Semiparametric Cox Model Research Articles

Bayesian analysis of semi-parametric Cox models with latent variables.

Respiratory cancer is one of the most commonly diagnosed cancers as well as the leading cause of cancer death. Numerous efforts have been devoted to reducing the death rate of respiratory cancer. In this article, we propose a semi-parametric Cox model with latent variables to assess the effects of observed and latent risk factors on survival time of respiratory cancer. The characteristics of latent risk factors are characterized via multiple observed indicators by a confirmatory factor analysis model. We develop a Bayesian estimation procedure to obtain the estimates of parameters. Simulation shows that the performance of the proposed methodology is satisfactory. The proposed method is applied to analyze the Surveillance, Epidemiology, and End Results Program data set.

Survival analysis with time-dependent covariates subject to missing data or measurement error: Multiple Imputation for Joint Modeling (MIJM)

Modern epidemiological studies collect data on time-varying individual-specific characteristics, such as body mass index and blood pressure. Incorporation of such time-dependent covariates in time-to-event models is of great interest, but raises some challenges. Of specific concern are measurement error, and the non-synchronous updating of covariates across individuals, due for example to missing data. It is well known that in the presence of either of these issues the last observation carried forward (LOCF) approach traditionally used leads to bias. Joint models of longitudinal and time-to-event outcomes, developed recently, address these complexities by specifying a model for the joint distribution of all processes and are commonly fitted by maximum likelihood or Bayesian approaches. However, the adequate specification of the full joint distribution can be a challenging modeling task, especially with multiple longitudinal markers. In fact, most available software packages are unable to handle more than one marker and offer a restricted choice of survival models. We propose a two-stage approach, Multiple Imputation for Joint Modeling (MIJM), to incorporate multiple time-dependent continuous covariates in the semi-parametric Cox and additive hazard models. Assuming a primary focus on the time-to-event model, the MIJM approach handles the joint distribution of the markers using multiple imputation by chained equations, a computationally convenient procedure that is widely available in mainstream statistical software. We developed an R package "survtd" that allows MIJM and other approaches in this manuscript to be applied easily, with just one call to its main function. A simulation study showed that MIJM performs well across a wide range of scenarios in terms of bias and coverage probability, particularly compared with LOCF, simpler two-stage approaches, and a Bayesian joint model. The Framingham Heart Study is used to illustrate the approach.

Migration sélective des adultes et inégalités face au décès entre milieux urbains et ruraux au Burkina Faso

En prenant l’exemple du Burkina Faso, où les migrations du milieu rural vers le milieu urbain continuent d’alimenter abondamment le processus d’urbanisation, cette recherche teste les effets nets de la migration sur le différentiel de mortalité entre milieux urbains et ruraux chez les adultes de 15 à 74 ans. Elle s’appuie sur les informations recueillies dans les observatoires de population situés à la campagne (Nouna) et en ville (Ouagadougou) sur une période récente (2009-2013). Les données longitudinales sont exploitées avec un modèle semi-paramétrique de Cox. Dans un milieu rural où les conditions sanitaires sont peu favorables, ce sont les individus en bonne santé qui migrent en direction des villes, renforçant ainsi à court terme l’avantage sanitaire urbain. Malgré cette sélection d’abord positive en termes de santé, ils perdent leur avantage sanitaire au fil du temps avec la résidence en milieu urbain, ce qui constitue probablement un frein à la transition de la mortalité à l’échelle du pays, dans la mesure où ces derniers étaient en meilleure santé dans leur milieu d’origine. Pour les migrants de retour (rural-urbain-rural), on n’observe pas d’effet de sélection. Au-delà des effets de composition et de contexte, la sélection positive des migrants rural-urbain contribue à exacerber le désavantage sanitaire du milieu rural vis-à-vis du milieu urbain.

