Parametric Proportional Hazards Model Research Articles

Predictors of faster virological suppression in early treated infants with perinatal HIV from Europe and Thailand.

To identify predictors of faster time to virological suppression among infants starting combination antiretroviral therapy (cART) early in infancy. Cohort study of infants from Europe and Thailand included in studies participating in the European Pregnancy and Paediatric HIV Cohort Collaboration. Infants with perinatal HIV starting cART aged less than 6 months with at least 1 viral load measurement within 15 months of cART initiation were included. Multivariable interval-censored flexible parametric proportional hazards models were used to assess predictors of faster virological suppression, with timing of suppression assumed to lie in the interval between last viral load at least 400 and first viral load less than 400 copies/ml. Of 420 infants, 59% were female and 56% from Central/Western Europe, 26% United Kingdom/Ireland, 15% Eastern Europe and 3% Thailand; 46 and 54% started a boosted protease inhibitor-based or nonnucleoside reverse transcriptase inhibitor-based regimen, respectively. At cART initiation, the median age, CD4% and viral load were 2.9 [interquartile range (IQR): 1.4-4.1] months, 34 (IQR: 24-45)% and 5.5 (IQR: 4.5-6.0) log10 copies/ml, respectively. Overall, an estimated 89% (95% confidence interval: 86-92%) achieved virological suppression within 12 months of cART start. In multivariable analysis, younger age [adjusted hazard ratio (aHR): 0.84 per month older; P < 0.001], higher CD4% (aHR: 1.11 per 10% higher; P = 0.010) and lower log10 viral load (aHR: 0.85 per log10 higher; P < 0.001) at cART initiation independently predicted faster virological suppression. We observed a significant independent effect of age at cART initiation, even within a narrow 6 months window from birth. These findings support the earliest feasible cART initiation in infants and suggest that early therapy influences key virological and immunological parameters that could have important consequences for long-term health.

Metabolic Obesity Phenotypes and Thyroid Cancer Risk: A Cohort Study.

No cohort studies have evaluated the effect of obesity on the incidence of thyroid cancer according to metabolic health status. Therefore, this study examined the association of body mass index (BMI) and metabolic health status with thyroid cancer risk. A cohort study was performed involving 255,051 metabolically healthy (MH) and metabolically unhealthy (MUH) adults free of thyroid cancer at baseline who were followed for a median of 5.3 years. A parametric proportional hazard model was used to estimate the adjusted hazard ratio (aHR) and confidence interval (CI). During 1,402,426.3 person-years of follow-up, 2927 incident thyroid cancers were identified. Among men, the multivariable aHR for thyroid cancer comparing obesity, defined as a BMI ≥25 kg/m2, with a BMI of 18.5-22.9 kg/m2 was 1.47 [CI 1.12-1.93] in MH individuals, whereas the corresponding HR in MUH individuals was 1.26 [CI 1.03-1.53]. Among women, the corresponding HR in MH individuals was 1.05 [CI 0.80-1.36], whereas the corresponding HR in MUH individuals was 1.43 [CI 1.22-1.69]. Increasing quartiles of waist circumference were positively associated with risk of thyroid cancer in MUH men and women (p for trend <0.005) but not in MH individuals. In both MH and MUH men, obesity was associated with an increased risk of incident thyroid cancer, indicating excessive adiposity per se as an independent risk factor for thyroid cancer. Conversely, women with MUH obesity but not MH obesity were found to have an increased risk of thyroid cancer, indicating that obesity with accompanying metabolic abnormalities may affect thyroid cancer risk in women.

Impact of Self-Rated Health on Progression to a Metabolically Unhealthy Phenotype in Metabolically Healthy Obese and Non-Obese Individuals.

