Fitting conditional survival models to meta-analytic data by using a transformation toward mixed-effects models

Summary .   Frailty models are widely used to model clustered survival data. Classical ways to fit frailty models are likelihood-based. We propose an alternative approach in which the original problem of "fitting a frailty model" is reformulated into the problem of "fitting a linear mixed model" using model transformation. We show that the transformation idea also works for multivariate proportional odds models and for multivariate additive risks models. It therefore bridges segregated methodologies as it provides a general way to fit conditional models for multivariate survival data by using mixed models methodology. To study the specific features of the proposed method we focus on frailty models. Based on a simulation study, we show that the proposed method provides a good and simple alternative for fitting frailty models for data sets with a sufficiently large number of clusters and moderate to large sample sizes within covariate-level subgroups in the clusters. The proposed method is applied to data from 27 randomized trials in advanced colorectal cancer, which are available through the Meta-Analysis Group in Cancer.     

Tractable Bayes of skew-elliptical link models for correlated binary data

Correlated binary response data with covariates are ubiquitous in longitudinal or spatial studies. Among the existing statistical models, the most well-known one for this type of data is the multivariate probit model, which uses a Gaussian link to model dependence at the latent level. However, a symmetric link may not be appropriate if the data are highly imbalanced. Here, we propose a multivariate skew-elliptical link model for correlated binary responses, which includes the multivariate probit model as a special case. Furthermore, we perform Bayesian inference for this new model and prove that the regression coefficients have a closed-form unified skew-elliptical posterior with an elliptical prior. The new methodology is illustrated by an application to COVID-19 data from three different counties of the state of California, USA. By jointly modeling extreme spikes in weekly new cases, our results show that the spatial dependence cannot be neglected. Furthermore, the results also show that the skewed latent structure of our proposed model improves the flexibility of the multivariate probit model and provides a better fit to our highly imbalanced dataset.     

Modeling longitudinal data with nonparametric multiplicative random effects jointly with survival data

Summary .   In clinical studies, longitudinal biomarkers are often used to monitor disease progression and failure time. Joint modeling of longitudinal and survival data has certain advantages and has emerged as an effective way to mutually enhance information. Typically, a parametric longitudinal model is assumed to facilitate the likelihood approach. However, the choice of a proper parametric model turns out to be more elusive than models for standard longitudinal studies in which no survival endpoint occurs. In this article, we propose a nonparametric multiplicative random effects model for the longitudinal process, which has many applications and leads to a flexible yet parsimonious nonparametric random effects model. A proportional hazards model is then used to link the biomarkers and event time. We use B-splines to represent the nonparametric longitudinal process, and select the number of knots and degrees based on a version of the Akaike information criterion (AIC). Unknown model parameters are estimated through maximizing the observed joint likelihood, which is iteratively maximized by the Monte Carlo Expectation Maximization (MCEM) algorithm. Due to the simplicity of the model structure, the proposed approach has good numerical stability and compares well with the competing parametric longitudinal approaches. The new approach is illustrated with primary biliary cirrhosis (PBC) data, aiming to capture nonlinear patterns of serum bilirubin time courses and their relationship with survival time of PBC patients.     

Polynomials to model the growth of young bulls in performance tests

The use of polynomial functions to describe the average growth trajectory and covariance functions of Nellore and MA (21/32 Charolais+11/32 Nellore) young bulls in performance tests was studied. The average growth trajectories and additive genetic and permanent environmental covariance functions were fit with Legendre (linear through quintic) and quadratic B-spline (with two to four intervals) polynomials. In general, the Legendre and quadratic B-spline models that included more covariance parameters provided a better fit with the data. When comparing models with the same number of parameters, the quadratic B-spline provided a better fit than the Legendre polynomials. The quadratic B-spline with four intervals provided the best fit for the Nellore and MA groups. The fitting of random regression models with different types of polynomials (Legendre polynomials or B-spline) affected neither the genetic parameters estimates nor the ranking of the Nellore young bulls. However, fitting different type of polynomials affected the genetic parameters estimates and the ranking of the MA young bulls. Parsimonious Legendre or quadratic B-spline models could be used for genetic evaluation of body weight of Nellore young bulls in performance tests, whereas these parsimonious models were less efficient for animals of the MA genetic group owing to limited data at the extreme ages.     

