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ABSTRACT Polygenic risk scores (PRS) aim to predict a trait from genetic information, relying on common genetic variants with low to medium effect sizes. As genotype data are high‐dimensional in nature, it is crucial to develop methods that can be applied to large‐scale data (large n$$ n $$ and large p$$ p $$). Many PRS tools aggregate univariate summary statistics from genome‐wide association studies into a single score. Recent advancements allow simultaneous modeling of variant effects from individual‐level genotype data. In this context, we introduced snpboost, an algorithm that applies statistical boosting on individual‐level genotype data to estimate PRS via multivariable regression models. By processing variants iteratively in batches, snpboost can deal with large‐scale cohort data. Having solved the technical obstacles due to data dimensionality, the methodological scope can now be broadened—focusing on key objectives for the clinical application of PRS. Similar to most methods in this context, snpboost has, so far, been restricted to quantitative and binary traits. Now, we incorporate more advanced alternatives—targeted to the particular aim and outcome. Adapting the loss function extends the snpboost framework to further data situations such as time‐to‐event and count data. Furthermore, alternative loss functions for continuous outcomes allow us to focus not only on the mean of the conditional distribution but also on other aspects that may be more helpful in the risk stratification of individual patients and can quantify prediction uncertainty, for example, median or quantile regression. This work enhances PRS fitting across multiple model classes previously unfeasible for this data type. [ABSTRACT FROM AUTHOR]

A clinical trial represents a large commitment from all individuals involved and a huge financial obligation given its high cost; therefore, it is wise to make the most of all collected data by learning as much as possible. A multistate model is a generalized framework to describe longitudinal events; multistate hazards models can treat multiple intermediate/final clinical endpoints as outcomes and estimate the impact of covariates simultaneously. Proportional hazards models are fitted (one per transition), which can be used to calculate the absolute risks, that is, the probability of being in a state at a given time, the expected number of visits to a state, and the expected amount of time spent in a state. Three publicly available clinical trial datasets, colon, myeloid, and rhDNase, in the survival package in R were used to showcase the utility of multistate hazards models. In the colon dataset, a very well-known and well-used dataset, we found that the levamisole+fluorouracil treatment extended time in the recurrence-free state more than it extended overall survival, which resulted in less time in the recurrence state, an example of the classic "compression of morbidity." In the myeloid dataset, we found that complete response (CR) is durable, patients who received treatment B have longer sojourn time in CR than patients who received treatment A, while the mutation status does not impact the transition rate to CR but is highly influential on the sojourn time in CR. We also found that more patients in treatment A received transplants without CR, and more patients in treatment B received transplants after CR. In addition, the mutation status is highly influential on the CR to transplant transition rate. The observations that we made on these three datasets would not be possible without multistate models. We want to encourage readers to spend more time to look deeper into clinical trial data. It has a lot more to offer than a simple yes/no answer if only we, the statisticians, are willing to look for it. [ABSTRACT FROM AUTHOR]

Prior distributions, which represent one's belief in the distributions of unknown parameters before observing the data, impact Bayesian inference in a critical and fundamental way. With the ability to incorporate external information from expert opinions or historical datasets, the priors, if specified appropriately, can improve the statistical efficiency of Bayesian inference. In survival analysis, based on the concept of unit information (UI) under parametric models, we propose the unit information Dirichlet process (UIDP) as a new class of nonparametric priors for the underlying distribution of time-to-event data. By deriving the Fisher information in terms of the differential of the cumulative hazard function, the UIDP prior is formulated to match its prior UI with the weighted average of UI in historical datasets and thus can utilize both parametric and nonparametric information provided by historical datasets. With a Markov chain Monte Carlo algorithm, simulations and real data analysis demonstrate that the UIDP prior can adaptively borrow historical information and improve statistical efficiency in survival analysis. [ABSTRACT FROM AUTHOR]

Many clinical trials assess time‐to‐event endpoints. To describe the difference between groups in terms of time to event, we often employ hazard ratios. However, the hazard ratio is only informative in the case of proportional hazards (PHs) over time. There exist many other effect measures that do not require PHs. One of them is the average hazard ratio (AHR). Its core idea is to utilize a time‐dependent weighting function that accounts for time variation. Though propagated in methodological research papers, the AHR is rarely used in practice. To facilitate its application, we unfold approaches for sample size calculation of an AHR test. We assess the reliability of the sample size calculation by extensive simulation studies covering various survival and censoring distributions with proportional as well as nonproportional hazards (N‐PHs). The findings suggest that a simulation‐based sample size calculation approach can be useful for designing clinical trials with N‐PHs. Using the AHR can result in increased statistical power to detect differences between groups with more efficient sample sizes. [ABSTRACT FROM AUTHOR]

Traditional predictive modeling techniques have significantly influenced the analysis of survival times and predictive markers in oncology. However, these models often do not fully address the complexities of cancer data, leading to a noticeable gap in accurately modeling both cancer survival and mortality. The aim of this study is to show a model that offers the best fit for cancer mortality and survival data, thereby improving treatment strategies and patient prognoses. I propose the a New Exponential-Weibull (NEWE) distribution within the New Exponential-Generated (NE-G) class of distributions to enhance oncological analytics with greater accuracy and comprehensiveness. An empirical analysis of Brazilian cancer mortality data is conducted., This data set covers children, head and neck, and cervical cancer. Concurrently, survival time-to-event data for bladder and advanced lung cancers patients are assessed to evaluate the model’s effectiveness. Based on standard metrics, extensive simulation experiments show the Maximum Product of Spacing Estimator as the best of seven-point estimation techniques. The NEWE distribution shows superior modeling capabilities, surpassing traditional models with lower values of Log-likelihood, Cramer-von Mises, and Anderson-Darling and higher Kolmogorov-Smirnov (KS) p-values. The study also discerns the most fitting estimators for distinct types of cancer mortality and survival data. This includes the Right Tail Anderson-Darling for child cancer deaths, the Maximum Product Spacing for head and neck cancer deaths, the Least Squares for cervical cancer deaths, the Weighted Least Squares for bladder cancer survival, and the Anderson-Darling for advanced lung cancer deaths. This shows that the NEWE distribution can be used in a number of different cancers settings. The development and implementation of the NEWE distribution marks a significant advancement in oncological modeling. By analyzing both cancer mortality and survival data with enhanced accuracy and flexibility, this novel approach surpasses traditional models, offering deeper insights into cancer progression and treatment outcomes. As a result, the NEWE distribution equips healthcare professionals with a powerful tool for improving clinical decisions, leading to better prognostic assessments and patient care in cancer treatment.