We examined the association between self-rated health (SRH), a subjective measure of an individual’s health status, and the incidence of metabolic abnormalities, as well as the effect of obesity on this association in metabolically healthy individuals. The cohort study included 85,377 metabolically healthy men and women who were followed annually or biennially for a median of 3.0 years (interquartile range, 1.9–4.1 years). A parametric proportional hazard model was used to assess hazard ratios (HRs) and 95% confidence intervals (CIs) for the association between SRH and the incidence of metabolic abnormalities. During 258,689.03 person-years, 40,858 participants developed metabolic abnormalities. Poorer SRH was significantly associated with increased risk of developing any metabolic abnormality including hypertriglyceridemia, high homeostasis model assessment of insulin resistance (HOMA-IR), and fatty liver in a dose-dependent manner (p for trend <0.05). The association between SRH and progression to metabolically unhealthy status was much stronger in individuals with obesity than those without, especially in relation to any metabolic abnormality, fatty liver, and high C-reactive protein (all p for interaction by obesity <0.05). The multivariable-adjusted HR (95% CI) for any metabolic abnormality comparing the “poor or very poor” vs. the “very good” self-rated health category was 0.97 (0.90–1.05) among non-obese subjects, whereas the corresponding HR (95% CI) among obese subjects was 1.25 (1.02–1.52). Low SRH, as assessed by a single question, was independently associated with increased risk of progression to metabolically unhealthy status in metabolically healthy individuals, especially metabolically healthy individuals with obesity. SRH may help identify individuals at high risk for progression to metabolically unhealthy status.

Nonheavy Drinking and Worsening of Noninvasive Fibrosis Markers in Nonalcoholic Fatty Liver Disease: A Cohort Study.

The effect of modest alcohol consumption on fibrosis progression in the general population with nonalcoholic fatty liver disease (NAFLD) remains unclear. We examined the association of nonheavy alcohol consumption with worsening of noninvasive fibrosis indices in a large-scale, low-risk population with NAFLD. A cohort study was performed in 58,927 Korean adults with NAFLD and low fibrosis scores who were followed for a median of 4.9 years. Non-, light, and moderate drinkers were defined as 0 g/day, 1-9.9 g/day, and 10-29.9 g/day (10-19.9 g/day for women), respectively. Progression from low to intermediate or high probability of advanced fibrosis was assessed using noninvasive indices including NAFLD fibrosis score (NFS) and Fibrosis-4 Index (FIB-4). A parametric proportional hazards model was used to estimate the multivariable-adjusted hazard ratios (HRs) and 95% confidence intervals (CIs). During 347,925.4 person-years of follow-up, 5,630 subjects with low FIB-4 progressed to intermediate or high FIB-4. The multivariable-adjusted HRs (95% CI) for worsening of FIB-4 comparing light and moderate drinkers with nondrinkers were 1.06 (0.98-1.16) and 1.29 (1.18-1.40), respectively. Similarly, using NFS, corresponding HRs (95% CI) comparing light and moderate drinkers with nondrinkers were 1.09 (1.02-1.16) and 1.31 (1.23-1.40), respectively. Furthermore, the association of moderate drinkers with worsening of either FIB-4 or NFS remained significant after introducing alcohol use and confounders treated as time-varying covariates. Conclusion: In this large-scale cohort of young and middle-aged individuals with NAFLD, nonheavy alcohol consumption, especially moderate alcohol consumption, was significantly and independently associated with worsening of noninvasive markers of fibrosis, indicating that even moderate alcohol consumption might be harmful.

Reliability-based covariate analysis for complex systems in heterogeneous environment: Case study of mining equipment

Operational heterogeneity and harsh environment lead to major variations in production system performance and safety. Traditional probabilistic model is dealt with time-to-event data analysis, which does not have the capability of quantifying and simulation of these types of complexities. This research proposes an integrated methodology for analyzing the impact of dominant explanatory variables on the complex system reliability. A flexible parametric proportional hazards model is developed by focusing on standard parametric Cox regression model for reliability evaluation in complex systems. To achieve this, natural cubic splines are utilized to create a smooth and flexible baseline hazards function where the standard parametric distribution functions do not fit into the failure data set. A real case study is considered to evaluate the reliability for multi-component mechanical systems such as mining equipment. Different operational and environmental explanatory variables are chosen for the analysis process. Research findings revealed that precise estimation of the baseline hazards function is a major part of the reliability evaluation in heterogeneous environment. It is concluded that an appropriate maintenance strategy potentially mitigate the equipment failure intensity.