Performance-based selection of likelihood models for phylogeny estimation

Phylogenetic estimation has largely come to rely on explicitly model-based methods. This approach requires that a model be chosen and that that choice be justified. To date, justification has largely been accomplished through use of likelihood-ratio tests (LRTs) to assess the relative fit of a nested series of reversible models. While this approach certainly represents an important advance over arbitrary model selection, the best fit of a series of models may not always provide the most reliable phylogenetic estimates for finite real data sets, where all available models are surely incorrect. Here, we develop a novel approach to model selection, which is based on the Bayesian information criterion, but incorporates relative branch-length error as a performance measure in a decision theory (DT) framework. This DT method includes a penalty for overfitting, is applicable prior to running extensive analyses, and simultaneously compares all models being considered and thus does not rely on a series of pairwise comparisons of models to traverse model space. We evaluate this method by examining four real data sets and by using those data sets to define simulation conditions. In the real data sets, the DT method selects the same or simpler models than conventional LRTs. In order to lend generality to the simulations, codon-based models (with parameters estimated from the real data sets) were used to generate simulated data sets, which are therefore more complex than any of the models we evaluate. On average, the DT method selects models that are simpler than those chosen by conventional LRTs. Nevertheless, these simpler models provide estimates of branch lengths that are more accurate both in terms of relative error and absolute error than those derived using the more complex (yet still wrong) models chosen by conventional LRTs. This method is available in a program called DT-ModSel.     

Genetic nature of individual frailty: comparison of two approaches.

The traditional frailty models used in genetic analysis of bivariate survival data assume that individual frailty (and longevity) is influenced by thousands of genes, and that the contribution of each separate gene is small. This assumption, however, does not have a solid biological basis. It may just happen that one or a small number of genes makes a major contribution to determining the human life span. To answer the questions about the nature of the genetic influence on life span using survival data, models are needed that specify the influence of major genes on individual frailty and longevity. The goal of this paper is to test the nature of genetic influences on individual frailty and longevity using survival data on Danish twins. We use a new bivariate survival model with one major gene influencing life span to analyse survival data on MZ (monozygotic) and DZ (dizygotic) twins. The analysis shows that two radically different classes of model provide an equally good fit to the data. However, the asymptotic behaviour of some conditional statistics is different in models from different classes. Because of the limited sample size of bivariate survival data we cannot draw reliable conclusions about the nature of genetic effects on life span. Additional information about tails of bivariate distribution or risk factors may help to solve this problem.     

Dynamic prediction of time to a clinical event with sparse and irregularly measured longitudinal biomarkers

In clinical research and practice, landmark models are commonly used to predict the risk of an adverse future event, using patients' longitudinal biomarker data as predictors. However, these data are often observable only at intermittent visits, making their measurement times irregularly spaced and unsynchronized across different subjects. This poses challenges to conducting dynamic prediction at any post-baseline time. A simple solution is the last-value-carry-forward method, but this may result in bias for the risk model estimation and prediction. Another option is to jointly model the longitudinal and survival processes with a shared random effects model. However, when dealing with multiple biomarkers, this approach often results in high-dimensional integrals without a closed-form solution, and thus the computational burden limits its software development and practical use. In this article, we propose to process the longitudinal data by functional principal component analysis techniques, and then use the processed information as predictors in a class of flexible linear transformation models to predict the distribution of residual time-to-event occurrence. The measurement schemes for multiple biomarkers are allowed to be different within subject and across subjects. Dynamic prediction can be performed in a real-time fashion. The advantages of our proposed method are demonstrated by simulation studies. We apply our approach to the African American Study of Kidney Disease and Hypertension, predicting patients' risk of kidney failure or death by using four important longitudinal biomarkers for renal functions.     

