Time-independent Covariates Research Articles

Regression analysis of interval-censored failure time data with time-dependent covariates

Interval-censored failure time data often occur in many areas and their analysis has recently attracted a great deal of attention. On the other hand, most of the existing literature for them can only deal with time-independent covariates. Sometimes one may face time dependent covariates and furthermore the covariates could also suffer measurement errors. For the situation, one approach is to conduct a joint analysis for which many methods have been developed in the literature under various framework. One drawback of these methods is that they usually assume that there are no more measurements on the covariates after the failure time and it is apparent that this may not be true. In this paper, a new joint analysis approach is proposed that can take into account the extra observations. In particular, for estimation, a MCEM algorithm is developed that is much more stable and converges much faster than the existing algorithms. To assess the finite sample performance of the proposed method, an extensive simulation study is conducted and suggests that it works well for practical situations. Also the method is applied to an AIDS study that motivated this investigation.

Stratified-extended cox model in survival modeling of non-proportional hazard

Cox proportional hazard model is frequently used in survival analysis. Cox proportional hazard model is time independent covariate while many models involve time as a dependent covariate causing incomplete proportional hazard assumption, known as non-proportional hazard. The proposed model in this paper was a non-proportional hazard involving time-independent and time-dependent covariates. The approaching model was carried out by joining a stratified Cox and extended Cox model termed as Stratified-Extended Cox (SE Cox) model. The simulation of the SE Cox model resulted in small MSE for the parameter estimates. In addition, the goodness of value was more appropriate compared to the existing non-proportional hazard model. Hence, the SE Cox model was applied to evaluate student persistence in Universitas Terbuka, Indonesia.

Changes in Oral Anticoagulation Therapy over One Year in 51,000 Atrial Fibrillation Patients at Risk for Stroke: A Practice-Derived Study.

This study assessed changes in anticoagulation therapy over time in patients with atrial fibrillation (AF). Analyses were performed on a claims-based dataset of 4 million health-insured individuals. The study population consisted of patients newly initiating a non-vitamin-K oral anticoagulants (NOACs) or vitamin K antagonist (VKA) for AF between 2013 and 2016. The study outcomes consisted of the proportion of patients who had (1) discontinued OAC treatment, (2) switched from VKA to NOAC, (3) switched from NOAC to VKA or (4) switched from one NOAC to another. Predictors of discontinuation or switching of OAC treatment were determined by Cox proportional hazards regression models with time-independent and time-dependent covariates. The study population comprised 51,606 AF patients initiating VKA (n = 21,468, 41.6%), apixaban (n = 8,832, 17.1%), dabigatran (n = 3,973, 7.7%) or rivaroxaban (n = 17,333, 33.6%). After 1 year, 29.9% of VKA and 29.5% of NOAC patients had discontinued OAC treatment without switching to another anticoagulant. A total of 10.7% of VKA patients switched to NOACs within 1 year, whereas 4.9% NOAC patients had switched to VKA. Of AF patients who were initiated on a NOAC, 5.2% switched to another NOAC. Treatment changes among NOAC starters were strongly associated with occurrence of stroke, myocardial infarction and gastrointestinal bleeding after treatment initiation. For VKA starters switching to a NOAC, stroke and bleeding events were associated with an increased likelihood of switching. Overall discontinuation rates of VKA and NOACs are comparable over the first year of therapy, while switching from VKA to NOAC was more common than from NOAC to VKA. The majority of treatment changes were associated with clinical events.