A Comparative Study of Cox Regression vs. Log-Logistic Regression (with and without its frailty) in Estimating Survival Time of Patients with Colorectal Cancer

Colorectal cancer is common and lethal disease with different incidence rate in different parts of the world which is taken into account as the third cause of cancer-related deaths. In the present study, using non-parametric Cox model and parametric Log-logistic model, factors influencing survival of patients with colorectal cancer were evaluated and the models efficiency were compared to provide the best model. This study is conducted on medical records of 1,127 patients with colorectal cancer referred to Taleghani Medical and Training Center of Tehran between 2001 - 2007 and were definitely diagnosed with cancer, pathologically. Semi-parametric Cox model and parametric log-logistic model were fitted. Akaike’s criterion of Cox Snell graph was used to compare the models. To take into account non-measured individual characteristics, frailty was added to Cox and log-logistic models. All calculations were carried out using STATA software version 12 and SPSS version 20.0, at the 0.05 level of significance. From a total of 1,127 patients studied in this research, there were 690 men and 437 women. According to non-parametric Kaplan-Meier method, chances of surviving for 1, 3, 5 and 7 years were 91.16, 73.20, 61.00, and 54.94, respectively. Addition of frailty parameter did not change the model outcome. The results of fitting classified Cox and log-logistic models showed that body mass index (BMI), tumor grade, tumor size, and spread to lymph nodes, were the factors affecting survival time. Based on comparisons, and according to Cox Snell residuals, Cox and log-logistic models had almost identical results; however, because of the benefits of parametric models, in surveying survival time of patients with colorectal cancer, log-logistic can be replaced, as a parametric model, with Cox model.Journal of Medical and Biomedical Sciences (2017) 6(1), 35-43Keywords: Colorectal cancer, Cox regression, Log-logistic model, Cox Snell residual

Cox Regression and Parametric Models: Comparison of How They Determine Factors Influencing Survival of Patients with Non-Small Cell Lung Carcinoma

Background and objectives:The present study of survival rate of patients with non-small cell carcinoma (NSCLC) compared the efficiency of Cox semi-parametric vs. parametric models in determination of influencing factors.Methods:In this retrospective cohort study, data were gathered from 190 patients with a confirmed diagnosis of NSCLC referred to Shahid Sadoughi and Shohadaye Kargar Hospitals in Yazd, Iran during 2005 to 2014. To identify and compare factors influencing the survival rate, a Cox semi-parametric model was fitted to the data. Data analysis was performed using the R software version R3.3.1, and the significance level was set at 0.05.Results:The average age was 64.5 years. About 40% of patients had stage 4 disease. The median survival was 8 months. After comparing the models, the more efficient was the log-normal distribution (AIC=889.3829), with which disease stage, type of therapy, and age were significant factors. Among the different types of therapy, chemotherapy and radiotherapy yielded higher survival rates, and increased age was associated with lower survival.Conclusion:The most efficient model was a log-normal model. Implementation of optimal therapies at early stages can improve the survival of patients.

Analyzing the profit-loss sharing contracts with Markov model

The purpose of this paper is to examine how to use first order Markov chain to build a reliable monitoring system for the profit-loss sharing based contracts (PLS) as the mode of financing contracts in Islamic bank with censored continuous-time observations. The paper adopts the longitudinal analysis with the first order Markov chain framework. Laplace transform was used with homogenous continuous time assumption, from discretized generator matrix, to generate the transition matrix. Various metrics, i.e.: eigenvalue and eigenvector were used to test the first order Markov chain assumption. Cox semi parametric model was used also to analyze the momentum and waiting time effect as non-Markov behavior. The result shows that first order Markov chain is powerful as a monitoring tool for Islamic banks. We find that waiting time negatively affected present rating downgrade (upgrade) significantly. Likewise, momentum covariate showed negative effect. Finally, the result confirms that different origin rating have different movement behavior. The paper explores the potential of Markov chain framework as a risk management tool for Islamic banks. It provides valuable insight and integrative model for banks to manage their borrower accounts. This model can be developed to be a powerful early warning system to identify which borrower needs to be monitored intensively. Ultimately, this model could potentially increase the efficiency, productivity and competitiveness of Islamic banks in Indonesia. The analysis used only rating data. Further study should be able to give additional information about the determinant factors of rating movement of the borrowers by incorporating various factors such as contract-related factors, bank-related factors, borrower-related factors and macroeconomic factors.