In observational studies with time‐to‐event outcomes, the g‐formula can be used to estimate a treatment effect in the presence of confounding factors. However, the asymptotic distribution of the corresponding stochastic process is complicated and thus not suitable for deriving confidence intervals or time‐simultaneous confidence bands for the average treatment effect. A common remedy are resampling‐based approximations, with Efron's nonparametric bootstrap being the standard tool in practice. We investigate the large sample properties of three different resampling approaches and prove their asymptotic validity in a setting with time‐to‐event data subject to competing risks. The usage of these approaches is demonstrated by an analysis of the effect of physical activity on the risk of knee replacement among patients with advanced knee osteoarthritis. [ABSTRACT FROM AUTHOR]

There are good reasons to perform a randomized controlled trial (RCT) even in early phases of clinical development. However, the low sample sizes in those settings lead to high variability of the treatment effect estimate. The variability could be reduced by adding external control data if available. For the common setting of suitable subject-level control group data only available from one external (clinical trial or real-world) data source, we evaluate different analysis options for estimating the treatment effect via hazard ratios. The impact of the external control data is usually guided by the level of similarity with the current RCT data. Such level of similarity can be determined via outcome and/or baseline covariate data comparisons. We provide an overview over existing methods, propose a novel option for a combined assessment of outcome and baseline data, and compare a selected set of approaches in a simulation study under varying assumptions regarding observable and unobservable confounder distributions using a time-to-event model. Our various simulation scenarios also reflect the differences between external clinical trial and real-world data. Data combinations via simple outcome-based borrowing or simple propensity score weighting with baseline covariate data are not recommended. Analysis options which conflate outcome and baseline covariate data perform best in our simulation study. [ABSTRACT FROM AUTHOR]

Spatial scan statistics are well‐known methods widely used to detect spatial clusters of events. Furthermore, several spatial scan statistics models have been applied to the spatial analysis of time‐to‐event data. However, these models do not take account of potential correlations between the observations of individuals within the same spatial unit or potential spatial dependence between spatial units. To overcome this problem, we have developed a scan statistic based on a Cox model with shared frailty and that takes account of the spatial dependence between spatial units. In simulation studies, we found that (i) conventional models of spatial scan statistics for time‐to‐event data fail to maintain the type I error in the presence of a correlation between the observations of individuals within the same spatial unit and (ii) our model performed well in the presence of such correlation and spatial dependence. We have applied our method to epidemiological data and the detection of spatial clusters of mortality in patients with end‐stage renal disease in northern France. [ABSTRACT FROM AUTHOR]

Nonparametric covariate adjustment is considered for log-rank-type tests of the treatment effect with right-censored time-to-event data from clinical trials applying covariate-adaptive randomization. Our proposed covariate-adjusted log-rank test has a simple explicit formula and a guaranteed efficiency gain over the unadjusted test. We also show that our proposed test achieves universal applicability in the sense that the same formula of test can be universally applied to simple randomization and all commonly used covariate-adaptive randomization schemes such as the stratified permuted block and the Pocock–Simon minimization, which is not a property enjoyed by the unadjusted log-rank test. Our method is supported by novel asymptotic theory and empirical results for Type-I error and power of tests. [ABSTRACT FROM AUTHOR]

Whenever we send a message via a channel such as E-mail, Facebook, WhatsApp, WeChat, or LinkedIn, we care about the response rate—the probability that our message will receive a response—and the response time—how long it will take to receive a reply. Recent studies have made considerable efforts to model the sending behaviors of messages in social networks with point processes. However, statistical research on modeling response rates and response times on social networks is still lacking. Compared with sending behaviors, which are often determined by the sender's characteristics, response rates and response times further depend on the relationship between the sender and the receiver. Here, we develop a survival mixed membership blockmodel (SMMB) that integrates semiparametric cure rate models with a mixed membership stochastic blockmodel to analyze time-to-event data observed for node pairs in a social network, and we are able to prove its model identifiability without the pure node assumption. We develop a Markov chain Monte Carlo algorithm to conduct posterior inference and select the number of social clusters in the network according to the conditional deviance information criterion. The application of the SMMB to the Enron E-mail corpus offers novel insights into the company's organization and power relations. for this article are available online. [ABSTRACT FROM AUTHOR]

The g-formula can be used to estimate the treatment effect while accounting for confounding bias in observational studies. With regard to time-to-event endpoints, possibly subject to competing risks, the construction of valid pointwise confidence intervals and time-simultaneous confidence bands for the causal risk difference is complicated, however. A convenient solution is to approximate the asymptotic distribution of the corresponding stochastic process by means of resampling approaches. In this paper, we consider three different resampling methods, namely the classical nonparametric bootstrap, the influence function equipped with a resampling approach as well as a martingale-based bootstrap version, the so-called wild bootstrap. For the latter, three sub-versions based on differing distributions of the underlying random multipliers are examined. We set up a simulation study to compare the accuracy of the different techniques, which reveals that the wild bootstrap should in general be preferred if the sample size is moderate and sufficient data on the event of interest have been accrued. For illustration, the resampling methods are further applied to data on the long-term survival in patients with early-stage Hodgkin’s disease. [ABSTRACT FROM AUTHOR]