Occurrence and Risk Factors for Acute Lung Injury (ALI) and Organizing Pneumonia (OP) after Lung Transplant

Purpose ALI and OP are histologic patterns of lung damage associated with poor long-term outcomes after lung transplantation. Yet the incidence of ALI and OP and associated clinical factors remain poorly understood. Methods The cohort was drawn from CTOT-20 (NCT02631720), a multicenter prospective lung transplant cohort study. The first 200 enrolled, transplanted subjects with ≥ 1 lung biopsy in the first year after transplant were included. Descriptive statistics were used to summarize ALI or OP events in the 1007 biopsies performed over the first posttransplant year in this cohort. Univariate Cox regression models were used to evaluate the impact of recipient factors on the time to first ALI or OP event. Time independent covariates included age, sex, native disease, transplant type, use of induction immunosuppression, type of primary maintenance immunosuppression, HLA mismatch, and grade 3 primary graft dysfunction (PGD) within 72 hours. Time dependent covariates included a positive fungal, bacterial, mycobacterial, or respiratory viral organism on a respiratory specimen and development of a donor specific antibody. Results Forty-eight patients (24%) experienced at least one ALI event over the first posttransplant year (max 4 per patient). Similarly, 50 patients (25%) experienced at least one OP event (max 3 per patient). The median time to first ALI event was 44 (IQR 24,90) days while the time to first OP was somewhat longer at 92 (IQR 35,203) days. Both ALI and OP were identified slightly more often on for cause vs. surveillance biopsies. The majority of ALI and OP events were not concurrent with other histologic findings, such as acute rejection. Cox analyses identified PGD (HR 2.27, p=0.01) and cyclosporine-based maintenance therapy (HR 2.15, p=0.01) as risk factors for ALI. Analyses for the outcome of OP also implicated PGD (HR 1.97, p=0.03) and cyclosporine maintenance (HR 2.59, p Conclusion OP and ALI are common patterns of lung allograft injury. We identified clinical risk factors for ALI and OP that are potentially modifiable. Ongoing analyses will validate these risks over extended cohort follow up using multivariable approaches. As such, this work may identify strategies to mitigate ALI and OP and improve lung recipient outcomes.

Estimating trends in the incidence rate with interval censored data and time-dependent covariates.

We propose a multiple imputation method for estimating the incidence rate with interval censored data and time-dependent (and/or time-independent) covariates. The method has two stages. First, we use a semi-parametric G-transformation model to estimate the cumulative baseline hazard function and the effects of the time-dependent (and/or time-independent covariates) on the interval censored infection times. Second, we derive the participant's unique cumulative distribution function and impute infection times conditional on the covariate values. To assess performance, we simulated infection times from a Cox proportional hazards model and induced interval censoring by varying the testing rate, e.g., participants test 100%, 75%, 50% of the time, etc. We then compared the incidence rate estimates from our G-imputation approach with single random-point and mid-point imputation. By comparison, our G-imputation approach gave more accurate incidence rate estimates and appropriate standard errors for models with time-independent covariates only, time-dependent covariates only, and a mixture of time-dependent and time-independent covariates across various testing rates. We demonstrate, for the first time, a multiple imputation approach for incidence rate estimation with interval censored data and time-dependent (and/or time-independent) covariates.

How long are The Survival Time in the Industrial Sector of Indonesian Companies?

Cox Hazard model with time independent covariates is used to view the functions of survival and hazard for each group of industrial sector of companies listed on the Indonesia Stock Exchange. The hazard explains whether events of financial distress will occur in companies that have survived for a certain period. The survival function shows the relationship between probabilities to survive and time, in which time indicates the duration of an event (financial distress). The results of statistical analysis show that the survival time for each industrial group varies from 10.5 to 12.5 years. The results can be used as a basic idea for companies to determine when the preventive actions should be conducted so that companies will sustain their business.

An empirical analysis of post-work grocery shopping activity duration using modified accelerated failure time model to differentiate time-dependent and time-independent covariates.

