On the Cox Model With Time-Varying Regression Coefficients

Delayed kernels for longitudinal survival analysis and dynamic prediction

Predicting patient survival probabilities based on observed covariates is an important assessment in clinical practice. These patient-specific covariates are often measured over multiple follow-up appointments. It is then of interest to predict survival based on the history of these longitudinal measurements, and to update predictions as more observations become available. The standard approaches to these so-called 'dynamic prediction' assessments are joint models and landmark analysis. Joint models involve high-dimensional parameterizations, and their computational complexity often prohibits including multiple longitudinal covariates. Landmark analysis is simpler, but discards a proportion of the available data at each 'landmark time'. In this work, we propose a 'delayed kernel' approach to dynamic prediction that sits somewhere in between the two standard methods in terms of complexity. By conditioning hazard rates directly on the covariate measurements over the observation time frame, we define a model that takes into account the full history of covariate measurements but is more practical and parsimonious than joint modelling. Time-dependent association kernels describe the impact of covariate changes at earlier times on the patient's hazard rate at later times. Under the constraints that our model (a) reduces to the standard Cox model for time-independent covariates, and (b) contains the instantaneous Cox model as a special case, we derive two natural kernel parameterizations. Upon application to three clinical data sets, we find that the predictive accuracy of the delayed kernel approach is comparable to that of the two existing standard methods.

Monitoring pediatric CNS non-germinomatous germ cell tumors via cerebrospinal fluid circulating tumor DNA

BACKGROUND

Accurate molecular and clinical stratification of patients with central nervous system (CNS) non-germinomatous germ cell tumors (NGGCTs) remains challenging, impeding the development of personalized therapeutic approaches. Herein, we investigated the translational significance of cerebrospinal fluid (CSF) circulating tumor DNA (ctDNA) in pediatric NGGCTs to identify characteristic features of CNS NGGCTs and to identify a subset of patients for whom the presence of residual disease is a risk factor and an indicator of shorter progression-free survival (PFS) and overall survival (OS).

METHODS

Medical records of patients with CNS NGGCTs between January 1, 2018 and December 31, 2022 were reviewed retrospectively.

RESULTS

The cohort consisted of 11 male and six female patients. Tumor markers were elevated in four of the five people who underwent surgery. The remaining 12 patients were diagnosed with malignant NGGCTs according to elevated tumor markers. Among them, ctDNA before chemotherapy as well as ctDNA clearance were consistently associated with PFS and OS (p < .05). By setting a ctDNA positivity threshold of 6%, patients with high ctDNA (above the threshold) levels, which had limitation due to the selection based on optimal statistic from the survival analysis, had significantly inferior 5-year PFS and OS compared to those with low levels (below the threshold). ctDNA or ctDNA clearance combined with the presence of residual disease predicted significantly worse OS and PFS (p < .05).

CONCLUSIONS

CSF ctDNA might allow the study of genomic evolution and the characterization of tumors in pediatric NGGCTs. CSF ctDNA analysis may facilitate the clinical management of pediatric NGGCT patients, and aid in designing personalized therapeutic strategies.

A discrete approximation method for modeling interval-censored multistate data

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.

Quantifying the time-varying association between objectively measured physical activity and mortality in US older adults over a 12-year follow-up period: the NHANES 2003-2006 study

Objectively measuring physical activity (PA) has consistently shown an association with reduced all-cause mortality risk in cross-sectional studies. However, the strength of this association may change over time. We quantify the time-varying, covariate-adjusted association between the total volume of PA and all-cause mortality over a 12-year follow-up period using Cox regression with a time varying effect of population-referenced quantile total activity count adjusted for traditional risk factors. Analyses focus on participants 50-84 years old with adequate accelerometer wear time and without missing covariates. The findings suggest that (1) the use of baseline PA in Cox models with long follow-up periods may be inappropriate without time-varying effects and (2) the use of accelerometry derived volume of PA in risk score calculations may be most appropriate for short-term to medium-term risk scores.