Generalized log-logistic proportional hazard model with applications in survival analysis

Proportional hazard (PH) models can be formulated with or without assuming a probability distribution for survival times. The former assumption leads to parametric models, whereas the latter leads to the semi-parametric Cox model which is by far the most popular in survival analysis. However, a parametric model may lead to more efficient estimates than the Cox model under certain conditions. Only a few parametric models are closed under the PH assumption, the most common of which is the Weibull that accommodates only monotone hazard functions. We propose a generalization of the log-logistic distribution that belongs to the PH family. It has properties similar to those of log-logistic, and approaches the Weibull in the limit. These features enable it to handle both monotone and nonmonotone hazard functions. Application to four data sets and a simulation study revealed that the model could potentially be very useful in adequately describing different types of time-to-event data.

Superação de dormência em sementes de Jatobá avaliadas por análise de sobrevivência

This work evaluated methods of overcoming dormancy in Jatoba seeds (Hymenaea courbaril L.) by utilizing survival analysis. 75 seeds per treatment were evaluated: without treatment (T1), immersion in water at outdoor temperature for 120 h (T2) and 72 h (T3), immersion in water at 90 oC and rest in the same water for 24 h (T4), mechanical scarification (T5) and mechanical scarification and soaking it in water for 24 h (T6). The seeds germinated per treatment were registered daily. The Kaplan-Meier method was utilized to estimate the curves of survival and median periods for the germination, the log-rank test and the Cox semiparametric model to estimate the effect of the treatments. The median periods of germination were 56 days (T4) and 33 days (T6). The seeds submitted to T4, T5 and T6 have respectively 22.5, 4.7 and 3.7 times higher capacity to germinate (shorter period for germination) than those seeds that were not submitted to overcoming dormancy.

Multiple imputation of a randomly censored covariate improves logistic regression analysis

ABSTRACTRandomly censored covariates arise frequently in epidemiologic studies. The most commonly used methods, including complete case and single imputation or substitution, suffer from inefficiency and bias. They make strong parametric assumptions or they consider limit of detection censoring only. We employ multiple imputation, in conjunction with semi-parametric modeling of the censored covariate, to overcome these shortcomings and to facilitate robust estimation. We develop a multiple imputation approach for randomly censored covariates within the framework of a logistic regression model. We use the non-parametric estimate of the covariate distribution or the semi-parametric Cox model estimate in the presence of additional covariates in the model. We evaluate this procedure in simulations, and compare its operating characteristics to those from the complete case analysis and a survival regression approach. We apply the procedures to an Alzheimer's study of the association between amyloid positivity and maternal age of onset of dementia. Multiple imputation achieves lower standard errors and higher power than the complete case approach under heavy and moderate censoring and is comparable under light censoring. The survival regression approach achieves the highest power among all procedures, but does not produce interpretable estimates of association. Multiple imputation offers a favorable alternative to complete case analysis and ad hoc substitution methods in the presence of randomly censored covariates within the framework of logistic regression.

Large-volume low apparent diffusion coefficient lesions predict poor survival in bevacizumab-treated glioblastoma patients.

Glioblastomas treated with bevacizumab may develop low-signal apparent diffusion coefficient (low-ADC) lesions, which may reflect increased tumor cellularity or atypical necrosis. The purpose of this study was to examine the relationship between low-ADC lesions and overall survival (OS). We hypothesized that growing low-ADC lesions would be associated with shorter OS. We retrospectively identified 52 patients treated with bevacizumab for the first (n = 42, 81%) or later recurrence of primary glioblastoma, who had low-ADC lesions and 2 post-bevacizumab scans ≤90 days apart. Low-ADC lesion volumes were measured, and normalized 5th percentile histogram low-ADC values were recorded. Using OS as the primary endpoint, semiparametric Cox models were fitted to ascertain univariate and multivariate hazard ratios (HRs) with significance at P = .05. Median OS was 9.1 months (95% CI = 7.2-14.3). At the second post-bevacizumab scan, the volume of the low-ADC lesion (median: 12.94 cm(3)) was inversely associated with OS, with larger volumes predicting shorter OS (HR = 1.014 [95% CI = 1.003-1.025], P = .009). The percent change in low-ADC volume (median: 6.8%) trended toward increased risk of death with growing volumes (P = .08). Normalized 5th percentile low-ADC value and its percent change were not associated with OS (P > .51). Also correlated with shorter OS were the pre-bevacizumab nonenhancing volume (P = .025), the first post-bevacizumab enhancing volume (P = .040), and the second post-bevacizumab enhancing volume (P = .004). The volume of low-ADC lesions at the second post-bevacizumab scan predicted shorter OS. This suggests that low-ADC lesions may be considered important imaging markers and included in treatment decision algorithms.

