Modelling heterogeneity in survival data

1991 ◽  
Vol 28 (03) ◽  
pp. 695-701 ◽  
Author(s):  
Philip Hougaard
Keyword(s):  
Survival Data ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Mixture Distribution ◽  
Survival Models ◽  
Risk Of Death ◽  
Hazards Model ◽  
Occupational Mortality ◽  
Heterogeneity Distribution ◽  
Biased Estimates

Ordinary survival models implicitly assume that all individuals in a group have the same risk of death. It may, however, be relevant to consider the group as heterogeneous, i.e. a mixture of individuals with different risks. For example, after an operation each individual may have constant hazard of death. If risk factors are not included, the group shows decreasing hazard. This offers two fundamentally different interpretations of the same data. For instance, Weibull distributions with shape parameter less than 1 can be generated as mixtures of constant individual hazards. In a proportional hazards model, neglect of a subset of the important covariates leads to biased estimates of the other regression coefficients. Different choices of distributions for the unobserved covariates are discussed, including binary, gamma, inverse Gaussian and positive stable distributions, which show both qualitative and quantitative differences. For instance, the heterogeneity distribution can be either identifiable or unidentifiable. Both mathematical and interpretational consequences of the choice of distribution are considered. Heterogeneity can be evaluated by the variance of the logarithm of the mixture distribution. Examples include occupational mortality, myocardial infarction and diabetes.

Modelling heterogeneity in survival data

1991 ◽  
Vol 28 (3) ◽  
pp. 695-701 ◽  
Author(s):  
Philip Hougaard
Keyword(s):  
Survival Data ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Mixture Distribution ◽  
Survival Models ◽  
Risk Of Death ◽  
Hazards Model ◽  
Occupational Mortality ◽  
Heterogeneity Distribution ◽  
Biased Estimates

Ordinary survival models implicitly assume that all individuals in a group have the same risk of death. It may, however, be relevant to consider the group as heterogeneous, i.e. a mixture of individuals with different risks. For example, after an operation each individual may have constant hazard of death. If risk factors are not included, the group shows decreasing hazard. This offers two fundamentally different interpretations of the same data. For instance, Weibull distributions with shape parameter less than 1 can be generated as mixtures of constant individual hazards. In a proportional hazards model, neglect of a subset of the important covariates leads to biased estimates of the other regression coefficients. Different choices of distributions for the unobserved covariates are discussed, including binary, gamma, inverse Gaussian and positive stable distributions, which show both qualitative and quantitative differences. For instance, the heterogeneity distribution can be either identifiable or unidentifiable. Both mathematical and interpretational consequences of the choice of distribution are considered. Heterogeneity can be evaluated by the variance of the logarithm of the mixture distribution. Examples include occupational mortality, myocardial infarction and diabetes.

scholarly journals Graft survival of Pinus engelmannii Carr. in relation to two grafting techniques with dormant and sprouting buds

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e12182
Author(s):  
Alberto Pérez-Luna ◽  
José Ciro Hernández-Díaz ◽  
Christian Wehenkel ◽  
Sergio Leonel Simental-Rodríguez ◽  
Javier Hernández-Velasco ◽  
...  
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Failure Time ◽  
Survival Models ◽  
Risk Of Death ◽  
Hazards Model ◽  
Grafting Technique ◽  
Average Survival ◽  
Forest Genetic ◽  
Improvement Programs

Developing methods for successfully grafting forest species will be helpful for establishing asexual seed orchards and increasing the success of forest genetic improvement programs in Mexico. In this study we investigated the effects of two grafting techniques (side veneer and top cleft) and two phenological stages of the scion buds (end of latency and beginning of sprouting), in combination with other seven grafting variables, on the sprouting and survival of 120 intraspecific grafts of Pinus engelmannii Carr. The scions used for grafting were taken from a 5.5-year-old commercial forest plantation. The first grafting was performed on January 18 (buds at the end of dormancy) and the second on February 21 (buds at the beginning of sprouting). The data were examined by analysis of variance and a test of means and were fitted to two survival models (the Weibull’s accelerated failure time and the Cox’s proportional hazards model) and the respective hazard ratios were calculated. Survival was higher in the top cleft grafts made with buds at the end of latency, with 80% sprouting and an estimated average survival time of between 164 and 457 days after the end of the 6-month evaluation period. Four variables (grafting technique, phenological stage of the scion buds, scion diameter and rootstock height) significantly affected the risk of graft death in both survival models. Use of top cleft grafts with buds at the end of the latency stage, combined with scion diameters smaller than 11.4 mm and rootstock heights greater than 58.5 cm, was associated with a lower risk of death.

scholarly journals Dementia Adjudication Triggers Associated With Increased Mortality for Older Australians: Evidence From ASPREE

2020 ◽  
Vol 4 (Supplement_1) ◽  
pp. 161-161
Author(s):  
Jane Banaszak-Holl ◽  
Xiaoping Lin ◽  
Jing Xie ◽  
Stephanie Ward ◽  
Henry Brodaty ◽  
...  
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
The Elderly ◽  
Cox Proportional Hazards ◽  
Service Planning ◽  
Cox Proportional Hazards Model ◽  
Cognitive Test ◽  
Risk Of Death ◽  
Hazards Model ◽  
Using Data

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.