Estimation and Prediction With HIV-Treatment Interruption Data

We consider longitudinal clinical data for HIV patients undergoing treatment interruptions. We use a nonlinear dynamical mathematical model in attempts to fit individual patient data. A statistically-based censored data method is combined with inverse problem techniques to estimate dynamic parameters. The predictive capabilities of this approach are demonstrated by comparing simulations based on estimation of parameters using only half of the longitudinal observations to the full longitudinal data sets.     

A Semiparametric Joint Model for Longitudinal and Survival Data with Application to Hemodialysis Study

Summary .  In many longitudinal clinical studies, the level and progression rate of repeatedly measured biomarkers on each subject quantify the severity of the disease and that subject's susceptibility to progression of the disease. It is of scientific and clinical interest to relate such quantities to a later time-to-event clinical endpoint such as patient survival. This is usually done with a shared parameter model. In such models, the longitudinal biomarker data and the survival outcome of each subject are assumed to be conditionally independent given subject-level severity or susceptibility (also called frailty in statistical terms). In this article, we study the case where the conditional distribution of longitudinal data is modeled by a linear mixed-effect model, and the conditional distribution of the survival data is given by a Cox proportional hazard model. We allow unknown regression coefficients and time-dependent covariates in both models. The proposed estimators are maximizers of an exact correction to the joint log likelihood with the frailties eliminated as nuisance parameters, an idea that originated from correction of covariate measurement error in measurement error models. The corrected joint log likelihood is shown to be asymptotically concave and leads to consistent and asymptotically normal estimators. Unlike most published methods for joint modeling, the proposed estimation procedure does not rely on distributional assumptions of the frailties. The proposed method was studied in simulations and applied to a data set from the Hemodialysis Study.     

Semiparametric approaches for joint modeling of longitudinal and survival data with time-varying coefficients

Summary .   We study joint modeling of survival and longitudinal data. There are two regression models of interest. The primary model is for survival outcomes, which are assumed to follow a time-varying coefficient proportional hazards model. The second model is for longitudinal data, which are assumed to follow a random effects model. Based on the trajectory of a subject's longitudinal data, some covariates in the survival model are functions of the unobserved random effects. Estimated random effects are generally different from the unobserved random effects and hence this leads to covariate measurement error. To deal with covariate measurement error, we propose a local corrected score estimator and a local conditional score estimator. Both approaches are semiparametric methods in the sense that there is no distributional assumption needed for the underlying true covariates. The estimators are shown to be consistent and asymptotically normal. However, simulation studies indicate that the conditional score estimator outperforms the corrected score estimator for finite samples, especially in the case of relatively large measurement error. The approaches are demonstrated by an application to data from an HIV clinical trial.     

Bayesian nonparametric regression analysis of data with random effects covariates from longitudinal measurements

We consider nonparametric regression analysis in a generalized linear model (GLM) framework for data with covariates that are the subject-specific random effects of longitudinal measurements. The usual assumption that the effects of the longitudinal covariate processes are linear in the GLM may be unrealistic and if this happens it can cast doubt on the inference of observed covariate effects. Allowing the regression functions to be unknown, we propose to apply Bayesian nonparametric methods including cubic smoothing splines or P-splines for the possible nonlinearity and use an additive model in this complex setting. To improve computational efficiency, we propose the use of data-augmentation schemes. The approach allows flexible covariance structures for the random effects and within-subject measurement errors of the longitudinal processes. The posterior model space is explored through a Markov chain Monte Carlo (MCMC) sampler. The proposed methods are illustrated and compared to other approaches, the "naive" approach and the regression calibration, via simulations and by an application that investigates the relationship between obesity in adulthood and childhood growth curves.     