Survival rates of patients with cancer of the lip, mouth and pharynx: a cohort study of 10 years.

Cancer of the lip, mouth and pharynx is a serious health problem. High incidence rates are found worldwide. In Brazil, the Southern and Southeastern regions have the highest incidences in the country. To describe 5 and 10-year survival rates in patients with cancer of the lip, mouth and pharynx at a referral center in Florianopolis, Santa Catarina, Brazil. Retrospective cohort study using data from patients diagnosed between January 1st and December 31st, 2001, with follow-up until December 31st, 2011. Descriptive analysis was performed and survival was estimated by Kaplan-Meier method. Cox semi-parametric model was used to estimate death risk. Survival rates at 5 and 10 years were 33.3 and 26.9%, respectively. Advanced clinical stage in the diagnosis increased death risk by 2.88 and 2.51, respectively. Sex, ethnicity, level of education, previous diagnosis and treatment, as well as age, did not show significant association. Survival rate at 5 years was 33.3% and, at 10 years, was 26.9%. Advanced stage was an independent risk factor for death due to cancer of the lip, mouth and pharynx in both periods analyzed.

Semiparametric modeling of grouped current duration data with preferential reporting.

Current duration data arise in cross-sectional studies from questions on the length of time from an initiating event to the time of interview. For example, in the National Survey on Family Growth, women who were considered at risk for pregnancy were asked (i) 'Are you currently attempting pregnancy?' and (ii) 'If yes, how many months have you been attempting to get pregnant?' The responses to (ii), referred to as the current durations, are length-biased because women with longer durations are more likely to answer yes to question (i) and therefore be included in the sample. Previous methods to analyze such data include continuous time nonparametric and parametric approaches. In this article, we propose a semiparametric Cox model and a piecewise constant baseline model (used to account for digit preference) to analyze grouped current duration data. We discuss and investigate through simulation studies, the robustness properties of the proposed methods when digit preference is present. Lastly, we present an analysis of the current duration data resulting from the 2002 National Survey on Family Growth. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

Recombining Activity Domains in Activity Systems: A Modularity Perspective

A firm’s system of activities can be decomposed into sub-domains of activities, which can adapt and innovate almost independently from one another because of few interdependencies across domains. S...

Comparison between Parametric and Semi-parametric Cox Models in Modeling Transition Rates of a Multi-state Model: Application in Patients with Gastric Cancer Undergoing Surgery at the Iran Cancer Institute

Research on cancers with a high rate of mortality such as those occurring in the stomach requires using models which can provide a closer examination of disease processes and provide researchers with more accurate data. Various models have been designed based on this issue and the present study aimed at evaluating such models. Data from 330 patients with gastric cancer undergoing surgery at Iran Cancer Institute from 1995 to 1999 were analyzed. Cox-Snell Residuals and Akaike Information Criterion were used to compare parametric and semi-parametric Cox models in modeling transition rates among different states of a multi-state model. R 2.15.1 software was used for all data analyses. Analysis of Cox-Snell Residuals and Akaike Information Criterion for all probable transitions among different states revealed that parametric models represented a better fitness. Log-logistic, Gompertz and Log-normal models were good choices for modeling transition rate for relapse hazard (state 1?state 2), death hazard without a relapse (state 1?state 3) and death hazard with a relapse (state 2?state 3), respectively. Although the semi-parametric Cox model is often used by most cancer researchers in modeling transition rates of multi- state models, parametric models in similar situations- as they do not need proportional hazards assumption and consider a specific statistical distribution for time to occurrence of next state in case this assumption is not made - are more credible alternatives.

A duration analysis of congressional widows’ careers

The extensive congressional politics literature on House member retirement has yet to consider an important and unique subgroup of members – congressional widows. Using a semi-parametric Cox Model, this paper examines the duration of widows’ careers in the United States House of Representatives. Of particular concern are the relationships between years in office and age, education, region, prior political experience, committee positions, career ceilings, majority/minority status, and majority party size. We find that age, region, and majority party size are most relevant to understanding lengths of widows’ careers. In doing so, we contribute to the literature on political widows, gender in politics, as well as more general scholarship centered on congressional careers.