A mark-specific quantile regression model

Quantile regression has become a widely used tool for analysing competing risk data. However, quantile regression for competing risk data with a continuous mark is still scarce. The mark variable is an extension of cause of failure in a classical competing risk model where cause of failure is replaced by a continuous mark only observed at uncensored failure times. An example of the continuous mark variable is the genetic distance that measures dissimilarity between the infecting virus and the virus contained in the vaccine construct. In this article, we propose a novel mark-specific quantile regression model. The proposed estimation method borrows strength from data in a neighbourhood of a mark and is based on an induced smoothed estimation equation, which is very different from the existing methods for competing risk data with discrete causes. The asymptotic properties of the resulting estimators are established across mark and quantile continuums. In addition, a mark-specific quantile-type vaccine efficacy is proposed and its statistical inference procedures are developed. Simulation studies are conducted to evaluate the finite sample performances of the proposed estimation and hypothesis testing procedures. An application to the first HIV vaccine efficacy trial is provided.

A sensitivity analysis approach for the causal hazard ratio in randomized and observational studies

The hazard ratio (HR) is often reported as the main causal effect when studying survival data. Despite its popularity, the HR suffers from an unclear causal interpretation. As already pointed out in the literature, there is a built-in selection bias in the HR, because similarly to the truncation by death problem, the HR conditions on post-treatment survival. A recently proposed alternative, inspired by the Survivor Average Causal Effect, is the causal HR, defined as the ratio between hazards across treatment groups among the study participants that would have survived regardless of their treatment assignment. We discuss the challenge in identifying the causal HR and present a sensitivity analysis identification approach in randomized controlled trials utilizing a working frailty model. We further extend our framework to adjust for potential confounders using inverse probability of treatment weighting. We present a Cox-based and a flexible non-parametric kernel-based estimation under right censoring. We study the finite-sample properties of the proposed estimation methods through simulations. We illustrate the utility of our framework using two real-data examples.

Using information criteria to select smoothing parameters when analyzing survival data with time-varying coefficient hazard models

Analyzing the large-scale survival data from the National Cancer Institute's Surveillance, Epidemiology, and End Results (SEER) Program may help guide the management of cancer. Detecting and characterizing the time-varying effects of factors collected at the time of diagnosis could reveal important and useful patterns. However, fitting a time-varying effect model by maximizing the partial likelihood with such large-scale survival data is not feasible with most existing software. Moreover, estimating time-varying coefficients using spline based approaches requires a moderate number of knots, which may lead to unstable estimation and over-fitting issues. To resolve these issues, adding a penalty term greatly aids estimation. The selection of penalty smoothing parameters is difficult in this time-varying setting, as traditional ways like using Akaike information criterion do not work, while cross-validation methods have a heavy computational burden, leading to unstable selections. We propose modified information criteria to determine the smoothing parameter and a parallelized Newton-based algorithm for estimation. We conduct simulations to evaluate the performance of the proposed method. We find that penalization with the smoothing parameter chosen by a modified information criteria is effective at reducing the mean squared error of the estimated time-varying coefficients. Compared to a number of alternatives, we find that the estimates of the variance derived from Bayesian considerations have the best coverage rates of confidence intervals. We apply the method to SEER head-and-neck, colon, prostate, and pancreatic cancer data and detect the time-varying nature of various risk factors.

Estimating Waning of Vaccine Effectiveness: A Simulation Study

BACKGROUND

Developing accurate and reliable methods to estimate vaccine protection is a key goal in immunology and public health. While several statistical methods have been proposed, their potential inaccuracy in capturing fast intraseasonal waning of vaccine-induced protection needs to be rigorously investigated.

METHODS

To compare statistical methods for estimating vaccine effectiveness (VE), we generated simulated data using a multiscale, agent-based model of an epidemic with an acute viral infection and differing extents of VE waning. We apply a previously proposed framework for VE measures based on the observational data richness to assess changes of vaccine-induced protection over time.

RESULTS

While VE measures based on hard-to-collect information (eg, the exact timing of exposures) were accurate, usually VE studies rely on time-to-infection data and the Cox proportional hazards model. We found that its extension using scaled Schoenfeld residuals, previously proposed for capturing VE waning, was unreliable in capturing both the degree of waning and its functional form and identified the mathematical factors contributing to this unreliability. We showed that partitioning time and including a time-vaccine interaction term in the Cox model significantly improved estimation of VE waning, even in the case of dramatic, rapid waning. We also proposed how to optimize the partitioning scheme.