G CSF association with prolonged survival in HIV infected patients with disseminated Mycobacterium avium complex infection

1998 ◽  
Vol 9 (7) ◽  
pp. 394-399 ◽  
Author(s):  
Philip Keiser ◽  
Steven Rademacher ◽  
James Smith ◽  
Daniel Skiest
Keyword(s):  
Mycobacterium Avium ◽  
Mycobacterium Avium Complex ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Cox Proportional Hazards ◽  
Cox Proportional Hazards Model ◽  
Cd4 Count ◽  
Risk Of Death ◽  
Hazards Model

Summary: Clarithromycin can ameliorate symptoms and improve survival in disseminated Mycobacterium avium complex DMAC infection. Optimal combina tions of this drug with other agents remain unknown. Granulocyte colony stimulating factor G CSF is a cytokine that can improve phagocytosis of M. avium complex in vitro . We aim to determine if G CSF administration is associated with improved survival in patients with DMAC in a retrospective, cohort study. Case records from 1991 to 1995 of 91 patients with DMAC at Parkland Memorial Hospital were reviewed for date of initial DMAC diagnosis, baseline CD4 count, race, sex, antiretroviral use, G CSF use, therapy for DMAC clarithromycin, ethambutol, ciprofloxacin and rifabutin and date of death. Of 91 cases identified, 25 were treated with G CSF and 66 never received this drug. Baseline characteristics were similar in each group including CD4 count 40 cells mm 3 vs 33 cells mm 3, P =0.68 , clarithromycin use 18 patients vs 52 patients, P =0.90 , and antiretroviral use 20 patients vs 42 patients, P =0.21 . Subjects treated with G CSF lived longer than those who did not receive this drug 355 days vs 211 days, P 0.01 . In the subgroup treated with clarithromycin, G CSF was also associated with increased survival 377 days vs 252 days, P 0.01 . Cox proportional hazards model showed a decreased risk of death in patients treated with G CSF RH=0.22, P 0.01 , clarithromycin RH=0.13, P 0.01 and ethambutol RH=0.51, P =0.02 . Ciprofloxacin and rifabutin use did not influence survival. These data support the use of clarithromycin and ethambutol in the treatment of DMAC. Addition of G CSF to a regimen of clarithromycin and ethambutol may increase survival in DMAC and should be studied prospectively.

A Proportional Hazards Neural Network for Performing Reliability Estimates and Risk Prognostics for Mobile Systems Subject to Stochastic Covariates

2005 ◽  
Author(s):  
George M. Lloyd ◽  
Timothy Hasselman ◽  
Thomas Paez
Keyword(s):  
Survival Data ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Mobile Systems ◽  
Linear Network ◽  
Model Free ◽  
Hazards Model ◽  
Reliability Estimates ◽  
Non Linear ◽  
Stochastic Covariates

We present a proportional hazards model (PHM) that establishes a framework suitable for performing reliability estimates and risk prognostics on complex multi-component systems which are transferred at arbitrary times among a discrete set of non-stationary stochastic environments. Such a scenario is not at all uncommon for portable and mobile systems. It is assumed that survival data, possibly interval censored, is available at several “typical” environments. This collection of empirical survival data forms the foundation upon which the basic effects of selected covariates are incorporated via the proportional hazards model. Proportional hazards models are well known in medical statistics, and can provide a variety of data-driven risk models which effectively capture the effects of the covariates. The paper describes three modifications we have found most suitable for this class of systems: development of suitable survival estimators that function well under realistic censoring scenarios, our modifications to the PHM which accommodate time-varying stochastic covariates, and implementation of said model in a non-linear network context which is itself model-free. Our baseline hazard is a parameterized reliability model developed from the empirical reliability estimates. Development of the risk score for arbitrary covariates arising from movement among different random environments is through interaction of the non-linear network and training data obtained from a Markov chain simulation based on stochastic environmental responses generated from Karhunen-Loe`ve models.