Nonlinear multiple imputation for continuous covariate within semiparametric Cox model: application to HIV data in Senegal

Multiple imputation is commonly used to impute missing covariate in Cox semiparametric regression setting. It is to fill each missing data with more plausible values, via a Gibbs sampling procedure, specifying an imputation model for each missing variable. This imputation method is implemented in several softwares that offer imputation models steered by the shape of the variable to be imputed, but all these imputation models make an assumption of linearity on covariates effect. However, this assumption is not often verified in practice as the covariates can have a nonlinear effect. Such a linear assumption can lead to a misleading conclusion because imputation model should be constructed to reflect the true distributional relationship between the missing values and the observed values. To estimate nonlinear effects of continuous time invariant covariates in imputation model, we propose a method based on B-splines function. To assess the performance of this method, we conducted a simulation study, where we compared the multiple imputation method using Bayesian splines imputation model with multiple imputation using Bayesian linear imputation model in survival analysis setting. We evaluated the proposed method on the motivated data set collected in HIV-infected patients enrolled in an observational cohort study in Senegal, which contains several incomplete variables. We found that our method performs well to estimate hazard ratio compared with the linear imputation methods, when data are missing completely at random, or missing at random.

Badanie determinant pozostawania bez pracy osób młodych z wykorzystaniem semiparametrycznego modelu Coxa

High unemployment rates are observed among people beginning job careers nowadays. The aim of the work is to identify demographic and socio-economic factors influencing the unemployment duration in this age group. In this research, Bayesian semiparametric Cox model for individual data has been used. The advantage of survival model is the possibility of the analysis of the impact of selected independent variables on unemployment duration. The Bayesian approach with a priori distribution makes the use of out of the sample knowledge possible. The model has been estimated using Markov chain Monte Carlo method with ARMS algorithm.

A parametric model fitting time to first event for overdispersed data: application to time to relapse in multiple sclerosis

In this article, we propose a parametric model for the distribution of time to first event when events are overdispersed and can be properly fitted by a Negative Binomial distribution. This is a very common situation in medical statistics, when the occurrence of events is summarized as a count for each patient and the simple Poisson model is not adequate to account for overdispersion of data. In this situation, studying the time of occurrence of the first event can be of interest. From the Negative Binomial distribution of counts, we derive a new parametric model for time to first event and apply it to fit the distribution of time to first relapse in multiple sclerosis (MS). We develop the regression model with methods for covariate estimation. We show that, as the Negative Binomial model properly fits relapse counts data, this new model matches quite perfectly the distribution of time to first relapse, as tested in two large datasets of MS patients. Finally we compare its performance, when fitting time to first relapse in MS, with other models widely used in survival analysis (the semiparametric Cox model and the parametric exponential, Weibull, log-logistic and log-normal models).

Association between Socioeconomic Position in Earlier and Later Life and Age at Natural Menopause: Estudo Pró-SaúDe, Brazil

This study was based on a prospective cohort of university staff in Rio de Janeiro, Brazil (the Estudo Pró-Saúde). In this article the association between socioeconomic position (SEP) earlier and later in life and age at menopause is investigated. The main indicators investigated were for earlier SEP: mother's and father's schooling; stature; leg and trunk length. For later SEP they were: schooling; home and/or car ownership. Median age at menopause was estimated and survival curves were generated by the Kaplan-Meier method, while the association between indicators of SEP and age at menopause was explored by means of Cox semiparametric models. Associations were found between earlier SEP - represented by trunk length - and earlier menopause and between later SEP - represented by the indicator 'present schooling' - and earlier menopause. The association between earlier and later SEP was confirmed. Adverse situations over the life course can impact age at menopause and related health outcomes.

Return to Work After Long Term Sickness

In this paper the impact of vocational interventions on the duration until reemployment of long term sick workers is studied, taking account of self-perceived health and other personal, health and vocational characteristics. We use a longitudinal dataset containing three waves of interviews with employees who were still on the sickness rolls 9 months after calling in sick. We compare a semi-parametric Cox model with a Weibull model to allow for unobserved heterogeneity. The results from these models are similar. They point to the importance of the set of accommodation and rehabilitation activities that employers and occupational health agencies employ and of a timely start of such activities. Their effectiveness shows that the series of reforms in sickness and disability schemes that were introduced from 2002 onwards have been quite successful.