CONCLUSIONS

While appropriate for rejecting the null hypothesis of no waning, scaled Schoenfeld residuals are unreliable for estimating the degree of waning. We propose a Cox-model-based method with a time-vaccine interaction term and further optimization of partitioning time. These findings may guide future analysis of VE waning data.

Additive hazards model with time-varying coefficients and imaging predictors

Conventional hazard regression analyses frequently assume constant regression coefficients and scalar covariates. However, some covariate effects may vary with time. Moreover, medical imaging has become an increasingly important tool in screening, diagnosis, and prognosis of various diseases, given its information visualization and quantitative assessment. This study considers an additive hazards model with time-varying coefficients and imaging predictors to examine the dynamic effects of potential scalar and imaging risk factors for the failure of interest. We develop a two-stage approach that comprises the high-dimensional functional principal component analysis technique in the first stage and the counting process-based estimating equation approach in the second stage. In addition, we construct the pointwise confidence intervals for the proposed estimators and provide a significance test for the effects of scalar and imaging covariates. Simulation studies demonstrate the satisfactory performance of the proposed method. An application to the Alzheimer's disease neuroimaging initiative study further illustrates the utility of the methodology.

Identifying surrogate markers in real-world comparative effectiveness research

In comparative effectiveness research (CER), leveraging short-term surrogates to infer treatment effects on long-term outcomes can guide policymakers evaluating new treatments. Numerous statistical procedures for identifying surrogates have been proposed for randomized clinical trials (RCTs), but no methods currently exist to evaluate the proportion of treatment effect (PTE) explained by surrogates in real-world data (RWD), which have become increasingly common. To address this knowledge gap, we propose inverse probability weighted (IPW) and doubly robust (DR) estimators of an optimal transformation of the surrogate and the corresponding PTE measure. We demonstrate that the proposed estimators are consistent and asymptotically normal, and the DR estimator is consistent when either the propensity score model or outcome regression model is correctly specified. Our proposed estimators are evaluated through extensive simulation studies. In two RWD settings, we show that our method can identify and validate surrogate markers for inflammatory bowel disease (IBD).

A Comprehensive Analysis of Proportional Intensity-Based Software Reliability Models with Covariates

This paper focuses on the so-called proportional intensity-based software reliability models (PI-SRMs), which are extensions of the common non-homogeneous Poisson process (NHPP)-based SRMs, and describe the probabilistic behavior of software fault-detection process by incorporating the time-dependent software metrics data observed in the development process. The PI-SRM is proposed by Rinsaka et al. in the paper “PISRAT: Proportional Intensity-Based Software Reliability Assessment Tool” in 2006. Specifically, we generalize this seminal model by introducing eleven well-known fault-detection time distributions, and investigate their goodness-of-fit and predictive performances. In numerical illustrations with four data sets collected in real software development projects, we utilize the maximum likelihood estimation to estimate model parameters with three time-dependent covariates (test execution time, failure identification work, and computer time-failure identification), and examine the performances of our PI-SRMs in comparison with the existing NHPP-based SRMs without covariates. It is shown that our PI-STMs could give better goodness-of-fit and predictive performances in many cases.

ODACH: a one-shot distributed algorithm for Cox model with heterogeneous multi-center data

We developed a One-shot Distributed Algorithm for Cox proportional-hazards model to analyze Heterogeneous multi-center time-to-event data (ODACH) circumventing the need for sharing patient-level information across sites. This algorithm implements a surrogate likelihood function to approximate the Cox log-partial likelihood function that is stratified by site using patient-level data from a lead site and aggregated information from other sites, allowing the baseline hazard functions and the distribution of covariates to vary across sites. Simulation studies and application to a real-world opioid use disorder study showed that ODACH provides estimates close to the pooled estimator, which analyzes patient-level data directly from all sites via a stratified Cox model. Compared to the estimator from meta-analysis, the inverse variance-weighted average of the site-specific estimates, ODACH estimator demonstrates less susceptibility to bias, especially when the event is rare. ODACH is thus a valuable privacy-preserving and communication-efficient method for analyzing multi-center time-to-event data.