Chronic hepatitis B virus infection and risk of dyslipidaemia: A cohort study

Hepatitis B virus (HBV) infection has been associated with a decreased prevalence of dyslipidaemia in cross-sectional studies, but cohort studies are limited. We investigated the longitudinal effects of chronic HBV infection on the development of dyslipidaemia. We performed a cohort study of 62287 non-cirrhotic adult men and women free of dyslipidaemia who underwent serologic testing for hepatitis B surface antigen (HBsAg) and were followed annually or biennially for an average of 4.46years. A parametric proportional hazard model was used to estimate the adjusted hazard ratio with 95% confidence interval (CI) for incident dyslipidaemia according to HBsAg seropositivity status. We identified 12331 incident cases of hypercholesterolaemia during 278004.4 person-years of follow-up (incident rate 44.4 per 1000 person-years). In models adjusted for age, sex, body mass index, year of screening exam, smoking status, alcohol intake, regular exercise and education level, the adjusted hazard ratios (95% CIs) for incident hypercholesterolaemia, high LDL cholesterolaemia; hypertriglyceridaemia, high non-HDL cholesterolaemia and low HDL cholesterolaemia comparing HBsAg-positive to HBsAg-negative participants was 0.71 (0.64-0.79), 0.83 (0.78-0.89), 0.61 (0.54-0.70), 0.69 (0.63-0.75) and 1.10 (0.98-1.24), respectively. An inverse association between HBsAg positivity and incident high apolipoprotein B were also identified, with a corresponding a hazard ratio of 0.63 (0.55-0.72). In a large cohort of apparently healthy Korean adults, HBsAg seropositivity was associated with lower risk of development of dyslipidaemia, suggesting a role of HBV infection in lipid metabolism.

Reliability evaluation of power cables considering the restoration characteristic

In this paper Weibull parametric proportional hazard model (PHM) is used to estimate the failure rate of every individual cable based on its age and a set of explanatory factors. The required information for the proposed method is obtained by exploiting available historical cable inventory and failure data. This data-driven method does not require any additional measurements on the cables, and allows the cables to be ranked for maintenance prioritization and repair actions.Furthermore, the results of reliability analysis of power cables are compared when the cables are considered as repairable or non-repairable components. The paper demonstrates that the methods which estimate the time-to-the-first failure (for non-repairable components) lead to incorrect conclusions about reliability of repairable power cables.The proposed method is used to evaluate the failure rate of each individual Paper Insulated Lead Cover (PILC) underground cables in a distribution grid in the south of Sweden.

Comparison of the flexible parametric survival model and Cox model in estimating Markov transition probabilities using real-world data.

Background and objectiveMarkov micro-simulation models are being increasingly used in health economic evaluations. An important feature of the Markov micro-simulation model is its ability to consider transition probabilities of heterogeneous subgroups with different risk profiles. A survival analysis is generally performed to accurately estimate the transition probabilities associated with the risk profiles. This study aimed to apply a flexible parametric survival model (FPSM) to estimate individual transition probabilities.Materials and methodsThe data were obtained from a cohort study investigating ischemic stroke outcomes in Western China. In total, 585 subjects were included in the analysis. To explore the goodness of fit of the FPSM, we compared the estimated hazard ratios and baseline cumulative hazards, both of which are necessary to the calculate individual transition probabilities, and the Markov micro-simulation models constructed using the FPSM and Cox model to determine the validity of the two Markov micro-simulation models and cost-effectiveness results.ResultsThe flexible parametric proportional hazards model produced hazard ratio and baseline cumulative hazard estimates that were similar to those obtained using the Cox proportional hazards model. The simulated cumulative incidence of recurrent ischemic stroke and 5-years cost-effectiveness of Incremental cost-effectiveness Ratios (ICERs) were also similar using the two approaches. A discrepancy in the results was evident between the 5-years cost-effectiveness and the 10-years cost-effectiveness of ICERs, which were approximately 0.9 million (China Yuan) and 0.5 million (China Yuan), respectively.ConclusionsThe flexible parametric survival model represents a good approach for estimating individual transition probabilities for a Markov micro-simulation model.