In this paper, the accelerated failure time (AFT) model is modified to analyze post-work grocery shopping activity duration. Much previous shopping duration analysis was conducted using the proportional hazard (PH) modeling approach. Once the proportionality assumption was violated, the traditional accelerated failure time (TAFT) model was usually selected as an alternative modeling approach. However, a TAFT model only has covariates with non-proportional and time-dependent effects on the hazard overtime while a PH model only accommodates covariates with proportional and time-independent effects. Neither of them considers the possibility that some of covariates may have proportional and time-independent effects and some may have non-proportional and time-dependent effects on the hazard value in one model. To address this issue, the paper generalizes the TAFT model and develops a modified accelerated failure time (MAFT) model to accommodate both time-dependent and time-independent covariates for activity duration analysis. Checking on the proportionality assumption indicates that the assumption is not valid in the post-work grocery shopping activity data extracted from the 2017 National Household Travel Survey (NHTS) conducted by the U.S. Department of Transportation (USDOT). Both TAFT and MAFT models are developed for comparisons and analysis. The empirical and statistical results show that there do exist two different types of covariates affecting shopping activity duration, including covariates only with proportional and time-independent effects (i.e. working duration, commute travel time) and those with non-proportional and time-dependent effects. The MAFT model can capture the subtleties in various types of covariate effects and help better understand how those covariates affect activity duration overtime. This paper also shows the importance to develop a flexible duration model with both time-dependent and time-independent covariates for accurately evaluating travel demand management (TDM) policies, like flexible work hours.

Survival analysis of caries incidence in African-American school-aged children.

To conduct an assessment of time-dependent covariates related to dental caries of the permanent dentition among a low socioeconomic status, understudied cohort of children, incorporating time-dependent covariates through the application of extended Cox proportional hazards modeling. This study modeled the time to first cavitated dental caries in permanent teeth among school-aged children and assessed factors associated with this event. A cohort of 98 low socioeconomic status African-American children with mean age of 5.85 years at baseline was recruited in Uniontown, Alabama and followed prospectively for 6 years. None of these children had dental caries on permanent teeth at baseline, and oral examinations were performed annually. Caries-free survival curves were generated to describe time to event (having first decayed, filled, or missing permanent surface). Bivariate and multivariable extended Cox hazards modeling was used to assess the relationships between time-dependent and time-independent covariates and time to event. Twenty-eight children (28.6 percent) had their first permanent tooth caries event during the 6-year follow-up. Multivariable results showed that greater consumption of water was associated with lower dental caries hazard, while previous primary tooth caries experience was associated with greater dental caries hazard after adjustment for frequency of consumptions of milk, added-sugar beverages, and 100 percent juice. There was a global/overall significant caries protective effect of water consumption during the school-age period of child development.

Instrumental variable estimation in semi-parametric additive hazards models.

SummaryInstrumental variable methods allow unbiased estimation in the presence of unmeasured confounders when an appropriate instrumental variable is available. Two‐stage least‐squares and residual inclusion methods have recently been adapted to additive hazard models for censored survival data. The semi‐parametric additive hazard model which can include time‐independent and time‐dependent covariate effects is particularly suited for the two‐stage residual inclusion method, since it allows direct estimation of time‐independent covariate effects without restricting the effect of the residual on the hazard. In this article, we prove asymptotic normality of two‐stage residual inclusion estimators of regression coefficients in a semi‐parametric additive hazard model with time‐independent and time‐dependent covariate effects. We consider the cases of continuous and binary exposure. Estimation of the conditional survival function given observed covariates is discussed and a resampling scheme is proposed to obtain simultaneous confidence bands. The new methods are compared to existing ones in a simulation study and are applied to a real data set. The proposed methods perform favorably especially in cases with exposure‐dependent censoring.

Simulation shows undesirable results for competing risks analysis with time-dependent covariates for clinical outcomes.