Counterfactual mediation analysis in the multistate model framework for surrogate and clinical time-to-event outcomes in randomized controlled trials

In cancer randomized controlled trials, surrogate endpoints are frequently time-to-event endpoints, subject to the competing risk from the time-to-event clinical outcome. In this context, we introduce a counterfactual-based mediation analysis for a causal assessment of surrogacy. We use a multistate model for risk prediction to account for both direct transitions towards the clinical outcome and indirect transitions through the surrogate outcome. Within the counterfactual framework, we define natural direct and indirect effects with a causal interpretation. Based on these measures, we define the proportion of the treatment effect on the clinical outcome mediated by the surrogate outcome. We estimate the proportion for both the cumulative risk and restricted mean time lost. We illustrate our approach by using 18-year follow-up data from the SPCG-4 randomized trial of radical prostatectomy for prostate cancer. We assess time to metastasis as a surrogate outcome for prostate cancer-specific mortality.

Comparing statistical methods for detecting and estimating waning efficacy of rotavirus vaccines in developing countries

INTRODUCTION

Vaccination has significantly reduced morbidity and mortality resulting from rotavirus infection worldwide. However, rotavirus vaccine efficacy (VE) appears to wane over the first 2 years since vaccination, particularly in developing countries. Statistical methods for detecting VE waning and estimating its rate have been used in a few studies, but comparisons of methods for evaluating VE waning have not yet been performed. In this work we present and compare three methods - Durham's method, Tian's method, and time-dependent covariate (TDC) method - based on generalizations of the Cox proportional hazard model.

METHODS

We developed a new stochastic agent-based simulation model to generate data from a hypothetical rotavirus vaccine trial where the protective efficacy of the vaccine may vary over time. Input parameters to the simulation model were obtained from studies on rotavirus infections in four developing countries. We applied each of the methods to four simulated datasets and compared the type-1 error probabilities and the powers of the resulting statistical tests. We also compared estimated and true values of VE over time.

RESULTS

Durham's method had the highest power of detecting true VE waning of the three methods. This method also provided quite accurate estimates of VE in each period and of the per-period drop in VE.

CONCLUSIONS

Durham's method is somewhat more powerful than the other two Cox proportional hazards model-based methods for detecting VE waning and provides more information about the temporal behavior of VE.

Variable selection for a mark-specific additive hazards model using the adaptive LASSO

In HIV vaccine efficacy trials, mark-specific hazards models have important applications and can be used to evaluate the strain-specific vaccine efficacy. Additive hazards models have been widely used in practice, especially when continuous covariates are present. In this article, we conduct variable selection for a mark-specific additive hazards model. The proposed method is based on an estimating equation with the first derivative of the adaptive LASSO penalty function. The asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a dataset from the first HIV vaccine efficacy trial is provided.

Developing and evaluating risk prediction models with panel current status data

Panel current status data arise frequently in biomedical studies when the occurrence of a particular clinical condition is only examined at several prescheduled visit times. Existing methods for analyzing current status data have largely focused on regression modeling based on commonly used survival models such as the proportional hazards model and the accelerated failure time model. However, these procedures have the limitations of being difficult to implement and performing sub-optimally in relatively small sample sizes. The performance of these procedures is also unclear under model misspecification. In addition, no methods currently exist to evaluate the prediction performance of estimated risk models with panel current status data. In this paper, we propose a simple estimator under a general class of nonparametric transformation (NPT) models by fitting a logistic regression working model and demonstrate that our proposed estimator is consistent for the NPT model parameter up to a scale multiplier. Furthermore, we propose nonparametric estimators for evaluating the prediction performance of the risk score derived from model fitting, which is valid regardless of the adequacy of the fitted model. Extensive simulation results suggest that our proposed estimators perform well in finite samples and the regression parameter estimators outperform existing estimators under various scenarios. We illustrate the proposed procedures using data from the Framingham Offspring Study.