Fitting semiparametric random effects models to large data sets

For large data sets, it can be difficult or impossible to fit models with random effects using standard algorithms due to memory limitations or high computational burdens. In addition, it would be advantageous to use the abundant information to relax assumptions, such as normality of random effects. Motivated by data from an epidemiologic study of childhood growth, we propose a 2-stage method for fitting semiparametric random effects models to longitudinal data with many subjects. In the first stage, we use a multivariate clustering method to identify G相似文献   

Impact of imperfect test sensitivity on determining risk factors: the case of bovine tuberculosis

Background

Imperfect diagnostic testing reduces the power to detect significant predictors in classical cross-sectional studies. Assuming that the misclassification in diagnosis is random this can be dealt with by increasing the sample size of a study. However, the effects of imperfect tests in longitudinal data analyses are not as straightforward to anticipate, especially if the outcome of the test influences behaviour. The aim of this paper is to investigate the impact of imperfect test sensitivity on the determination of predictor variables in a longitudinal study.

Methodology/Principal Findings

To deal with imperfect test sensitivity affecting the response variable, we transformed the observed response variable into a set of possible temporal patterns of true disease status, whose prior probability was a function of the test sensitivity. We fitted a Bayesian discrete time survival model using an MCMC algorithm that treats the true response patterns as unknown parameters in the model. We applied our approach to epidemiological data of bovine tuberculosis outbreaks in England and investigated the effect of reduced test sensitivity in the determination of risk factors for the disease. We found that reduced test sensitivity led to changes to the collection of risk factors associated with the probability of an outbreak that were chosen in the ‘best’ model and to an increase in the uncertainty surrounding the parameter estimates for a model with a fixed set of risk factors that were associated with the response variable.

Conclusions/Significance

We propose a novel algorithm to fit discrete survival models for longitudinal data where values of the response variable are uncertain. When analysing longitudinal data, uncertainty surrounding the response variable will affect the significance of the predictors and should therefore be accounted for either at the design stage by increasing the sample size or at the post analysis stage by conducting appropriate sensitivity analyses.     

Joint modeling of longitudinal and survival data via a common frailty

We develop a joint model for the analysis of longitudinal and survival data in the presence of data clustering. We use a mixed effects model for the repeated measures that incorporates both subject- and cluster-level random effects, with subjects nested within clusters. A Cox frailty model is used for the survival model in order to accommodate the clustering. We then link the two responses via the common cluster-level random effects, or frailties. This model allows us to simultaneously evaluate the effect of covariates on the two types of responses, while accounting for both the relationship between the responses and data clustering. The model was motivated by a study of end-stage renal disease patients undergoing hemodialysis, where we wished to evaluate the effect of iron treatment on both the patients' hemoglobin levels and survival times, with the patients clustered by enrollment site.     

Directly parameterized regression conditioning on being alive: analysis of longitudinal data truncated by deaths

For observational longitudinal studies of geriatric populations, outcomes such as disability or cognitive functioning are often censored by death. Statistical analysis of such data may explicitly condition on either vital status or survival time when summarizing the longitudinal response. For example a pattern-mixture model characterizes the mean response at time t conditional on death at time S = s (for s > t), and thus uses future status as a predictor for the time t response. As an alternative, we define regression conditioning on being alive as a regression model that conditions on survival status, rather than a specific survival time. Such models may be referred to as partly conditional since the mean at time t is specified conditional on being alive (S > t), rather than using finer stratification (S = s for s > t). We show that naive use of standard likelihood-based longitudinal methods and generalized estimating equations with non-independence weights may lead to biased estimation of the partly conditional mean model. We develop a taxonomy for accommodation of both dropout and death, and describe estimation for binary longitudinal data that applies selection weights to estimating equations with independence working correlation. Simulation studies and an analysis of monthly disability status illustrate potential bias in regression methods that do not explicitly condition on survival.     