Many longitudinal studies are designed to monitor participants for major events related to the progression of diseases. Data arising from such longitudinal studies are usually subject to interval censoring since the events are only known to occur between two monitoring visits. In this work, we propose a new method to handle interval‐censored multistate data within a proportional hazards model framework where the hazard rate of events is modeled by a nonparametric function of time and the covariates affect the hazard rate proportionally. The main idea of this method is to simplify the likelihood functions of a discrete‐time multistate model through an approximation and the application of data augmentation techniques, where the assumed presence of censored information facilitates a simpler parameterization. Then the expectation‐maximization algorithm is used to estimate the parameters in the model. The performance of the proposed method is evaluated by numerical studies. Finally, the method is employed to analyze a dataset on tracking the advancement of coronary allograft vasculopathy following heart transplantation. [ABSTRACT FROM AUTHOR]

In recent years, meta-analysis has evolved to a critically important field of Statistics, and has significant applications in Medicine and Health Sciences. In this work we briefly present existing methodologies to conduct meta-analysis along with any discussion and recent developments accompanying them. Undoubtedly, studies brought together in a systematic review will differ in one way or another. This yields a considerable amount of variability, any kind of which may be termed heterogeneity. To this end, reports of meta-analyses commonly present a statistical test of heterogeneity when attempting to establish whether the included studies are indeed similar in terms of the reported output or not. We intend to provide an overview of the topic, discuss the potential sources of heterogeneity commonly met in the literature and provide useful guidelines on how to address this issue and to detect heterogeneity. Moreover, we review the recent developments in the Bayesian approach along with the various graphical tools and statistical software that are currently available to the analyst. In addition, we discuss sensitivity analysis issues and other approaches of understanding the causes of heterogeneity. Finally, we explore heterogeneity in meta-analysis for time to event data in a nutshell, pointing out its unique characteristics. [ABSTRACT FROM AUTHOR]

There are many Bayesian design methods allowing for the incorporation of historical data for sample size determination (SSD) in situations where the outcome in the historical data is the same as the outcome of a new study. However, there is a dearth of methods supporting the incorporation of data from a previously completed clinical trial that investigated the same or similar treatment as the new trial but had a primary outcome that is different. We propose a simulation-based Bayesian SSD framework using the partial-borrowing scale transformed power prior (straPP). The partial-borrowing straPP is developed by applying a novel scale transformation to a traditional power prior on the parameters from the historical data model to make the information better align with the new data model. The scale transformation is based on the assumption that the standardized parameters (i.e., parameters multiplied by the square roots of their respective Fisher information matrices) are equal. To illustrate the method, we present results from simulation studies that use real data from a previously completed clinical trial to design a new clinical trial with a primary time-to-event endpoint. [ABSTRACT FROM AUTHOR]

In non-inferiority (NI) trials with time-to-event data, different types and patterns of censoring may occur, but their impact on trial results is not entirely clear. We investigated the influence of informative and non-informative censoring by conducting extensive simulation studies under the assumption that the NI margin is defined as a maximum acceptable hazard ratio and scenarios typically observed in recent NI trials. We found that while non-informative censoring tends to only affect the power, informative censoring can impact the treatment effect estimates, type I error rate, and power. The magnitude of these effects depends on the between-group differences in the failure and informative censoring risks, as well as the correlation between censoring and failure times, among other factors. The adverse impact of informative censoring was generally decreased with larger NI margins. [ABSTRACT FROM AUTHOR]

Survival models are used to analyze time-to-event data in a variety of disciplines. Proportional hazard models provide interpretable parameter estimates, but proportional hazard assumptions are not always appropriate. Non-parametric models are more flexible but often lack a clear inferential framework. We propose a Bayesian treed hazards partition model that is both flexible and inferential. Inference is obtained through the posterior tree structure and flexibility is preserved by modeling the log-hazard function in each partition using a latent Gaussian process. An efficient reversible jump Markov chain Monte Carlo algorithm is accomplished by marginalizing the parameters in each partition element via a Laplace approximation. Consistency properties for the estimator are established. The method can be used to help determine subgroups as well as prognostic and/or predictive biomarkers in time-to-event data. The method is compared with some existing methods on simulated data and a liver cirrhosis dataset. [ABSTRACT FROM AUTHOR]

When modeling competing risks (CR) survival data, several techniques have been proposed in both the statistical and machine learning literature. State‐of‐the‐art methods have extended classical approaches with more flexible assumptions that can improve predictive performance, allow high‐dimensional data and missing values, among others. Despite this, modern approaches have not been widely employed in applied settings. This article aims to aid the uptake of such methods by providing a condensed compendium of CR survival methods with a unified notation and interpretation across approaches. We highlight available software and, when possible, demonstrate their usage via reproducible R vignettes. Moreover, we discuss two major concerns that can affect benchmark studies in this context: the choice of performance metrics and reproducibility. [ABSTRACT FROM AUTHOR]

Local association measures provide useful insights in time-varying changes in association, especially between time-to-event variables. Such local dependence between two correlated random variables can be measured using the cross ratio function. The cross ratio function is defined as the ratio of conditional hazard functions which have been estimated using Bernstein polynomials before. Alternatively, the cross ratio function can be expressed in terms of (derivatives of) the joint survival function of the two random variables. In this paper, we discuss an alternative Bernstein-based plug-in estimator of the cross ratio function in which each of the ingredients is estimated separately. Next to asymptotic normality of the nonparametric estimator, a simulation study is used to assess its finite-sample performance. Finally, the novel estimator is applied to a real-life data application. [ABSTRACT FROM AUTHOR]

Classical survival models assume homogeneity among the population of individuals who are susceptible to the event of interest. However, in many practical circumstances, there is a certain amount of unobserved heterogeneity that can be caused by a variety of sources, such as environmental or genetic factors. If the heterogeneity is ignored, many issues could arise, including an overestimation of the hazard rate and inaccurate estimates of the regression coefficients. Frailty models are usually used to model the heterogeneity among individuals. In this paper, we propose a novel univariate frailty model. The frailty variable is assumed to follow the Two Parameter Lindley distribution. The maximum likelihood method is used to estimate the model parameters. The baseline hazard functions are assumed to follow Weibull, Exponential, Gompertz, and Pareto distributions, and a simulation study is performed under this assumption. We examine the characteristics of the distribution and assess its performance compared to other distributions that are frequently applied in frailty modeling by using both Nikulin-Rao-Robson and Bagdonavicius-Nikulin goodness-of-fit tests to determine the adequacy of the model. We analyze a fresh medical dataset collected from an emergency hospital in Algeria to evaluate the effectiveness and applicability of the proposed model. [ABSTRACT FROM AUTHOR]