Stratified Cox models with time-varying effects for national kidney transplant patients: A new blockwise steepest ascent method

Analyzing the national transplant database, which contains about 300,000 kidney transplant patients treated in over 290 transplant centers, may guide the disease management and inform the policy of kidney transplantation. Cox models stratified by centers provide a convenient means to account for the clustered data structure, while studying more than 160 predictors with effects that may vary over time. As fitting a time-varying effect model with such a large sample size may defy any existing software, we propose a blockwise steepest ascent procedure by leveraging the block structure of parameters inherent from the basis expansions for each coefficient function. The algorithm iteratively updates the optimal blockwise search direction, along which the increment of the partial likelihood is maximized. The proposed method can be interpreted from the perspective of the minorization-maximization algorithm and increases the partial likelihood until convergence. We further propose a Wald statistic to test whether the effects are indeed time varying. We evaluate the utility of the proposed method via simulations. Finally, we apply the method to analyze the national kidney transplant data and detect the time-varying nature of the effects of various risk factors.

Motion-Control Shoes Reduce the Risk of Pronation-Related Pathologies in Recreational Runners: A Secondary Analysis of a Randomized Controlled Trial

OBJECTIVE

To investigate whether motion-control shoes reduce the risk of pronation-related injuries in recreational runners.

DESIGN

Secondary analysis of a randomized controlled trial of the effect of shoes on running injuries.

METHODS

Three hundred seventy-two recreational runners were randomized to receive either standard neutral or motion-control shoes and were followed up for 6 months regarding running activity and injury. Running injuries that occurred during this period were registered and classified as pronation-related injuries (Achilles tendinopathy, plantar fasciopathy, exercise-related lower-leg pain, and anterior knee pain) or other running-related injuries. With the use of competing risk analysis, the relationship between pronation-related and other running-related injuries and shoe type was evaluated by estimating the cause-specific hazard, controlling for other possible confounders like age, sex, body mass index, previous injury, and sport participation pattern.

RESULTS

Twenty-five runners sustained pronation-related running injuries and 68 runners sustained other running-related injuries. Runners wearing the motion-control shoes had a lower risk of pronation-related running injuries compared with runners who wore standard neutral shoes (hazard ratio = 0.41; 95% confidence interval: 0.17, 0.98). There was no effect of shoe type (hazard ratio = 0.68; 95% confidence interval: 0.41, 1.10) on the risk of other running-related injuries.

CONCLUSION

Motion-control shoes may reduce the risk of pronation-related running injuries, but did not influence the risk of other running-related injuries. J Orthop Sports Phys Ther 2021;51(3):135-143. Epub 11 Dec 2020. doi:10.2519/jospt.2021.9710.

Varying coefficient frailty models with applications in single molecular experiments

Motivated by an analysis of single molecular experiments in the study of T-cell signaling, a new model called varying coefficient frailty model with local linear estimation is proposed. Frailty models have been extensively studied, but extensions to nonconstant coefficients are limited to spline-based methods that tend to produce estimation bias near the boundary. To address this problem, we introduce a local polynomial kernel smoothing technique with a modified expectation-maximization algorithm to estimate the unknown parameters. Theoretical properties of the estimators, including their unbiased property near the boundary, are derived along with discussions on the asymptotic bias-variance trade-off. The finite sample performance is examined by simulation studies, and comparisons with existing spline-based approaches are conducted to show the potential advantages of the proposed approach. The proposed method is implemented for the analysis of T-cell signaling. The fitted varying coefficient model provides a rigorous quantification of an early and rapid impact on T-cell signaling from the accumulation of bond lifetime, which can shed new light on the fundamental understanding of how T cells initiate immune responses.

A kernel regression model for panel count data with nonparametric covariate functions

The local kernel pseudo-partial likelihood is employed for estimation in a panel count model with nonparametric covariate functions. An estimator of the derivative of the nonparametric covariate function is derived first, and the nonparametric function estimator is then obtained by integrating the derivative estimator. Uniform consistency rates and pointwise asymptotic normality are obtained for the local derivative estimator under some regularity conditions. Moreover, the baseline function estimator is shown to be uniformly consistent. Demonstration of the asymptotic results strongly relies on the modern empirical theory, which generally does not require the Poisson assumption. Simulation studies also illustrate that the local derivative estimator performs well in a finite-sample regardless of whether the Poisson assumption holds. We also implement the proposed methodology to analyze a clinical study on childhood wheezing.