BackgroundWe evaluate three methods for competing risks analysis with time-dependent covariates in comparison with the corresponding methods with time-independent covariates.MethodsWe used cause-specific hazard analysis and two summary approaches for in-hospital death: logistic regression and regression of the subdistribution hazard. We analysed real hospital data (n=1864) and considered pneumonia on admission / hospital-acquired pneumonia as time-independent / time-dependent covariates for the competing events ’discharge alive’ and ’in-hospital death’. Several simulation studies with time-constant hazards were conducted.ResultsAll approaches capture the effect of time-independent covariates, whereas the approaches perform differently with time-dependent covariates. The subdistribution approach for time-dependent covariates detected effects in a simulated no-effects setting and provided counter-intuitive effects in other settings.ConclusionsThe extension of the Fine and Gray model to time-dependent covariates is in general not a helpful synthesis of the cause-specific hazards. Cause-specific hazard analysis and, for uncensored data, the odds ratio are capable of handling competing risks data with time-dependent covariates but the use of the subdistribution approach should be neglected until the problems can be resolved. For general right-censored data, cause-specific hazard analysis is the method of choice.

Semiparametric Regression Analysis of Panel Count Data: A Practical Review.

Panel count data arise in many applications when the event history of a recurrent event process is only examined at a sequence of discrete time points. In spite of the recent methodological developments, the availability of their software implementations has been rather limited. Focusing on a practical setting where the effects of some time-independent covariates on the recurrent events are of primary interest, we review semiparametric regression modelling approaches for panel count data that have been implemented in R package spef. The methods are grouped into two categories depending on whether the examination times are associated with the recurrent event process after conditioning on covariates. The reviewed methods are illustrated with a subset of the data from a skin cancer clinical trial.

Multilevel Analysis for Repeated Measures Data in Lambs1

The study was conducted to compare the individual growth curves models and to detect individual differences in the growth rate by a performing multilevel analysis. The data set used for this purpose consisted of live weight records of 52 crossbred lambs from birth to 182 days of age. There were 670 observations in level-1 units which were the repeated measurements over time, and there were 52 observations in level-2 units which were lambs. In the study, parameter estimation of timeindependent covariate factors, such as gender, birth type and birth weight, was performed by using five different models within the framework of multilevel modeling. LRT, AIC and BIC were used for the selection of the best model. The “Conditional Quadratic Growth Model-B” provided the best fit to the data set. The multilevel analysis indicated that linear and quadratic growth in lambs was significant. According to the results of the study, individual growth curves can be investigated using multilevel modeling in animal studies which is an important parameter of the individual growth rate.

Determinants and Heterogeneity of Time -to- Recovery from Obstetric Fistula Patients; Comparison of Acceleration Failure Time and Parametric Shared Frailty Models.

Obstetric Fistula is a medical condition that involves an opening or perforation between the vagina and the bladder or the vagina and the rectum. It is a serious, life threatening and often debilitating medical condition that affects thousands of women in developing countries.The study consists of 270 obstetric fistula patients having all required information who were taking treatment at Jimma University Specialized Hospital in south west Ethiopia from January, 2011 to January ,2017. The log-rank and generalized wilcoxon test were used to explore the association between the recovery time and different independent categorical covariates. Then using different baseline distribution parametric models were employed to have an appropriate model for the recovery time/status of the patients based on Akaike information criteria (AIC) of the model. Result of Both log-rank and generalized wilcoxon test showed that there were significant differences among obstetric fistula patients in survival experience of weight , marital status, Residence, Incontinence, Antenatal care, mode of delivery, status of urethra and types of fistula of patients at 5% level of significance. Based on AIC log-normal gamma shared frailty model is an appropriate model and there is heterogeneity between patients with zone. The final model showed that marital status, Residence, Incontinence, Antenatal care, status of urethra and types of fistula were the determinants of recovery status of the patients at 5% level of significance. In Conclusion, the result showed that married women, rural residence, incontinence of urine more than 3 months, hadn’t antenatal care and completely damaged urethra were prolonged time recovery time of patients whereas having recto-vaginal-fistula shorten recovery status than vesico-vaginal fistula group of patients.