A common practice in clinical trials is to evaluate a treatment effect on an intermediate outcome when the true outcome of interest would be difficult or costly to measure. We consider how to validate intermediate outcomes in a causally‐valid way when the trial outcomes are time‐to‐event. Using counterfactual outcomes, those that would be observed if the counterfactual treatment had been given, the causal association paradigm assesses the relationship of the treatment effect on the surrogate outcome with the treatment effect on the true, primary outcome. In particular, we propose illness‐death models to accommodate the censored and semicompeting risk structure of survival data. The proposed causal version of these models involves estimable and counterfactual frailty terms. Via these multistate models, we characterize what a valid surrogate would look like using a causal effect predictiveness plot. We evaluate the estimation properties of a Bayesian method using Markov chain Monte Carlo and assess the sensitivity of our model assumptions. Our motivating data source is a localized prostate cancer clinical trial where the two survival outcomes are time to distant metastasis and time to death. [ABSTRACT FROM AUTHOR]

In many important applications of precision medicine, the outcome of interest is time to an event (e.g., death, relapse of disease) and the primary goal is to identify the optimal individualized decision rule (IDR) to prolong survival time. Existing work in this area have been mostly focused on estimating the optimal IDR to maximize the restricted mean survival time in the population. We propose a new robust framework for estimating an optimal static or dynamic IDR with time-to-event outcomes based on an easy-to-interpret quantile criterion. The new method does not need to specify an outcome regression model and is robust for heavy-tailed distribution. The estimation problem corresponds to a nonregular M-estimation problem with both finite and infinite-dimensional nuisance parameters. Employing advanced empirical process techniques, we establish the statistical theory of the estimated parameter indexing the optimal IDR. Furthermore, we prove a novel result that the proposed approach can consistently estimate the optimal value function under mild conditions even when the optimal IDR is nonunique, which happens in the challenging setting of exceptional laws. We also propose a smoothed resampling procedure for inference. The proposed methods are implemented in the R-package QTOCen. We demonstrate the performance of the proposed new methods via extensive Monte Carlo studies and a real data application. for this article are available online. [ABSTRACT FROM AUTHOR]

Summary: In immuno‐oncology clinical trials, multiple immunological biomarkers are usually examined over time to comprehensively and appropriately evaluate the efficacy of treatments. Because predicting patients' future survival statuses on the basis of such recorded longitudinal information might be of great interest, joint modeling of longitudinal and time‐to‐event data has been intensively discussed as a toolkit to implement such a prediction. To achieve a desirable predictive performance, averaging over multiple candidate predictive models to account for the model uncertainty might be a more suitable statistical approach than selecting the single best model. Although Bayesian model averaging can be one of the approaches, several problems related to model weights with marginal likelihoods have been discussed. To address these problems, we here propose a Bayesian predictive model averaging (BPMA) method that uses Bayesian leave‐one‐out cross‐validation predictive densities to account for the subject‐specific and time‐dependent nature of the prediction. We examine the operating characteristics of the proposed BPMA method in terms of the predictive accuracy (ie, the calibration and discrimination abilities) in extensive simulation studies. In addition, we discuss the strengths and limitations of the proposed method by applying it to an immuno‐oncology clinical trial in patients with advanced ovarian cancer. [ABSTRACT FROM AUTHOR]

Recent years have seen the development of many novel scoring tools for disease prognosis and prediction. To become accepted for use in clinical applications, these tools have to be validated on external data. In practice, validation is often hampered by logistical issues, resulting in multiple small‐sized validation studies. It is therefore necessary to synthesize the results of these studies using techniques for meta‐analysis. Here we consider strategies for meta analyzing the concordance probability for time‐to‐event data ("C‐index"), which has become a popular tool to evaluate the discriminatory power of prediction models with a right‐censored outcome. We show that standard meta‐analysis of the C‐index may lead to biased results, as the magnitude of the concordance probability depends on the length of the time interval used for evaluation (defined e.g., by the follow‐up time, which might differ considerably between studies). To address this issue, we propose a set of methods for random‐effects meta‐regression that incorporate time directly as covariate in the model equation. In addition to analyzing nonlinear time trends via fractional polynomial, spline, and exponential decay models, we provide recommendations on suitable transformations of the C‐index before meta‐regression. Our results suggest that the C‐index is best meta‐analyzed using fractional polynomial meta‐regression with logit‐transformed C‐index values. Classical random‐effects meta‐analysis (not considering time as covariate) is demonstrated to be a suitable alternative when follow‐up times are small. Our findings have implications for the reporting of C‐index values in future studies, which should include information on the length of the time interval underlying the calculations. [ABSTRACT FROM AUTHOR]

Joint modelling of longitudinal and time-to-event data is usually described by a joint model which uses shared or correlated latent effects to capture associations between the two processes. Under this framework, the joint distribution of the two processes can be derived straightforwardly by assuming conditional independence given the random effects. Alternative approaches to induce interdependency into sub-models have also been considered in the literature and one such approach is using copulas to introduce non-linear correlation between the marginal distributions of the longitudinal and time-to-event processes. The multivariate Gaussian copula joint model has been proposed in the literature to fit joint data by applying a Monte Carlo expectation-maximisation algorithm. In this paper, we propose an exact likelihood estimation approach to replace the more computationally expensive Monte Carlo expectation-maximisation algorithm and we consider results based on using both the multivariate Gaussian and t copula functions. We also provide a straightforward way to compute dynamic predictions of survival probabilities, showing that our proposed model is comparable in prediction performance to the shared random effects joint model. [ABSTRACT FROM AUTHOR]