Semi-parametric survival analysis via Dirichlet process mixtures of the First Hitting Time model

Time-to-event data often violate the proportional hazards assumption inherent in the popular Cox regression model. Such violations are especially common in the sphere of biological and medical data where latent heterogeneity due to unmeasured covariates or time varying effects are common. A variety of parametric survival models have been proposed in the literature which make more appropriate assumptions on the hazard function, at least for certain applications. One such model is derived from the First Hitting Time (FHT) paradigm which assumes that a subject's event time is determined by a latent stochastic process reaching a threshold value. Several random effects specifications of the FHT model have also been proposed which allow for better modeling of data with unmeasured covariates. While often appropriate, these methods often display limited flexibility due to their inability to model a wide range of heterogeneities. To address this issue, we propose a Bayesian model which loosens assumptions on the mixing distribution inherent in the random effects FHT models currently in use. We demonstrate via simulation study that the proposed model greatly improves both survival and parameter estimation in the presence of latent heterogeneity. We also apply the proposed methodology to data from a toxicology/carcinogenicity study which exhibits nonproportional hazards and contrast the results with both the Cox model and two popular FHT models.

The added value of new covariates to the brier score in cox survival models

Calibration is an important measure of the predictive accuracy for a prognostic risk model. A widely used measure of calibration when the outcome is survival time is the expected Brier score. In this paper, methodology is developed to accurately estimate the difference in expected Brier scores derived from nested survival models and to compute an accompanying variance estimate of this difference. The methodology is applicable to time invariant and time-varying coefficient Cox survival models. The nested survival model approach is often applied to the scenario where the full model consists of conventional and new covariates and the subset model contains the conventional covariates alone. A complicating factor in the methodologic development is that the Cox model specification cannot, in general, be simultaneously satisfied for nested models. The problem has been resolved by projecting the properly specified full survival model onto the lower dimensional space of conventional markers alone. Simulations are performed to examine the method's finite sample properties and a prostate cancer data set is used to illustrate its application.

Trends in Use and Timing of Intratympanic Corticosteroid Injections for Sudden Sensorineural Hearing Loss

OBJECTIVE

Oral corticosteroids are treatment mainstays for idiopathic sudden sensorineural hearing loss (SSNHL). Recent studies suggest that intratympanic (IT) steroid injections may be effective as an alternate or adjunctive therapy. We sought to investigate nationwide trends in treatment patterns for SSNHL.

STUDY DESIGN

Retrospective cross-sectional study.

SETTING

A large nationwide health care claims database spanning 2007 to 2016.

METHODS

Patients with SSNHL were identified from the IBM Watson Health MarketScan Database. Multivariable logistic, linear, and Cox regression were used for demographic- and comorbidity-adjusted analyses.

RESULTS

Overall, 19,670 patients were included. Between 2007 and 2016, use of oral corticosteroids alone decreased (83.6% to 64.6%, P < .001), while use of IT corticosteroids alone and combination IT-oral corticosteroids increased (IT only, 7.9% to 15.1%, P = .002; IT-oral, 8.5% to 20.4%, P < .001). During the study period, time to treatment initiation decreased for both administration modalities, though more dramatically for IT corticosteroids (IT, 124.0 to 10.6 days, P < .001; oral, 42.6 to 12.7 days, P < .001). In patients receiving both IT and oral corticosteroids, concurrent first-line use increased (25.2% to 52.8%, P < .001). Repeat injections have also become more common but may raise risk of persistent tympanic membrane perforations (vs no injection; hazard ratio [first injection] = 7.95, 95% CI = 5.54-11.42; hazard ratio [fifth or higher injection] = 17.47, 95% CI = 6.93-44.05).

CONCLUSION

SSNHL management increasingly involves early IT steroids as an alternative or adjunctive option to oral steroids. Use of repeat IT corticosteroid injections has also increased but may raise risk of persistent tympanic membrane perforations and subsequent tympanoplasty. Future decision analysis and cost-effectiveness studies are necessary to identify an optimal care pattern for SSNHL.

