Random-effects Cox proportional hazards model: General variance components methods for time-to-event data

2005 ◽  
Vol 28 (2) ◽  
pp. 97-109 ◽  
Author(s):  
V. Shane Pankratz ◽  
Mariza de Andrade ◽  
Terry M. Therneau
2016 ◽  
Vol 27 (3) ◽  
pp. 955-965 ◽  
Author(s):  
Xiaonan Xue ◽  
Xianhong Xie ◽  
Howard D Strickler

The commonly used statistical model for studying time to event data, the Cox proportional hazards model, is limited by the assumption of a constant hazard ratio over time (i.e., proportionality), and the fact that it models the hazard rate rather than the survival time directly. The censored quantile regression model, defined on the quantiles of time to event, provides an alternative that is more flexible and interpretable. However, the censored quantile regression model has not been widely adopted in clinical research, due to the complexity involved in interpreting its results properly and consequently the difficulty to appreciate its advantages over the Cox proportional hazards model, as well as the absence of adequate validation procedure. In this paper, we addressed these limitations by (1) using both simulated examples and data from National Wilms’ Tumor clinical trials to illustrate proper interpretation of the censored quantile regression model and the differences and the advantages of the model compared to the Cox proportional hazards model; and (2) developing a validation procedure for the predictive censored quantile regression model. The performance of this procedure was examined using simulation studies. Overall, we recommend the use of censored quantile regression model, which permits a more sensitive analysis of time to event data together with the Cox proportional hazards model.


Author(s):  
Evangelos Kritsotakis ◽  
Guillermo Castilla Fernandez ◽  
Mark Strong

Background: Intensive-care unit (ICU) patients are prone to healthcare-associated infections which are often recurrent. Such infections are influenced by previous occurrences and hence correlation between events needs to be taken into account when modelling the risk of infection recurrence. Objective: To compare five different survival-time models, the Cox proportional hazards model (CPH) and three of its extensions to recurrent event data: Andersen-Gill (AG), Prentice-Williams-Peterson (PWP) and Frailty models. Methods: The models were empirically assessed by direct application to data from a cohort study of 550 patients with ICU-acquired infections. Covariate data included patients sex, age, Glasgow, Apache-II and comorbidity scores, and exposures to medical devices, treatment appropriateness and infection site and resistance to carbapenems. Models were compared using accuracy criteria and goodness-of-fit statistics. Results: 180/550 (33%) patients had infection recurrence, of whom 128 had a first, 40 a second and 12 a third recurrence. All models agreed in the direction of effect for all covariates. However, the CPH model for the risk of first recurrence disregarded data on 64 (26%) of infections, produced the more pronounced hazard ratio estimates, and presented the poorest data fit and accuracy measures. Model fit and accuracy improved in all extended models, with PWP performing best in terms of log-likelihood, Akaike and Bayesian information criteria. Conclusion: The PWP model is based on plausible assumptions in the context of modelling the risk of infection recurrence and was shown in this study to outperform alternative extensions for modelling recurrent events.


BMC Cancer ◽  
2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Wei Liu ◽  
Bolong Yu ◽  
Yunfan Luo ◽  
Junzheng Li ◽  
Xiaofei Yuan ◽  
...  