Determinants of trip duration for international tourists in Norway; a parametric survival analysis

AbstractHow long a tourist stays in a host country acts as an indicator of tourism industry’s contribution towards the national economy. The purpose of this study is to examine how socio-demographic characteristics of international tourists, their travelling purpose, tourism products and characteristics of the destination influence the length of stay in Norway, by estimating a parametric survival model. Total cost of trip, purpose of travel, type of accommodation and transportation, age of tourist and geographical area are key elements that explain the variation in the length of tourist stay in Norway. The Cox proportional hazard model with time-independent covariates indicates the survival probability of tourists with less budget constraints and younger ages is higher than that of low-spending tourists and elderly travelers. Moreover, tourists with the purpose of friend and family visitation are at lower risk of leaving Norway than are tourists with other purposes. In terms of tourism products, choosing camping sites as the type of accommodation and road transport as the mode of transportation are associated with the highest survival probability. Another key finding is that tourists stay longer in northern Norway than in southern Norway; hence, on average, tourists’ overall expenditures are higher in northern Norway.

Context-driven mean residual life estimation of mining machinery

ABSTRACTMaintenance is crucial to ensure production/output and customer satisfaction in the mining sector. The cost of maintenance of mechanised and automated mining systems is very high, necessitating efforts to enhance the effectiveness of maintenance systems and organisation. For effective maintenance planning, it is important to have a good understanding of the reliability and availability characteristics of the systems. Determining the Mean Residual Life (MRL) of systems allows organisations to more effectively plan maintenance tasks. In this paper, we use a statistical approach to estimate MRL and consider a Weibull proportional hazard model (PHM) with time-independent covariates to model the hazard function so that the operating environment could be integrated into the reliability analysis. The paper explains our methods for calculating the conditional reliability function and computing the MRL as a function of the current conditions. The model is verified and validated using data from the hydraulic system of LHD equipment in a Swedish mine. The results are useful to estimate the remaining useful life of such systems; the method can be used for maintenance planning, helping to control unplanned stoppages of highly mechanised and automated systems.

Partially time-varying coefficient proportional hazards models with error-prone time-dependent covariates—an application to the AIDS Clinical Trial Group 175 data

Due to cost and time considerations, interest has focused on identifying surrogate markers that could be substituted for the clinical endpoint, time to an event of interest, in evaluation of treatment efficacy. Joint models are often used to assess the effect of surrogate markers and treatment. Motivated by recent works studying the AIDS Clinical Trial Group (ACTG) 175 data, we propose a partially time-varying coefficient proportional hazards model for modeling the relationship between the hazard of failure and time-dependent and time-independent covariates. The time-varying coefficients are approximated by polynomial splines, and the corrected score and conditional score approaches are adopted to estimate the regression coefficients. The proposed estimators are consistent, and the asymptotic normality is established for the constant coefficients, which enables us to construct confidence intervals and permits joint inference. The finite-sample performance of the proposed method is assessed by Monte Carlo simulation studies. The proposed model is applied to ACTG 175 data to assess the temporal dynamics of the effect of treatment and CD4 count on time to AIDS or death.

Tire demand planning based on reliability and operating environment

Tires represent a critical spare part in mines. There is a shortage of medium and large tires. In addition, with increased mining activities and the creation of new mines, the demand for tires has increased significantly. Thus, it is particularly important for mining engineers to identify tire characteristics and correctly manage the spare part inventory. Spare parts management is critical from an operational perspective, especially in asset intensive industries, such as mining, as well as in organizations owning and operating costly assets. A knowledge of the tires’ behavior (historical data) must be considered together with the operating environment conditions (covariates). This study uses multiple regression analysis based on Cox’s regression model to incorporate machine operating environment information into systems reliability analysis to estimate spare parts. It considers a proportional hazard model and a stratified Cox regression model for time independent and dependent covariates. Based on the results, the study develops a mathematical model for spare parts estimation at the component level for non-repairable parts (tires). It validates the outcomes using a case study of loader tires in Sungun mine in Iran. There is a significant difference in the results of spare parts forecasting and inventory management when considering and not considering covariates.