Analysis of the time-varying Cox model for the cause-specific hazard functions with missing causes

This paper studies the Cox model with time-varying coefficients for cause-specific hazard functions when the causes of failure are subject to missingness. Inverse probability weighted and augmented inverse probability weighted estimators are investigated. The latter is considered as a two-stage estimator by directly utilizing the inverse probability weighted estimator and through modeling available auxiliary variables to improve efficiency. The asymptotic properties of the two estimators are investigated. Hypothesis testing procedures are developed to test the null hypotheses that the covariate effects are zero and that the covariate effects are constant. We conduct simulation studies to examine the finite sample properties of the proposed estimation and hypothesis testing procedures under various settings of the auxiliary variables and the percentages of the failure causes that are missing. These simulation results demonstrate that the augmented inverse probability weighted estimators are more efficient than the inverse probability weighted estimators and that the proposed testing procedures have the expected satisfactory results in sizes and powers. The proposed methods are illustrated using the Mashi clinical trial data for investigating the effect of randomization to formula-feeding versus breastfeeding plus extended infant zidovudine prophylaxis on death due to mother-to-child HIV transmission in Botswana.

Evaluation of Risk Factors Associated With Herds With an Increased Duration of Bovine Tuberculosis Breakdowns in Castilla y Leon, Spain (2010-2017)

The persistence of bovine tuberculosis (bTB) in certain cattle herds is a major concern in countries pursuing disease eradication worldwide. The chronic nature of the disease, the lack of performance of diagnostic tools, and the presence of wildlife reservoirs may lead infected herds to require longer periods to achieve the officially tuberculosis-free (OTF) status. Here, we evaluated the impact of farm and breakdown characteristics on the probability of disease persistence in infected farms in Castilla y Leon, a bTB-endemic region of Spain, using survival and logistic regression models. Data from bTB breakdowns occurring in 3,550 bTB-positive herds detected in 2010–2017 were analyzed. A multivariable Cox proportional hazards model was fitted using time to recover OTF status as the response variable, and a multivariable logistic regression model using the chronic status (yes/no) for herds experiencing particularly long breakdowns as the outcome variable was also used. Both analyses revealed that county-level bTB herd prevalence, herd size, number of incoming animals in the previous 3 years, number of skin test reactors in the disclosing test, and number of days between the disclosing and follow-up tests were associated with increased breakdown duration. Production type was not consistently associated with chronic infection, suggesting that once infected, it is not a significant predictor of outbreak duration beyond the initial stages of the breakdown. Province-level location and number of animals that are bacteriology-positive also affected significantly the expected herd breakdown duration, but their effect became less significant over time. Risk factors identified in this study may help to identify herds more prone to suffer chronic bTB infection that may require additional control measures early on in a breakdown.

Tree-based modeling of time-varying coefficients in discrete time-to-event models

Hazard models are popular tools for the modeling of discrete time-to-event data. In particular two approaches for modeling time dependent effects are in common use. The more traditional one assumes a linear predictor with effects of explanatory variables being constant over time. The more flexible approach uses the class of semiparametric models that allow the effects of the explanatory variables to vary smoothly over time. The approach considered here is in between these modeling strategies. It assumes that the effects of the explanatory variables are piecewise constant. It allows, in particular, to evaluate at which time points the effect strength changes and is able to approximate quite complex variations of the change of effects in a simple way. A tree-based method is proposed for modeling the piecewise constant time-varying coefficients, which is embedded into the framework of varying-coefficient models. One important feature of the approach is that it automatically selects the relevant explanatory variables and no separate variable selection procedure is needed. The properties of the method are investigated in several simulation studies and its usefulness is demonstrated by considering two real-world applications.

Variable selection for joint models with time-varying coefficients

Many clinical studies collect longitudinal and survival data concurrently. Joint models combining these two types of outcomes through shared random effects are frequently used in practical data analysis. The standard joint models assume that the coefficients for the longitudinal and survival components are time-invariant. In many applications, the assumption is overly restrictive. In this research, we extend the standard joint model to include time-varying coefficients, in both longitudinal and survival components, and we present a data-driven method for variable selection. Specifically, we use a B-spline decomposition and penalized likelihood with adaptive group LASSO to select the relevant independent variables and to distinguish the time-varying and time-invariant effects for the two model components. We use Gaussian-Legendre and Gaussian-Hermite quadratures to approximate the integrals in the absence of closed-form solutions. Simulation studies show good selection and estimation performance. Finally, we use the proposed procedure to analyze data generated by a study of primary biliary cirrhosis.