Extracting biological age from biomedical data via deep learning: too much of a good thing?

Age-related physiological changes in humans are linearly associated with age. Naturally, linear combinations of physiological measures trained to estimate chronological age have recently emerged as a practical way to quantify aging in the form of biological age. In this work, we used one-week long physical activity records from a 2003–2006 National Health and Nutrition Examination Survey (NHANES) to compare three increasingly accurate biological age models: the unsupervised Principal Components Analysis (PCA) score, a multivariate linear regression, and a state-of-the-art deep convolutional neural network (CNN). We found that the supervised approaches produce better chronological age estimations at the expense of a loss of the association between the aging acceleration and all-cause mortality. Consequently, we turned to the NHANES death register directly and introduced a novel way to train parametric proportional hazards models suitable for out-of-the-box implementation with any modern machine learning software. As a demonstration, we produced a separate deep CNN for mortality risks prediction that outperformed any of the biological age or a simple linear proportional hazards model. Altogether, our findings demonstrate the emerging potential of combined wearable sensors and deep learning technologies for applications involving continuous health risk monitoring and real-time feedback to patients and care providers.

Modeling Heterogeneity in Healthcare Utilization Using Massive Medical Claims Data

ABSTRACTWe introduce a modeling approach for characterizing heterogeneity in healthcare utilization using massive medical claims data. We first translate the medical claims observed for a large study population and across five years into individual-level discrete events of care called utilization sequences. We model the utilization sequences using an exponential proportional hazards mixture model to capture heterogeneous behaviors in patients’ healthcare utilization. The objective is to cluster patients according to their longitudinal utilization behaviors and to determine the main drivers of variation in healthcare utilization while controlling for the demographic, geographic, and health characteristics of the patients. Due to the computational infeasibility of fitting a parametric proportional hazards model for high-dimensional, large-sample size data we use an iterative one-step procedure to estimate the model parameters and impute the cluster membership. The approach is used to draw inferences on utilization behaviors of children in the Medicaid system with persistent asthma across six states. We conclude with policy implications for targeted interventions to improve adherence to recommended care practices for pediatric asthma. Supplementary materials for this article are available online.

Survival Analysis with Parametric Proportional Hazards Model of Random Censorship

SYNOPTIC ABSTRACTThis article presents the survival analysis in a proportional hazards model of random censorship using Weibull distribution. It is well known for Weibull distribution that the conjugate prior of the scale and shape parameters does not exist while considering the Bayesian analysis. It is assumed here that the scale and shape parameters have gamma prior distributions. In the case of no suitable prior information about the parameters, non-informative gamma priors for the scale and shape parameters are proposed. It is seen that the closed-form expressions for the Bayes estimates cannot be obtained; we suggest Lindley's method to approximate the Bayes estimates. Unfortunately, it is not possible to construct the Bayesian credible intervals while using this method. We propose an importance sampling procedure to obtain the Bayes estimates and to also construct the Bayesian credible intervals. The method of maximum likelihood estimation is presented in a novel way. A simulation study is carried out to observe the behavior of the maximum likelihood estimators and the Bayes estimators for different combinations of sample sizes, priors, parameters, and censoring rates. One real data analysis is performed to illustrate the proposed methodology.