Analysis of exposure-time-response relationships using a spline weight function

To examine the time-dependent effects of exposure histories on disease, we estimate a weight function within a generalized linear model. The shape of the weight function, which is modeled as a cubic B-spline, gives information about the impact of exposure increments at different times on disease risk. The method is evaluated in a simulation study and is applied to data on smoking histories and lung cancer from a recent case-control study in Germany.     

A varying‐coefficient generalized odds rate model with time‐varying exposure: An application to fitness and cardiovascular disease mortality

Varying‐coefficient models have become a common tool to determine whether and how the association between an exposure and an outcome changes over a continuous measure. These models are complicated when the exposure itself is time‐varying and subjected to measurement error. For example, it is well known that longitudinal physical fitness has an impact on cardiovascular disease (CVD) mortality. It is not known, however, how the effect of longitudinal physical fitness on CVD mortality varies with age. In this paper, we propose a varying‐coefficient generalized odds rate model that allows flexible estimation of age‐modified effects of longitudinal physical fitness on CVD mortality. In our model, the longitudinal physical fitness is measured with error and modeled using a mixed‐effects model, and its associated age‐varying coefficient function is represented by cubic B‐splines. An expectation‐maximization algorithm is developed to estimate the parameters in the joint models of longitudinal physical fitness and CVD mortality. A modified pseudoadaptive Gaussian‐Hermite quadrature method is adopted to compute the integrals with respect to random effects involved in the E‐step. The performance of the proposed method is evaluated through extensive simulation studies and is further illustrated with an application to cohort data from the Aerobic Center Longitudinal Study.     

Estimating average cellular turnover from 5-bromo-2'-deoxyuridine (BrdU) measurements

Cellular turnover rates in the immune system can be determined by labelling dividing cells with 5-bromo-2'-deoxyuridine (BrdU) or deuterated glucose ((2)H-glucose). To estimate the turnover rate from such measurements one has to fit a particular mathematical model to the data. The biological assumptions underlying various models developed for this purpose are controversial. Here, we fit a series of different models to BrdU data on CD4(+) T cells from SIV(-) and SIV(+) rhesus macaques. We first show that the parameter estimates obtained using these models depend strongly on the details of the model. To resolve this lack of generality we introduce a new parameter for each model, the 'average turnover rate', defined as the cellular death rate averaged over all subpopulations in the model. We show that very different models yield similar estimates of the average turnover rate, i.e. ca. 1% day(-1) in uninfected monkeys and ca. 2% day(-1) in SIV-infected monkeys. Thus, we show that one can use BrdU data from a possibly heterogeneous population of cells to estimate the average turnover rate of that population in a robust manner.     

Strategies to fit pattern-mixture models

Whereas most models for incomplete longitudinal data are formulated within the selection model framework, pattern-mixture models have gained considerable interest in recent years (Little, 1993, 1994). In this paper, we outline several strategies to fit pattern-mixture models, including the so-called identifying restrictions strategy. Multiple imputation is used to apply this strategy to realistic settings, such as quality-of-life data from a longitudinal study on metastatic breast cancer patients.     

A reduced muscle model and planar musculoskeletal model fit for the simulation of whole-body movements

Musculoskeletal models are made to reflect the capacities of the human body in general, and often a specific subject in particular. It remains challenging to both model the musculoskeletal system and then fit the modelled muscles to a specific human subject. We present a reduced muscle model, a planar musculoskeletal model, and a fitting method that can be used to find a feasible set of active and passive muscle parameters for a specific subject. At a minimum, the fitting method requires inverse dynamics data of the subject, a scalar estimate of the peak activation reached during the movement, and a plausible initial estimate for the strength and flexibility of that subject. While additional data can be used to result in a more accurate fit, this data is not required for the method solve for a feasible fit. The minimal input requirements of the proposed fitting method make it well suited for subjects who cannot undergo a maximum voluntary contraction trial, or for whom recording electromyographic data is not possible. To evaluate the model and fitting method we adjust the musculoskeletal model so that it can perform an experimentally recorded stoop-lift of a 15 kg box.