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.

Analysis of generalized semiparametric mixed varying-coefficients models for longitudinal data

The generalized semiparametric mixed varying-coefficient effects model for longitudinal data can accommodate a variety of link functions and flexibly model different types of covariate effects, including time-constant, time-varying, and covariate-varying effects. The time-varying effects are unspecified functions of time and the covariate-varying effects are nonparametric functions of a possibly time-dependent exposure variable. A semiparametric estimation procedure is developed that uses local linear smoothing and profile weighted least squares, which requires smoothing in the two different and yet connected domains of time and the time-dependent exposure variable. The asymptotic properties of the estimators of both nonparametric and parametric effects are investigated. In addition, hypothesis testing procedures are developed to examine the covariate effects. The finite-sample properties of the proposed estimators and testing procedures are examined through simulations, indicating satisfactory performances. The proposed methods are applied to analyze the ACTG 244 clinical trial to investigate the effects of antiretroviral treatment switching in HIV-infected patients before and after developing the T215Y antiretroviral drug resistance mutation.

Multiple imputation in Cox regression when there are time-varying effects of covariates

In Cox regression, it is important to test the proportional hazards assumption and sometimes of interest in itself to study time-varying effects (TVEs) of covariates. TVEs can be investigated with log hazard ratios modelled as a function of time. Missing data on covariates are common and multiple imputation is a popular approach to handling this to avoid the potential bias and efficiency loss resulting from a "complete-case" analysis. Two multiple imputation methods have been proposed for when the substantive model is a Cox proportional hazards regression: an approximate method (Imputing missing covariate values for the Cox model in Statistics in Medicine (2009) by White and Royston) and a substantive-model-compatible method (Multiple imputation of covariates by fully conditional specification: accommodating the substantive model in Statistical Methods in Medical Research (2015) by Bartlett et al). At present, neither accommodates TVEs of covariates. We extend them to do so for a general form for the TVEs and give specific details for TVEs modelled using restricted cubic splines. Simulation studies assess the performance of the methods under several underlying shapes for TVEs. Our proposed methods give approximately unbiased TVE estimates for binary covariates with missing data, but for continuous covariates, the substantive-model-compatible method performs better. The methods also give approximately correct type I errors in the test for proportional hazards when there is no TVE and gain power to detect TVEs relative to complete-case analysis. Ignoring TVEs at the imputation stage results in biased TVE estimates, incorrect type I errors, and substantial loss of power in detecting TVEs. We also propose a multivariable TVE model selection algorithm. The methods are illustrated using data from the Rotterdam Breast Cancer Study. R code is provided.

Hypothesis tests for stratified mark-specific proportional hazards models with missing covariates, with application to HIV vaccine efficacy trials

This article develops hypothesis testing procedures for the stratified mark-specific proportional hazards model with missing covariates where the baseline functions may vary with strata. The mark-specific proportional hazards model has been studied to evaluate mark-specific relative risks where the mark is the genetic distance of an infecting HIV sequence to an HIV sequence represented inside the vaccine. This research is motivated by analyzing the RV144 phase 3 HIV vaccine efficacy trial, to understand associations of immune response biomarkers on the mark-specific hazard of HIV infection, where the biomarkers are sampled via a two-phase sampling nested case-control design. We test whether the mark-specific relative risks are unity and how they change with the mark. The developed procedures enable assessment of whether risk of HIV infection with HIV variants close or far from the vaccine sequence are modified by immune responses induced by the HIV vaccine; this question is interesting because vaccine protection occurs through immune responses directed at specific HIV sequences. The test statistics are constructed based on augmented inverse probability weighted complete-case estimators. The asymptotic properties and finite-sample performances of the testing procedures are investigated, demonstrating double-robustness and effectiveness of the predictive auxiliaries to recover efficiency. The finite-sample performance of the proposed tests are examined through a comprehensive simulation study. The methods are applied to the RV144 trial.