Spatsurv: An R Package for Bayesian Inference with Spatial Survival Models

Survival methods are used for the statistical modelling of time-to-event data. Survival data are characterized by a set of complete records, in which the time of the event is known; and a set of censored records, in which the event was known to have occurred in an interval. When survival data are spatially referenced, the spatial variation in survival times may be of scientific interest. In this article, we introduce a new R package, spatsurv, for inference with spatially referenced survival data. The specific type of model fitted by this package is a parametric proportional hazards model in which the spatially correlated frailties are modelled by a log-Gaussian stochastic process. The package is extensible in that it allows the user to easily create new models for the baseline hazard function and spatial covariance function. The package implements an advanced adaptive Markov chain Monte Carlo algorithm to deliver Bayesian inference with minimal input from the user. A particular feature of the new package is the ability to handle large datasets via the use of auxiliary frailties on a regular grid and the technique of circulant embedding for fast matrix computations. We demonstrate the new package on a real-life dataset.

Model robust designs for survival trials

The exponential-based proportional hazards model is often assumed in time-to-event experiments but may only approximately hold. Deviations in different neighbourhoods of this model are considered that include other widely used parametric proportional hazards models and the data are assumed to be subject to censoring. Minimax designs are then found explicitly, based on criteria corresponding to classical c- and D-optimality. Analytical characterisations of optimal designs are provided which, unlike optimal designs for related problems in the literature, have finite support and thus avoid the issues of implementing a density-based design in practice. Finally, the proposed designs are compared with the balanced design that is traditionally used in practice, and recommendations for practitioners are given.

Generalized Likelihood Procedures for Data Analysis and Modeling

We present a generalized likelihood (GL) methodology derived from the information generating function. The GL (or GI-based score function in the case of censored or binary data) depends on a user-specified index c, which takes values in a neighborhood of 0. If c = 0, the classical likelihood procedures result. For c > 0, attractive joint robust M-estimators of all model parameters are obtained. Variation of c generates a sensitivity analysis, or informal assessment of consistency of data and assumed model. We apply our framework in univariate and multivariate settings including regression, designed experiments, time series, survival data, parametric proportional hazards models, censored data and binary data. We provide large sample inference results and present formal and informal techniques for model building including order selection, outlier identification, treatment of missing values, and estimation of a transformation power. We examine several examples and special cases.

Spatial Modelling of Emergency Service Response Times

Summary The paper concerns the statistical modelling of emergency service response times. We apply advanced methods from spatial survival analysis to deliver inference for data collected by the London Fire Brigade on response times to reported dwelling fires. Existing approaches to the analysis of these data have been mainly descriptive; we describe and demonstrate the advantages of a more sophisticated approach. Our final parametric proportional hazards model includes harmonic regression terms to describe how the response time varies with the time of day and shared spatially correlated frailties on an auxiliary grid for computational efficiency. We investigate the short-term effect of fire station closures in 2014. Although the London Fire Brigade are working hard to keep response times down, our findings suggest that there is a limit to what can be achieved logistically: the paper identifies areas around the now closed Belsize, Bow, Downham, Kingsland, Knightsbridge, Silvertown, Southwark, Westminster and Woolwich fire stations in which there should perhaps be some concern about the provision of fire services.

Joint longitudinal hurdle and time-to-event models: an application related to viral load and duration of the first treatment regimen in patients with HIV initiating therapy.