Abstract Background Although the National Comprehensive Cancer Network (NCCN) Guidelines recommend CCRT+AC and IC + CCRT as level 2A evidence for treatment of the locoregionally advanced NPC (II-IVa), IC + CCRT+AC could also be an alternative but it is seldom used because of the low completion rates. This article aimed to compare the effectiveness of the three radiotherapy regimens using a large-scale retrospective study. Methods This retrospective single center analysis enrolled 1812 diagnosed NPC patients at Nanfang Hospital from January 2005 to December 2015 and only 729 patients met the inclusion criteria and were analyzed. Patients without distant metastasis, age of 18–70 years, Karnofsky scores of at least 70,stage III-IVb, and adequate adequate bone marrow, liver and renal function. Were enrolled. Adverse events and other categorical variables were compared by Pearson chi-square test or Fishier exact test. Time-to-event data were described with the Kaplan-Meier curves, time-to-event intervals compared with the log-rank test. We did multivariable analyses with the Cox proportional hazards model to test the independent signifi cance of diff erent factors. Cox proportional hazards model was used to estimate the β regression coeffi cient, p value, and hazard ratio and its 95% CI for each of the selected risk predictors. Results The median follow-up time was 47 months. Kaplan-Meier analyses revealed no significant differences among three groups in 3-year failure-free survival (FFS, P = 0.225), 3-year overall survival (OS, P = 0.992), 3-year locoregional failure-free survival (LFFS, P = 0.549), and 3-year distant failure-free survival (DFFS, P = 0.174). Stratified survival analysis based on the risk scoring model revealed no differences in FFS, OS, LFFS, and DFFS between IC + CCRT and CCRT+AC groups for low-risk patients, however, the 3-year OS (88.3% vs. 77.6%, P = 0.049) and 3-year DFFS (84.0% vs.66.8%, P = 0.032) were respectively significantly better in IC + CCRT group compared with CCRT+AC group for high-risk patients. Conclusions Compared with CCRT+AC, IC + CCRT lowers distant metastasis rate and improves OS among patients with locally advanced NPC in high risk group.


2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Maryam Farhadian ◽  
Sahar Dehdar Karsidani ◽  
Azadeh Mozayanimonfared ◽  
Hossein Mahjub

Abstract Background Due to the limited number of studies with long term follow-up of patients undergoing Percutaneous Coronary Intervention (PCI), we investigated the occurrence of Major Adverse Cardiac and Cerebrovascular Events (MACCE) during 10 years of follow-up after coronary angioplasty using Random Survival Forest (RSF) and Cox proportional hazards models. Methods The current retrospective cohort study was performed on 220 patients (69 women and 151 men) undergoing coronary angioplasty from March 2009 to March 2012 in Farchshian Medical Center in Hamadan city, Iran. Survival time (month) as the response variable was considered from the date of angioplasty to the main endpoint or the end of the follow-up period (September 2019). To identify the factors influencing the occurrence of MACCE, the performance of Cox and RSF models were investigated in terms of C index, Integrated Brier Score (IBS) and prediction error criteria. Results Ninety-six patients (43.7%) experienced MACCE by the end of the follow-up period, and the median survival time was estimated to be 98 months. Survival decreased from 99% during the first year to 39% at 10 years' follow-up. By applying the Cox model, the predictors were identified as follows: age (HR = 1.03, 95% CI 1.01–1.05), diabetes (HR = 2.17, 95% CI 1.29–3.66), smoking (HR = 2.41, 95% CI 1.46–3.98), and stent length (HR = 1.74, 95% CI 1.11–2.75). The predictive performance was slightly better by the RSF model (IBS of 0.124 vs. 0.135, C index of 0.648 vs. 0.626 and out-of-bag error rate of 0.352 vs. 0.374 for RSF). In addition to age, diabetes, smoking, and stent length, RSF also included coronary artery disease (acute or chronic) and hyperlipidemia as the most important variables. Conclusion Machine-learning prediction models such as RSF showed better performance than the Cox proportional hazards model for the prediction of MACCE during long-term follow-up after PCI.


Author(s):  
Yuko Yamaguchi ◽  
Marta Zampino ◽  
Toshiko Tanaka ◽  
Stefania Bandinelli ◽  
Yusuke Osawa ◽  
...  