Factors Influencing Winter Mortality Risk for Pronghorn Exposed to Wind Energy Development

Evaluating the influence of energy development on pronghorn (Antilocapra americana) winter mortality risk is particularly critical given that northern populations already experience decreased survival due to harsh environmental conditions and increased energetic demands during this season. The purpose of our study was to evaluate pronghorn mortality risk over 3 winters (2010, 2010–2011, 2011–2012) on a landscape developed in 2010 for wind energy production (Dunlap Ranch) in south-central Wyoming, United States. We obtained locational data and survival status of 47 adult female pronghorn captured and equipped with Global Positioning System (GPS) transmitters. Overall, 17 pronghorn died during winter seasons, with 76.4% (13) of deaths occurring during the winter with highest snow accumulation (2010–2011). Survival (Ŝ) was lowest in winter 2010–2011 (Ŝ = 0.53, 90% confidence interval [CI]: 0.37–0.70) and highest in winters 2010 (Ŝ = 0.97, 90% CI: 0.92–1.00) and 2011–2012 (Ŝ = 0.91, 90% CI: 0.82–1.00). We modeled mortality risk for pronghorn using Cox’s proportional hazards model inclusive of time-dependent and time-independent covariates within anthropogenic, environmental, and wind energy variable classes. Across winters, pronghorn winter mortality risk decreased by 20% with every 1.0-km increase in average distance from major roads (hazard ratio = 0.80, 90% CI: 0.66–0.98), decreased by 4.0% with every 1% increase in average time spent in sagebrush (Artemisia spp. L.; hazard ratio = 0.96, 90% CI: 0.95–0.98), and decreased by 92% with every 1 unit (VRM × 1000) increase in terrain ruggedness (hazard ratio = 0.08, 90% CI: 0.01–0.68). Pronghorn winter survival was not influenced by exposure to wind energy infrastructure; however, pronghorn survival may be impacted by larger-scale wind energy developments than those examined in our study. We recommend wildlife managers focus on conserving sagebrush stands in designated pronghorn winter range.

Dynamic spare parts transportation model for Arctic production facility

Timely delivery of the required spare parts plays an important role in meeting the availability target and reducing the downtime of production facilities. Spare parts logistics is affected in complex ways while operating in the Arctic, since the area is sparsely populated and has insufficient infrastructure. It is also greatly affected by the distinctive operational environment of the region, such as cold temperature, varying forms of sea ice, blizzards, heavy fog, etc. Therefore, in order to have an effective logistic plan, the effect of all influencing factors, called covariates, on the transportation of the spare parts need to be identified, modelled and quantified by the use of an appropriate dynamic model. The traditional models, however, lack the comprehensive integration of the effect of covariates on the spare parts transportation. The purpose of this paper is to introduce the concept of a dynamic model for spare parts transportation in Arctic conditions by considering the time-independent and time-dependent covariates. The model continuously updates the prior probabilities according to the most recent time-dependent covariates to provide posterior probabilities. The application of the model is illustrated using a case study.

GMM logistic regression models for longitudinal data with time-dependent covariates and extended classifications.

When analyzing longitudinal data, it is essential to account both for the correlation inherent from the repeated measures of the responses as well as the correlation realized on account of the feedback created between the responses at a particular time and the predictors at other times. As such one can analyze these data using generalized estimating equation with the independent working correlation. However, because it is essential to include all the appropriate moment conditions as you solve for the regression coefficients, we explore an alternative approach using a generalized method of moments for estimating the coefficients in such data. We develop an approach that makes use of all the valid moment conditions necessary with each time-dependent and time-independent covariate. This approach does not assume that feedback is always present over time, or if present occur at the same degree. Further, we make use of continuously updating generalized method of moments in obtaining estimates. We fit the generalized method of moments logistic regression model with time-dependent covariates using SAS PROC IML and also in R. We used p-values adjusted for multiple correlated tests to determine the appropriate moment conditions for determining the regression coefficients. We examined two datasets for illustrative purposes. We looked at re-hospitalization taken from a Medicare database. We also revisited data regarding the relationship between the body mass index and future morbidity among children in the Philippines. We conducted a simulated study to compare the performances of extended classifications.