In this paper, a convenient and parsimonious family of the quantile functions is proposed for modeling time-to-event data. Detailed mathematical arguments are presented for deriving the explicit expressions of the quantile density, quantile hazard and quantile mean remaining life functions. Their functional properties are also explored. Some important members of the family are provided. A special case, the so-called additive power logarithmic quantile family, is discussed with detailed properties, parameter estimation and application to time-to-event data. Measures of skewness and kurtosis for the proposed quantile function are derived. Important statistical measures useful for reliability analysis are also provided with their explicit expressions. Stochastic ordering, tail weight and order statistics are also discussed. L-moments are explicitly derived for the proposed quantile function. Estimation is approached using the likelihood function and percentiles. A real data set consists of times between occurrence of the coal-mining accidents is analyzed for illustration purposes. [ABSTRACT FROM AUTHOR]

Modeling and predicting time-to-event phenomena in engineering, sports, and medical sectors are very crucial. Numerous models have been proposed for modeling such types of data sets. These models are introduced by adding one or more parameters to the traditional distributions. The addition of new parameters to the traditional distributions leads to serious issues, such as estimation consequences and re-parametrization problems. To avoid such problems, this paper introduces a new method for generating new probability distributions without any additional parameters. The proposed method may be called a weighted cosine-G family of distributions. Different distributional properties of the weighted cosine-G family, along with the maximum likelihood estimators, are obtained. A special model of the weighted cosine-G family, by utilizing the Weibull model, is considered. The special model of the weighted cosine-G family may be called a weighted cosine-Weibull distribution. A simulation study of the weighted cosine-Weibull model is conducted to evaluate the performances of its estimators. Finally, the applications of the weighted cosine-Weibull distribution are shown by considering three data sets related to the time-to-event phenomena. [ABSTRACT FROM AUTHOR]

Summary: Multiple randomized controlled trials, each comparing a subset of competing interventions, can be synthesized by means of a network meta‐analysis to estimate relative treatment effects between all interventions in the evidence base. Here we focus on estimating relative treatment effects for time‐to‐event outcomes. Cancer treatment effectiveness is frequently quantified by analyzing overall survival (OS) and progression‐free survival (PFS). We introduce a method for the joint network meta‐analysis of PFS and OS that is based on a time‐inhomogeneous tri‐state (stable, progression, and death) Markov model where time‐varying transition rates and relative treatment effects are modeled with parametric survival functions or fractional polynomials. The data needed to run these analyses can be extracted directly from published survival curves. We demonstrate use by applying the methodology to a network of trials for the treatment of non‐small‐cell lung cancer. The proposed approach allows the joint synthesis of OS and PFS, relaxes the proportional hazards assumption, extends to a network of more than two treatments, and simplifies the parameterization of decision and cost‐effectiveness analyses. [ABSTRACT FROM AUTHOR]

The PAIN-CONTRoLS trial compared four medications in treating Cryptogenic sensory polyneuropathy. The primary outcome was a utility function that combined two outcomes, patients' pain score reduction and patients' quit rate. However, additional analysis of the individual outcomes could also be leveraged to inform selecting an optimal medication for future patients. We demonstrate how joint modeling of longitudinal and time-to-event data from PAIN-CONTRoLS can be used to predict the effects of medication in a patient-specific manner and helps to make patient-focused decisions. A joint model was used to evaluate the two outcomes while accounting for the association between the longitudinal process and the time-to-event processes. Results suggested no significant association between the patients' pain scores and time to the medication quit in the PAIN-CONTRoLS study, but the joint model still provided robust estimates and a better model fit. Using the model estimates, given patients' baseline characteristics, a drug profile on both the pain reduction and medication time could be obtained for each drug, providing information on how likely they would quit and how much pain reduction they should expect. Our analysis suggested that drugs viable for one patient may not be beneficial for others. [ABSTRACT FROM AUTHOR]

The classical approach to analyze time-to-event data, e.g. in clinical trials, is to fit Kaplan–Meier curves yielding the treatment effect as the hazard ratio between treatment groups. Afterwards, a log-rank test is commonly performed to investigate whether there is a difference in survival or, depending on additional covariates, a Cox proportional hazard model is used. However, in numerous trials these approaches fail due to the presence of non-proportional hazards, resulting in difficulties of interpreting the hazard ratio and a loss of power. When considering equivalence or non-inferiority trials, the commonly performed log-rank based tests are similarly affected by a violation of this assumption. Here we propose a parametric framework to assess equivalence or non-inferiority for survival data. We derive pointwise confidence bands for both, the hazard ratio and the difference of the survival curves. Further we propose a test procedure addressing non-inferiority and equivalence by directly comparing the survival functions at certain time points or over an entire range of time. Once the model's suitability is proven the method provides a noticeable power benefit, irrespectively of the shape of the hazard ratio. On the other hand, model selection should be carried out carefully as misspecification may cause type I error inflation in some situations. We investigate the robustness and demonstrate the advantages and disadvantages of the proposed methods by means of a simulation study. Finally, we demonstrate the validity of the methods by a clinical trial example. [ABSTRACT FROM AUTHOR]

Joint modeling of longitudinal rank and time‐to‐event data with random effects model using a Bayesian approach is presented. Accelerated failure time (AFT) models can be used for the analysis of time‐to‐event data to estimate the effects of covariates on acceleration/deceleration of the survival time. The parametric AFT models require determining the event time distribution. So, we suppose that the time variable is modeled with Weibull AFT distribution. In many real‐life applications, it is difficult to determine the appropriate distribution. To avoid this restriction, several semiparametric AFT models were proposed, containing spline‐based model. So, we propose a flexible extension of the accelerated failure time model. Furthermore, the usual joint linear model, a joint partially linear model, is also considered containing the nonlinear effect of time on the longitudinal rank responses and nonlinear and time‐dependent effects of covariates on the hazard. Also, a Bayesian approach that yields Bayesian estimates of the model's parameters is used. Some simulation studies are conducted to estimate parameters of the considered models. The model is applied to a real brain tumor patient's data set that underwent surgery. The results of analyzing data are presented to represent the method. [ABSTRACT FROM AUTHOR]