Abstract Background Anemia is common in older adults and associated with greater morbidity and mortality. The causes of anemia in older adults have not been completely characterized. Although elevated circulating growth and differentiation factor 15 (GDF-15) has been associated with anemia in older adults, it is not known whether elevated GDF-15 predicts the development of anemia. Methods We examined the relationship between plasma GDF-15 concentrations at baseline in 708 non-anemic adults, aged 60 years and older, with incident anemia during 15 years of follow-up among participants in the Invecchiare in Chianti (InCHIANTI) Study. Results During follow-up, 179 (25.3%) participants developed anemia. The proportion of participants who developed anemia from the lowest to highest quartile of plasma GDF-15 was 12.9%, 20.1%, 21.2%, and 45.8%, respectively. Adults in the highest quartile of plasma GDF-15 had an increased risk of developing anemia (Hazards Ratio 1.15, 95% Confidence Interval 1.09, 1.21, P<.0001) compared to those in the lower three quartiles in a multivariable Cox proportional hazards model adjusting for age, sex, serum iron, soluble transferrin receptor, ferritin, vitamin B12, congestive heart failure, diabetes mellitus, and cancer. Conclusions Circulating GDF-15 is an independent predictor for the development of anemia in older adults.


2020 ◽  
Vol 4 (Supplement_1) ◽  
pp. 161-161
Author(s):  
Jane Banaszak-Holl ◽  
Xiaoping Lin ◽  
Jing Xie ◽  
Stephanie Ward ◽  
Henry Brodaty ◽  
...  

Abstract Research Aims: This study seeks to understand whether those with dementia experience higher risk of death, using data from the ASPREE (ASPirin in Reducing Events in the Elderly) clinical trial study. Methods: ASPREE was a primary intervention trial of low-dose aspirin among healthy older people. The Australian cohort included 16,703 dementia-free participants aged 70 years and over at enrolment. Participants were triggered for dementia adjudication if cognitive test results were poorer than expected, self-reporting dementia diagnosis or memory problems, or dementia medications were detected. Incidental dementia was adjudicated by an international adjudication committee using the Diagnostic and Statistical Manual for Mental Disorders (DSM-IV) criteria and results of a neuropsychological battery and functional measures with medical record substantiation. Statistical analyses used a cox proportional hazards model. Results: As previously reported, 1052 participants (5.5%) died during a median of 4.7 years of follow-up and 964 participants had a dementia trigger, of whom, 575 (60%) were adjucated as having dementia. Preliminary analyses has shown that the mortality rate was higher among participants with a dementia trigger, regardless of dementia adjudication outcome, than those without (15% vs 5%, Χ2 = 205, p <.001). Conclusion: This study will provide important analyses of differences in the hazard ratio for mortality and causes of death among people with and without cognitive impairment and has important implications on service planning.


Risks ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 121
Author(s):  
Beata Bieszk-Stolorz ◽  
Krzysztof Dmytrów

The aim of our research was to compare the intensity of decline and then increase in the value of basic stock indices during the SARS-CoV-2 coronavirus pandemic in 2020. The survival analysis methods used to assess the risk of decline and chance of rise of the indices were: Kaplan–Meier estimator, logit model, and the Cox proportional hazards model. We observed the highest intensity of decline in the European stock exchanges, followed by the American and Asian plus Australian ones (after the fourth and eighth week since the peak). The highest risk of decline was in America, then in Europe, followed by Asia and Australia. The lowest risk was in Africa. The intensity of increase was the highest in the fourth and eleventh week since the minimal value had been reached. The highest odds of increase were in the American stock exchanges, followed by the European and Asian (including Australia and Oceania), and the lowest in the African ones. The odds and intensity of increase in the stock exchange indices varied from continent to continent. The increase was faster than the initial decline.


BMC Nutrition ◽  
2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Akiko Nakanishi ◽  
Erika Homma ◽  
Tsukasa Osaki ◽  
Ri Sho ◽  
Masayoshi Souri ◽  
...  

