shared frailty survival models.

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 modeled by including a subject-specific (or cluster-specific) frailty term that follows a given distribution (eg, gamma or lognormal). Despite that, in the context of parametric frailty models, little is known about the impact of misspecifying the baseline hazard or 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, whereas misspecifying the latter affects absolute risk estimates and measures of heterogeneity.