Shared parameter joint models provide a framework under which a longitudinal response and a time to event can be modelled simultaneously. A common assumption in shared parameter joint models has been to assume that the longitudinal response is normally distributed. In this paper, we instead propose a joint model that incorporates a two-part 'hurdle' model for the longitudinal response, motivated in part by longitudinal response data that is subject to a detection limit. The first part of the hurdle model estimates the probability that the longitudinal response is observed above the detection limit, whilst the second part of the hurdle model estimates the mean of the response conditional on having exceeded the detection limit. The time-to-event outcome is modelled using a parametric proportional hazards model, assuming a Weibull baseline hazard. We propose a novel association structure whereby the current hazard of the event is assumed to be associated with the current combined (expected) outcome from the two parts of the hurdle model. We estimate our joint model under a Bayesian framework and provide code for fitting the model using the Bayesian software Stan. We use our model to estimate the association between HIV RNA viral load, which is subject to a lower detection limit, and the hazard of stopping or modifying treatment in patients with HIV initiating antiretroviral therapy. Copyright © 2016 John Wiley & Sons, Ltd.

Parametric and Non-Parametric Approaches on Survival Analysis for Diabetic Retinopathy Data

This article provides a review of techniques for the analysis of survival data arising from retinopathy health studies. Popular techniques such as the Kaplan–Meier survival plot and the Cox proportional hazards model are presented and illustrated using data from a DRS(Diabetic Retinopathy Study). Advanced issues are also discussed, including parametric proportional hazards models, and accelerated failure time models, a novel measure of the effect of treatment.

Estimating excess hazard ratios and net survival when covariate data are missing: strategies for multiple imputation.

Net survival is the survival probability we would observe if the disease under study were the only cause of death. When estimated from routinely collected population-based cancer registry data, this indicator is a key metric for cancer control. Unfortunately, such data typically contain a non-negligible proportion of missing values on important prognostic factors (eg, tumor stage). We carried out an empirical study to compare the performance of complete records analysis and several multiple imputation strategies when net survival is estimated via a flexible parametric proportional hazards model that includes stage, a partially observed categorical covariate. Starting from fully observed cancer registry data, we induced missingness on stage under three scenarios. For each of these scenarios, we simulated 100 incomplete datasets and evaluated the performance of the different strategies. Ordinal logistic models are not suitable for the imputation of tumor stage. Complete records analysis may lead to grossly misleading estimates of net survival, even when the missing data mechanism is conditionally independent of survival time given the covariates and the bias on the excess hazard ratios estimates is negligible. As key covariates are unlikely missing completely at random, studies estimating net survival should not use complete records. When the missingness can be inferred from available data, appropriate multiple imputation should be performed. In the context of flexible parametric proportional hazards models with a partially observed stage covariate, a multinomial logistic imputation model for stage should be used and should include the Nelson-Aalen cumulative hazard estimate and the event indicator.

Bayesian Inference in Marshall–Olkin Bivariate Exponential Shared Gamma Frailty Regression Model under Random Censoring

Many analyses in the epidemiological and the prognostic studies and in the studies of event history data require methods that allow for unobserved covariates or “frailties”. We consider the shared frailty model in the framework of parametric proportional hazard model. There are certain assumptions about the distribution of frailty and baseline distribution. The exponential distribution is the commonly used distribution for analyzing lifetime data. In this paper, we consider shared gamma frailty model with bivariate exponential of Marshall and Olkin (1967) distribution as baseline hazard for bivariate survival times. We solve the inferential problem in a Bayesian framework with the help of a comprehensive simulation study and real data example. We fit the model to the real-life bivariate survival data set of diabetic retinopathy data. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the proposed model and then compare the true values of the parameters with the estimated values for different sample sizes.

Residual plots to reveal the functional form for covariates in parametric accelerated failure time models.

We study residual plots for parametric accelerated failure time (AFT) models, using both standardized residuals and Cox-Snell residuals. Two different approaches are discussed in the case of censored data; adjusting censored residuals by adding a residual time, and using nonparametric exponential regression of non-adjusted censored Cox-Snell residuals. The main object of the paper is to show how residuals can be used to infer the correct functional form for possibly misspecified covariates. We demonstrate the use of the methods by analysis of two reliability data sets and by a simulation study using Weibull-distributed data. We also consider briefly a corresponding approach for parametric proportional hazards models.