Abstract Background Dairy products are known as health-promoting foods. This study prospectively examined the association between milk and yogurt intake and mortality in a community-based population. Methods The study population comprised of 14,264 subjects aged 40–74 years who participated in an annual health checkup. The frequency of yogurt and milk intake was categorized as none (< 1/month), low (< 1/week), moderate (1–6/week), and high (> 1/day) intake. The association between yogurt and milk intake and total, cardiovascular, and cancer-related mortalities was determined using the Cox proportional hazards model. Results During the follow-up period, there were 265 total deaths, 40 cardiovascular deaths and 90 cancer-related deaths. Kaplan–Meier analysis showed that the total mortality in high/moderate/low yogurt intake and moderate/low milk intake groups was lower than that in none group (log-rank, P < 0.01). In the multivariate Cox proportional hazard analysis adjusted for possible confounders, the hazard ratio (HR) for total mortality significantly decreased in high/moderate yogurt intake group (HR: 0.62, 95% confidence interval [CI]: 0.42–0.91 for high intake, HR: 0.70, 95%CI: 0.49–0.99 for moderate intake) and moderate milk intake group (HR: 0.67, 95% CI: 0.46–0.97) compared with the none yogurt and milk intake groups. A similar association was observed for cancer-related mortality, but not for cardiovascular mortality. Conclusions Our study showed that yogurt and milk intake was independently associated with a decrease in total and cancer-related mortalities in the Japanese population.


2020 ◽  
Vol 41 (Supplement_2) ◽  
Author(s):  
A Fujino ◽  
H Ogawa ◽  
S Ikeda ◽  
K Doi ◽  
Y Hamatani ◽  
...  

Abstract Background Atrial fibrillation (AF) commonly progresses from paroxysmal type to sustained type in the natural course of the disease, and we previously demonstrated that the progression of AF was associated with increased risk of clinical adverse events. There are some patients, though less frequently, who regress from sustained to paroxysmal AF, but the clinical impact of the regression of AF remains unknown. Purpose We sought to investigate whether regression from sustained to paroxysmal AF is associated with better clinical outcomes. Methods Using the dataset of the Fushimi AF Registry, patients who were diagnosed as sustained (persistent or permanent) AF at baseline were studied. Conversion of sustained AF to paroxysmal AF during follow-up was defined as regression of AF. Major adverse cardiac events (MACE) were defined as the composite of cardiac death, stroke, and hospitalization for heart failure (HF). Event rates were compared between the patients with and without regression of AF. In patients with sustained AF at baseline, predictors of MACE were identified using Cox proportional hazards model. Results Among 2,253 patients who were diagnosed as sustained AF at baseline, regression of AF was observed in 9.0% (202/2,253, 2.0 per 100 patient-years) during a median follow-up of 4.0 years. Of these, 24.3% (49/202, 4.6 per 100 patient-years) of the patients finally recurred to sustained AF during follow-up. The proportion of asymptomatic patients was lower in patients with regression of AF than those without (with vs without regression; 49.0% vs 69.5%, p&lt;0.01). The percentage of beta-blocker use at baseline was similar between the two groups (37.2% vs 33.8%, p=0.34). The prevalence of patients who underwent catheter ablation or electrical cardioversion during follow-up was higher in patients with regression of AF (catheter ablation: 15.8% vs 5.5%; p&lt;0.01, cardioversion: 4.0% vs 1.4%; p&lt;0.01, respectively). The rate of MACE was significantly lower in patients with regression of AF as compared with patients who maintained sustained AF (3.7 vs 6.2 per 100 patient-years, log-rank p&lt;0.01). Figure shows the Kaplan-Meier curves for MACE, cardiac death, hospitalization for heart failure, and stroke. In patients with sustained AF at baseline, multivariable Cox proportional hazards model demonstrated that regression of AF was an independent predictor of lower MACE (adjusted hazard ratio [HR]: 0.50, 95% confidence interval [CI]: 0.28 to 0.88, p=0.02), stroke (HR: 0.51, 95% CI: 0.30 to 0.88, p=0.02), and hospitalization for HF (HR: 0.50, 95% CI: 0.29 to 0.85, p=0.01). Conclusion Regression from sustained to paroxysmal AF was associated with a lower incidence of adverse cardiac events. Funding Acknowledgement Type of funding source: None


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