Extension of the Cox Proportional Hazards Model for Time-Dependent Variables

2011 ◽  
pp. 241-288 ◽  
Author(s):  
David G. Kleinbaum ◽  
Mitchel Klein
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Time Dependent ◽  
Hazards Model ◽  
Dependent Variables

scholarly journals Does the Anti-Mullerian Hormone Decline Rate Improve the Prediction of Age at Menopause?

2021 ◽  
Vol 12 ◽  
Author(s):  
Fahimeh Ramezani Tehrani ◽  
Ali Sheidaei ◽  
Faezeh Firouzi ◽  
Maryam Tohidi ◽  
Fereidoun Azizi ◽  
...  
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Time Dependent ◽  
Age At Menopause ◽  
C Statistic ◽  
Hazards Model ◽  
Decline Rate

ObjectivesThere are controversial studies investigating whether multiple anti-Mullerian hormone (AMH) measurements can improve the individualized prediction of age at menopause in the general population. This study aimed to reexplore the additive role of the AMH decline rate in single AMH measurement for improving the prediction of age at physiological menopause, based on two common statistical models for analysis of time-to-event data, including time-dependent Cox regression and Cox proportional-hazards regression models.MethodsA total of 901 eligible women, aged 18–50 years, were recruited from the Tehran Lipid and Glucose Study (TLGS) population and followed up every 3 years for 18 years. The serum AMH level was measured at the time of recruitment and twice after recruitment within 6-year intervals using the Gen II AMH assay. The added value of repeated AMH measurements for the prediction of age at menopause was explored using two different statistical approaches. In the first approach, a time-dependent Cox model was plotted, with all three AMH measurements as time-varying predictors and the baseline age and logarithm of annual AMH decline as time-invariant predictors. In the second approach, a Cox proportional-hazards model was fitted to the baseline data, and improvement of the complex model, which included repeated AMH measurements and the logarithm of the AMH annual decline rate, was assessed using the C-statistic.ResultsThe time-dependent Cox model showed that each unit increase in the AMH level could reduce the risk of menopause by 87%. The Cox proportional-hazards model also improved the prediction of age at menopause by 3%, according to the C-statistic. The subgroup analysis for the prediction of early menopause revealed that the risk of early menopause increased by 10.8 with each unit increase in the AMH annual decline rate.ConclusionThis study confirmed that multiple AMH measurements could improve the individual predictions of the risk of at physiological menopause compared to single AMH measurements. Different alternative statistical approaches can also offer the same interpretations if the essential assumptions are met.

scholarly journals HOUT-20. TIME-DEPENDENT ANALYSIS OF SELECTIVE SEROTONIN REUPTAKE INHIBITOR TREATMENT ON OVERALL SURVIVAL OF PATIENTS WITH GLIOBLASTOMA

2019 ◽  
Vol 21 (Supplement_6) ◽  
pp. vi116-vi116
Author(s):  
Sebastian Otto-Meyer ◽  
Rian DeFaccio ◽  
Corey Dussold ◽  
Erik Ladomersky ◽  
Rimas Lukas ◽  
...  
Keyword(s):  
Overall Survival ◽  
Serotonin Reuptake ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Time Dependent ◽  
Selective Serotonin ◽  
Hazards Model ◽  
Ssri Treatment

Abstract Glioblastoma (GBM) is the most common and aggressive form of primary brain tumor in adults. We recently investigated the hypothesis that treating GBM patients with psychosocial modifiers would be associated with improved overall survival (OS). Our study retrospectively analyzed 497 patients with GBM treated at Northwestern Medicine with or without selective serotonin reuptake inhibitors (SSRI) between the years 2000 and 2018. Information from the Northwestern Medicine Enterprise Data Warehouse was analyzed for baseline covariates including sex, age at diagnosis, type of surgery, and Charlson Comorbidity Index Score. Approximately one-third of analyzed patients were prescribed SSRIs, with highly variable treatment times. Several statistical methods were used to perform adjusted analyses including: (i) an extended Cox Proportional Hazards Model with SSRI as a time-dependent variable; (ii) a Cox Model using inverse probability weights; and (iii) a Cox Proportional Hazards model with landmark analyses. The hazard ratios (95% CIs) for each statistical model analyzing the association between SSRI treatment and OS were (i) 1.26 (0.97–1.63), (ii) 1.06 (0.8–1.4), and (iii) ranged from 1.01 (0.74–1.38) to 1.26 (0.75–2.09). Our analysis found no significant association between the time of SSRI treatment and GBM patient OS. Future work will study additional considerations for psychosocial modifier treatment and their potential effect(s) on GBM patient OS including: (i) confounders due to the extent of cancer treatment; (ii) comorbidities not associated with tumor burden; (iii) absolute leukocyte counts; and (iv) length of treatment time required for enhancing immune-mediated anti-GBM mechanisms.

scholarly journals Risk factors associated with major adverse cardiac and cerebrovascular events following percutaneous coronary intervention: a 10-year follow-up comparing random survival forest and Cox proportional-hazards model

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Maryam Farhadian ◽  
Sahar Dehdar Karsidani ◽  
Azadeh Mozayanimonfared ◽  
Hossein Mahjub
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Coronary Intervention ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Hazards Model ◽  
Cerebrovascular Events ◽  
Long Term Follow Up ◽  
Stent Length

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.

scholarly journals Elevated plasma growth and differentiation factor 15 predicts incident anemia in older adults aged 60 years and older

2020 ◽  
Author(s):  
Yuko Yamaguchi ◽  
Marta Zampino ◽  
Toshiko Tanaka ◽  
Stefania Bandinelli ◽  
Yusuke Osawa ◽  
...  
Keyword(s):  
Older Adults ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Differentiation Factor ◽  
Hazards Model ◽  
Increased Risk ◽  
The Relationship

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.

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