Abstract Background The association structure linking the longitudinal and survival sub-models is of fundamental importance in the joint modeling framework and the choice of this structure should be made based on the clinical background of the study. However, this information may not always be accessible and rationale for selecting this association structure has received relatively little attention in the literature. To this end, we aim to explore four alternative functional forms of the association structure between the CD4 count and the risk of death and provide rationale for selecting the optimal association structure for our data. We also aim to compare the results obtained from the joint model to those obtained from the time-varying Cox model. Methods We used data from the Centre for the AIDS Programme of Research in South Africa (CAPRISA) AIDS Treatment programme, the Starting Antiretroviral Therapy at Three Points in Tuberculosis (SAPiT) study, an open-label, three armed randomised, controlled trial between June 2005 and July 2010 (N=642). In our analysis, we combined the early and late integrated arms and compared results to the sequential arm. We utilized the Deviance Information Criterion (DIC) to select the final model with the best structure, with smaller values indicating better model adjustments to the data. Results Patient characteristics were similar across the study arms. Combined integrated therapy arms had a reduction of 55% in mortality (HR:0.45, 95% CI:0.28-0.72) compared to the sequential therapy arm. The joint model with a cumulative effects functional form was chosen as the best association structure. In particular, our joint model found that the area under the longitudinal profile of CD4 count was strongly associated with a 21% reduction in mortality (HR:0.79, 95% CI:0.72-0.86). Where as results from the time-varying Cox model showed a 19% reduction in mortality (HR:0.81, 95% CI:0.77-0.84). Conclusions In this paper we have shown that the “current value” association structure is not always the best structure that expresses the correct relationship between the outcomes in all settings, which is why it is crucial to explore alternative clinically meaningful association structures that links the longitudinal and survival processes.

Abstract Background There is increasing interest in the development and use of clinical prediction models, but a lack of evidence-supported guidance on the merits of different modelling approaches. This is especially true for time-to-event outcomes, where limited studies have compared the vast number of modelling approaches available. This study compares prediction accuracy and variable importance measures for four modelling approaches in prediction of time-to-revision surgery following total knee arthroplasty (TKA) and total hip arthroplasty (THA). Methods The study included 321,945 TKA and 151,113 THA procedures performed between 1 January 2003 and 31 December 2017. Accuracy of the Cox model, Weibull parametric model, flexible parametric model, and random survival forest were compared, with patient age, sex, comorbidities, and prosthesis characteristics considered as predictors. Prediction accuracy was assessed using the Index of Prediction Accuracy (IPA), c-index, and smoothed calibration curves. Variable importance rankings from the Cox model and random survival forest were also compared. Results Overall, the Cox and flexible parametric survival models performed best for prediction of both TKA (integrated IPA 0.056 (95% CI [0.054, 0.057]) compared to 0.054 (95% CI [0.053, 0.056]) for the Weibull parametric model), and THA revision. (0.029 95% CI [0.027, 0.030] compared to 0.027 (95% CI [0.025, 0.028]) for the random survival forest). The c-index showed broadly similar discrimination between all modelling approaches. Models were generally well calibrated, but random survival forest underfitted the predicted risk of TKA revision compared to regression approaches. The most important predictors of revision were similar in the Cox model and random survival forest for TKA (age, opioid use, and patella resurfacing) and THA (femoral cement, depression, and opioid use). Conclusion The Cox and flexible parametric models had superior overall performance, although all approaches performed similarly. Notably, this study showed no benefit of a tuned random survival forest over regression models in this setting.

Simulation studies play an important role in evaluating the performance of statistical models developed for analyzing complex survival data such as those with competing risks and clustering. This article aims to provide researchers with a basic understanding of competing risks data generation, techniques for inducing cluster-level correlation, and ways to combine them together in simulation studies, in the context of randomized clinical trials with a binary exposure or treatment. We review data generation with competing and semi-competing risks and three approaches of inducing cluster-level correlation for time-to-event data: the frailty model framework, the probability transform, and Moran's algorithm. Using exponentially distributed event times as an example, we discuss how to introduce cluster-level correlation into generating complex survival outcomes, and illustrate multiple ways of combining these methods to simulate clustered, competing and semi-competing risks data with pre-specified correlation values or degree of clustering. [ABSTRACT FROM AUTHOR]

Background: There is increasing interest in the development and use of clinical prediction models, but a lack of evidence-supported guidance on the merits of different modelling approaches. This is especially true for time-to-event outcomes, where limited studies have compared the vast number of modelling approaches available. This study compares prediction accuracy and variable importance measures for four modelling approaches in prediction of time-to-revision surgery following total knee arthroplasty (TKA) and total hip arthroplasty (THA).Methods: The study included 321,945 TKA and 151,113 THA procedures performed between 1 January 2003 and 31 December 2017. Accuracy of the Cox model, Weibull parametric model, flexible parametric model, and random survival forest were compared, with patient age, sex, comorbidities, and prosthesis characteristics considered as predictors. Prediction accuracy was assessed using the Index of Prediction Accuracy (IPA), c-index, and smoothed calibration curves. Variable importance rankings from the Cox model and random survival forest were also compared.Results: Overall, the Cox and flexible parametric survival models performed best for prediction of both TKA (integrated IPA 0.056 (95% CI [0.054, 0.057]) compared to 0.054 (95% CI [0.053, 0.056]) for the Weibull parametric model), and THA revision. (0.029 95% CI [0.027, 0.030] compared to 0.027 (95% CI [0.025, 0.028]) for the random survival forest). The c-index showed broadly similar discrimination between all modelling approaches. Models were generally well calibrated, but random survival forest underfitted the predicted risk of TKA revision compared to regression approaches. The most important predictors of revision were similar in the Cox model and random survival forest for TKA (age, opioid use, and patella resurfacing) and THA (femoral cement, depression, and opioid use).Conclusion: The Cox and flexible parametric models had superior overall performance, although all approaches performed similarly. Notably, this study showed no benefit of a tuned random survival forest over regression models in this setting. [ABSTRACT FROM AUTHOR]