Early Hb Response to ESA Treatment May Be An Indicator of Better Survival Prognosis

Blood ◽  
2008 ◽  
Vol 112 (11) ◽  
pp. 4587-4587
Author(s):  
Jesse A Berlin ◽  
Peter Bowers ◽  
Sudhakar Rao ◽  
Suresh Aravind ◽  
Steven Sun ◽  
...  
Keyword(s):  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Performance Status ◽  
Epoetin Alfa ◽  
Survival Prognosis ◽  
Risk Of Death ◽  
Hazards Model ◽  
Kaplan Meier ◽  
Increased Risk ◽  
Baseline Covariates

Abstract Chemotherapy induced anemia patients who respond to ESA treatment have hemoglobin increases within 4–8 weeks. Patients with inadequate Hb response after several weeks treatment often have their ESA dose escalated.. We conducted an exploratory analysis to test the hypothesis that safety outcomes in randomized studies of epoetin alfa might differ depending on the Hb response after 4–8 weeks of treatment. Methods: The analysis compared the survival across subsets of epoetin-alfa treated patients. Specifically, a landmark analysis was used, which defines a hemoglobin responder at a pre-specified point in time (in this case 4 & 8 weeks post treatment), and then examines survival subsequent to that point in time.Patients were categorized as “Hb responder” when their Hb increased by >0.5 g/dL; “Hb stable” when Hb change within ≤ 0.5g/dL; “Hb non-responder” when the Hb decreased >0.5 g/dL, compared to the value prior to epoetin-alfa treatment. Survival was estimated using the Kaplan-Meier method and comparisons were made between the responders and non-responders versus the stable group. Cox’s proportional hazards model was used to adjust for the following baseline covariates: hemoglobin prior to treatment, baseline performance status, and advanced disease at baseline. All analyses were stratified by study to account for any differences in the study populations and study conduct. Results: These exploratory findings suggest the possibility that patients identified as non-responders to ESAs after 4 or 8 weeks of ESA treatment may be at increased risk of death, and that this effect is most pronounced in the studies that treated patients beyond the correction of anemia. Although these analyses were adjusted for several key baseline covariates, it is unclear whether these effects result from treatment, or whether patients who fail to respond to epoetin alfa are inherently at increased risk of death (e.g., due underlying malignancy), regardless of their treatment status.

Multiplicative Piecewise Gamma in Survival Data Analysis

2014 ◽  
Vol 70 (1) ◽  
Author(s):  
Noraslinda Mohamed Ismail ◽  
Zarina Mohd Khalid ◽  
Norhaiza Ahmad
Keyword(s):  
Survival Data ◽  
Hazard Function ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Bayesian Estimator ◽  
Proportional Hazard ◽  
Proportional Hazard Model ◽  
Hazards Model ◽  
Proposed Model ◽  
Leukemia Data

The proportional hazard model is the most general of the regression models since it is not based on any assumptions concerning the nature or shape of the underlying survival distribution. The model assumes that the underlying hazard rate is a function of the covariates (independent variables) and there are no assumptions about the nature or shape of the hazard function. Proportional hazards model in survival analysis is used to estimate the effects of different covariates which was influenced by the survival data. This paper proposes the new multiplicative piecewise gamma in the hazard function using OpenBugs Statistical Packages. The proposed model is a flexible survival model for any types of non-informative censored data in estimating the parameters using Bayesian approach and also an alternative model to the existing model. We used the Markov Chain Monte Carlo method in computing the Bayesian estimator on leukemia data. The results obtained show that the proposed model can be an alternative to the existing multiplicative model since it can estimate the parameters using any types of survival data compared to the existing model that can only be used for leukemia data.  

Survival of Red Maasai, Dorper and crossbred lambs in the sub-humid tropics

2003 ◽  
Vol 76 (1) ◽  
pp. 3-17 ◽  
Author(s):  
R. Nguti ◽  
P. Janssen ◽  
G.J. Rowlands ◽  
J.O. Audho ◽  
R.L. Baker
Keyword(s):  
Body Weight ◽  
Standard Error ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Survival Rates ◽  
Risk Of Death ◽  
Intestinal Nematode ◽  
Hazards Model ◽  
Faecal Egg Count ◽  
Time Varying Covariates

AbstractThe survival rates of Dorper, Red Maasai and crossbred lambs born over a period of 6 years at Diani Estate, Coast Province, Kenya were compared using the Cox mixed proportional hazards model with a random (frailty) term for sire. Of the 1785 lambs born, proportionately 0·44 died before they were 1 year old. Almost half of these deaths occurred before weaning; a third were associated with mis-mothering and a fifth with gastro-intestinal nematode parasite (endoparasite) infections. Half of the deaths post weaning were associated with endoparasite infections, predominantly Haemonchus contortus. The Red Maasai lambs had a lower risk of death than the Dorper lambs with a relative hazard of 0·27 pre-weaning and 0·25 post weaning. Other crosses and back crosses had relative hazards in between these values and 1; there was no evidence of heterosis. Survival rates were different among years and appeared to be associated to some degree with variations in rainfall. There were highly significant effects of both birth weight and weaning weight on survival. Body weight, together with packed red cell volume and faecal egg count, were also introduced into the proportional hazard model as time-varying covariates. All three variables had major influences on survival. The risk of death over the following month in animals individually treated with an anthelmintic drug pre weaning was reduced by 0·61 compared with those not treated. The sire frailty variance estimate was similar to its standard error pre-weaning but larger post weaning. When adjusted for lamb body weight the sire variance post weaning increased to three times its standard error.

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