When to initiate treatment on patients is an important problem in many medical studies such as AIDS and cancer. In this article, we formulate the treatment initiation time problem for time‐to‐event data and propose an optimal individualized regime that determines the best treatment initiation time for individual patients based on their characteristics. Different from existing optimal treatment regimes where treatments are undertaken at a pre‐specified time, here new challenges arise from the complicated missing mechanisms in treatment initiation time data and the continuous treatment rule in terms of initiation time. To tackle these challenges, we propose to use restricted mean residual lifetime as a value function to evaluate the performance of different treatment initiation regimes, and develop a nonparametric estimator for the value function, which is consistent even when treatment initiation times are not completely observable and their distribution is unknown. We also establish the asymptotic properties of the resulting estimator in the decision rule and its associated value function estimator. In particular, the asymptotic distribution of the estimated value function is nonstandard, which follows a weighted chi‐squared distribution. The finite‐sample performance of the proposed method is evaluated by simulation studies and is further illustrated with an application to a breast cancer data. [ABSTRACT FROM AUTHOR]

Abstract Background Lung clearance index (LCI) is accepted as an early marker of lung disease in cystic fibrosis (CF), however the utility of LCI to identify subgroups of CF disease in the paediatric age group has never been explored. The aim of the study was to characterize phenotypes of children with CF using LCI as a marker of ventilation inhomogeneity and to investigate whether these phenotypes distinguished patients based on time to pulmonary exacerbation (PE). Methods Data were collected on patients with CF aged

Adaptive enrichment allows for pre-defined patient subgroups of interest to be investigated throughout the course of a clinical trial. These designs have gained attention in recent years because of their potential to shorten the trial's duration and identify effective therapies tailored to specific patient groups. We describe enrichment trials which consider long-term time-to-event outcomes but also incorporate additional short-term information from routinely collected longitudinal biomarkers. These methods are suitable for use in the setting where the trajectory of the biomarker may differ between subgroups and it is believed that the long-term endpoint is influenced by treatment, subgroup and biomarker. Methods are most promising when the majority of patients have biomarker measurements for at least two time points. We implement joint modelling of longitudinal and time-to-event data to define subgroup selection and stopping criteria and we show that the familywise error rate is protected in the strong sense. To assess the results, we perform a simulation study and find that, compared to the study where longitudinal biomarker observations are ignored, incorporating biomarker information leads to increases in power and the (sub)population which truly benefits from the experimental treatment being enriched with higher probability at the interim analysis. The investigations are motivated by a trial for the treatment of metastatic breast cancer and the parameter values for the simulation study are informed using real-world data where repeated circulating tumour DNA measurements and HER2 statuses are available for each patient and are used as our longitudinal data and subgroup identifiers, respectively. [ABSTRACT FROM AUTHOR]

Time-to-event methods have been proposed in the agricultural sciences, as one of the most suitable options for the analysis of seed germination data. In contrast to traditional linear/nonlinear regression, time-to-event methods can easily account for all statistical peculiarities inherited in germination assays, such as censoring, and they can produce unbiased estimates of model parameters and their standard errors. So far, these methods have only been used in combination with empirical models of germination, which are lacking biological underpinnings. We bridge the gap between statistical requirements and biological understanding by developing a general method that formulates biologically-oriented hydro time (HT), thermal time (TT) and hydrothermal time (HTT) models into a time-to-event framework. HT, TT, and HTT models are widely used for describing seed germination and emergence of plants as affected by the environmental temperature and/or water potential. Owing to their simplicity and the direct biological interpretation of model parameters, these models have become one of the most common tools for both predicting germination as well as understanding the physiology of germination responses to environmental factors. However, these models are usually fitted by using nonlinear regression and, therefore, they fall short of statistical rigor when inference about model parameters is of interest. In this study, we develop HT-to-event, TT-to-event and HTT-to-event models and provide a readily available implementation relying on the package “drc” in the R statistical environment. Examples of usage are also provided and we highlight the possible advantages of this procedure, such as efficiency and flexibility.

Time-to-event methods have been proposed in the agricultural sciences, as one of the most suitable options for the analysis of seed germination data. In contrast to traditional linear/nonlinear regression, time-to-event methods can easily account for all statistical peculiarities inherited in germination assays, such as censoring, and they can produce unbiased estimates of model parameters and their standard errors. So far, these methods have only been used in combination with empirical models of germination, which are lacking biological underpinnings. We bridge the gap between statistical requirements and biological understanding by developing a general method that formulates biologically-oriented hydro time (HT), thermal time (TT) and hydrothermal time (HTT) models into a time-to-event framework. HT, TT, and HTT models are widely used for describing seed germination and emergence of plants as affected by the environmental temperature and/or water potential. Owing to their simplicity and the direct biological interpretation of model parameters, these models have become one of the most common tools for both predicting germination as well as understanding the physiology of germination responses to environmental factors. However, these models are usually fitted by using nonlinear regression and, therefore, they fall short of statistical rigor when inference about model parameters is of interest. In this study, we develop HT-to-event, TT-to-event and HTT-to-event models and provide a readily available implementation relying on the package “drc” in the R statistical environment. Examples of usage are also provided and we highlight the possible advantages of this procedure, such as efficiency and flexibility.

Background: The association structure linking the longitudinal and survival sub-models is of fundamental importance in the joint modeling framework and the choice of this structure should be made based on the clinical background of the study. However, this information may not always be accessible and rationale for selecting this association structure has received relatively little attention in the literature. To this end, we aim to explore four alternative functional forms of the association structure between the CD4 count and the risk of death and provide rationale for selecting the optimal association structure for our data. We also aim to compare the results obtained from the joint model to those obtained from the time-varying Cox model.Methods: We used data from the Centre for the AIDS Programme of Research in South Africa (CAPRISA) AIDS Treatment programme, the Starting Antiretroviral Therapy at Three Points in Tuberculosis (SAPiT) study, an open-label, three armed randomised, controlled trial between June 2005 and July 2010 (N=642). In our analysis, we combined the early and late integrated arms and compared results to the sequential arm. We utilized the Deviance Information Criterion (DIC) to select the final model with the best structure, with smaller values indicating better model adjustments to the data.Results: Patient characteristics were similar across the study arms. Combined integrated therapy arms had a reduction of 55% in mortality (HR:0.45, 95% CI:0.28-0.72) compared to the sequential therapy arm. The joint model with a cumulative effects functional form was chosen as the best association structure. In particular, our joint model found that the area under the longitudinal profile of CD4 count was strongly associated with a 21% reduction in mortality (HR:0.79, 95% CI:0.72-0.86). Where as results from the time-varying Cox model showed a 19% reduction in mortality (HR:0.81, 95% CI:0.77-0.84).Conclusions: In this paper we have shown that the "current value" association structure is not always the best structure that expresses the correct relationship between the outcomes in all settings, which is why it is crucial to explore alternative clinically meaningful association structures that links the longitudinal and survival processes. [ABSTRACT FROM AUTHOR]

Pregnancy in-vitro fertilization (IVF) cases are associated with adverse first-trimester outcomes in comparison to spontaneously achieved pregnancies. Human chorionic gonadotrophin β subunit (β-HCG) is a well-known biomarker for the diagnosis and monitoring of pregnancy after IVF. Low levels of β-HCG during this period are related to miscarriage, ectopic pregnancy, and IVF procedure failures. Longitudinal profiles of β-HCG can be used to distinguish between normal and abnormal pregnancies and to assist and guide the clinician in better management and monitoring of post-IVF pregnancies. Therefore, assessing the association between longitudinally measured β-HCG serum concentration and time to early miscarriage is of crucial interest to clinicians. A common joint modeling approach is to use the longitudinal β-HCG trajectory to determine the risk of miscarriage. This work was motivated by a follow-up study with normal and abnormal pregnancies where β-HCG serum concentrations were measured in 173 young women during a gestational age of 9-86 days in Santiago, Chile. Some women experienced a miscarriage event, and their exact event times were unknown, so we have interval-censored data, with the event occurring between the last time of the observed measurement and ten days later. However, for those women belonging to the normal pregnancy group; that is, carrying a pregnancy to a full-term event, right censoring data are observed. Estimation procedures are based on the Stochastic Approximation of the Expectation-Maximization (SAEM) algorithm., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

Modeling and predicting time-to-event phenomena in engineering, sports, and medical sectors are very crucial. Numerous models have been proposed for modeling such types of data sets. These models are introduced by adding one or more parameters to the traditional distributions. The addition of new parameters to the traditional distributions leads to serious issues, such as estimation consequences and re-parametrization problems. To avoid such problems, this paper introduces a new method for generating new probability distributions without any additional parameters. The proposed method may be called a weighted cosine-G family of distributions. Different distributional properties of the weighted cosine-G family, along with the maximum likelihood estimators, are obtained. A special model of the weighted cosine-G family, by utilizing the Weibull model, is considered. The special model of the weighted cosine-G family may be called a weighted cosine-Weibull distribution. A simulation study of the weighted cosine-Weibull model is conducted to evaluate the performances of its estimators. Finally, the applications of the weighted cosine-Weibull distribution are shown by considering three data sets related to the time-to-event phenomena.

• Joint models (JM) are a useful tool to analyze longitudinal data with informative dropout. • Joint Latent Process Models (LPM) extend JM to markers (of possibly different nature) measuring the same underlying quantity. • Maximum Likelihood Estimation of the joint LPM is available in the R-package JLPM. • The case study quantifies the progression of dysphagia during Multiple-System Atrophy (MSA) and its association with death risk. In health cohort studies, repeated measures of markers are often used to describe the natural history of a disease. Joint models allow to study their evolution by taking into account the possible informative dropout usually due to clinical events. However, joint modeling developments mostly focused on continuous Gaussian markers while, in an increasing number of studies, the actual quantity of interest is non-directly measurable; it constitutes a latent variable evaluated by a set of observed indicators from questionnaires or measurement scales. Classical examples include anxiety, fatigue, cognition. In this work, we explain how joint models can be extended to the framework of a latent quantity measured over time by indicators of different nature (e.g. continuous, binary, ordinal). The longitudinal submodel describes the evolution over time of the quantity of interest defined as a latent process in a structural mixed model, and links the latent process to each observation of the indicators through appropriate measurement models. Simultaneously, the risk of multi-cause event is modelled via a proportional cause-specific hazard model that includes a function of the mixed model elements as linear predictor to take into account the association between the latent process and the risk of event. Estimation, carried out in the maximum likelihood framework and implemented in the R-package JLPM, has been validated by simulations. The methodology is illustrated in the French cohort on Multiple-System Atrophy (MSA), a rare and fatal neurodegenerative disease, with the study of dysphagia progression over time stopped by the occurrence of death. [ABSTRACT FROM AUTHOR]

Simple Summary: This paper presents an extended version of the Cox regression model to examine heterogeneous effects of risk factors on disease subtypes defined by a continuous biomarker. This approach can be easily applied to cancer studies and is accessible to researchers via user-friendly R scripts. Molecular pathologic diagnosis is important in clinical (oncology) practice. Integration of molecular pathology into epidemiological methods (i.e., molecular pathological epidemiology) allows for investigating the distinct etiology of disease subtypes based on biomarker analyses, thereby contributing to precision medicine and prevention. However, existing approaches for investigating etiological heterogeneity deal with categorical subtypes. We aimed to fully leverage continuous measures available in most biomarker readouts (gene/protein expression levels, signaling pathway activation, immune cell counts, microbiome/microbial abundance in tumor microenvironment, etc.). We present a cause-specific Cox proportional hazards regression model for evaluating how the exposure–disease subtype association changes across continuous subtyping biomarker levels. Utilizing two longitudinal observational prospective cohort studies, we investigated how the association of alcohol intake (a risk factor) with colorectal cancer incidence differed across the continuous values of tumor epigenetic DNA methylation at long interspersed nucleotide element-1 (LINE-1). The heterogeneous alcohol effect was modeled using different functions of the LINE-1 marker to demonstrate the method's flexibility. This real-world proof-of-principle computational application demonstrates how the new method enables visualizing the trend of the exposure effect over continuous marker levels. The utilization of continuous biomarker data without categorization for investigating etiological heterogeneity can advance our understanding of biological and pathogenic mechanisms. [ABSTRACT FROM AUTHOR]