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Christopher Gandrud - One of the best experts on this subject based on the ideXlab platform.
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simph an r package for illustrating estimates from cox Proportional Hazard models including for interactive and nonlinear effects
Journal of Statistical Software, 2015Co-Authors: Christopher GandrudAbstract:The R package simPH provides tools for effectively communicating results from Cox Proportional Hazard (PH) models, including models with interactive and nonlinear effects. The Cox (PH) model is a popular tool for examining event data. However, previously available computational tools have not made it easy to explore and communicate quantities of interest and associated uncertainty estimated from them. This is especially true when the effects are interactions or nonlinear transformations of continuous variables. These transformations are especially useful with Cox PH models because they can be employed to correctly specifying models that would otherwise violate the nonProportional Hazards assumption. Package simPH makes it easy to simulate and then plot quantities of interest for a variety of effects estimated from Cox PH models including interactive effects, nonlinear effects, as well as standard linear effects. Package simPH employs visual weighting in order to effectively communicate estimation uncertainty. There are options to show either the standard central interval of the simulation's distribution or the shortest probability interval - which can be useful for asymmetrically distributed estimates. This paper uses hypothetical and empirical examples to illustrate package simPH 's syntax and capabilities.
Bin Liu - One of the best experts on this subject based on the ideXlab platform.
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reliability inference of stress strength model for the truncated Proportional Hazard rate distribution under progressively type ii censored samples
Applied Mathematical Modelling, 2019Co-Authors: Xuchao Bai, Yimin Shi, Yiming Liu, Bin LiuAbstract:Abstract This paper considers the reliability inference for the truncated Proportional Hazard rate stress–strength model based on progressively Type-II censoring scheme. When the stress and strength variables follow the truncated Proportional Hazard rate distributions, the maximum likelihood estimation and the pivotal quantity estimation of stress–strength reliability are derived. Based on the percentile bootstrap sampling technique, the 95% confidence interval of stress–strength reliability is obtained, as well as the related coverage percentage. Moreover, based on the Fisher Z transformation and the modified generalized pivotal quantity, the 95% modified generalized confidence interval for the stress–strength reliability is obtained. The performance of the proposed method is evaluated by the Monte Carlo simulation. The numerical results show that the pivotal quantity estimators performs better than the maximum likelihood estimators. At last, two real datasets are analyzed by the proposed methodology for illustrative purpose. The results of real example analysis show that our model can be applied to the practical problem, the truncated Proportional Hazard rate distribution can fit the failure data better than other distributions, and the algorithms in this paper are suitable to handle the small sample data.
Vincent Ducrocq - One of the best experts on this subject based on the ideXlab platform.
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Phenotypic relationships between type traits and productive life using a piecewise Weibull Proportional Hazard model
Scientia Agricola, 2018Co-Authors: Elisandra Lurdes Kern, J.a. Cobuci, C.n. Costa, Vincent DucrocqAbstract:Longevity is an important trait due to its relationship with profitability. Type traits have been used as indirect predictors for productive life. The objective of this study was to evaluate the relationship of 20 type traits on length of productive life in Brazilian Holsteins, using a piecewise Weibull Proportional Hazard model. Three analyses were performed i) productive life was corrected for within herd level of production as a proxy for functional longevity, which included the time-dependent effects of region within year, class of milk production within herdyear, milk production class within lactation number, fat class and protein contents within herd and (variation in) herd size as well as the time-independent fixed effect of age at first catering and the type trait score; ii) the effects related to production were omitted from the first model (true longevity) and iii) with the first model, the effect of type was also studied considering five classes of percentage of type-scored cows within the herd. All analyses were performed using the Survival Kit program. The final score, angularity, top line, udder texture and suspensory ligament showed the strongest relationship with productive life. When type traits were available only for a small fraction of the herd, the cows had a better chance of remaining longer in the herd. The absence of type trait phenotypes was associated with a strong increase of culling risk for the cows. Type traits were not found to be good indirect predictors of productive life in Brazil.
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survival analysis of productive life in brazilian holstein using a piecewise weibull Proportional Hazard model
Livestock Science, 2016Co-Authors: Elisandra Lurdes Kern, J.a. Cobuci, C.n. Costa, Vincent DucrocqAbstract:The objectives of this study were to assess the most important factors that influence productive life (PL) of Brazilian Holstein cows and to estimate genetic parameters for PL using a piecewise Weibull Proportional Hazard model. Records of PL from first calving to last recording (culling) of 132,922 cows coming from 945 herds were used. They had to have their first calving occurring between 1989 and 2013 and they were daughters of 6,804 sires. The model included the time-dependent effects of region within year, class of milk production within herd-year, class of milk production within lactation number, class of fat and protein contents within herd and (variation in) herd size as well as the time-independent fixed effect of age at first calving, the random effects of herd-year, sire and maternal grand sire. All fixed effects had a significant effect on PL (P<0.001). The relative risk (RR) for within herd class of milk yield varied from 3.16 for the worst 20% class to 0.41 for the best 20% class. RR also increased as protein and fat decreased, but to a lesser extent compared to milk yield. Significant effects on PL were found for region-year, with large yearly changes in some cases. RR increased with age at first calving and with herd size but lower risks were observed when herd size was increasing or decreasing, compared to stable herds. The Weibull shape parameters (and therefore RR) increased with lactation number and with stage of lactation. The sire genetic variance estimate was 0.030±0.002 which corresponds to an equivalent heritability estimate of 6.1% accounting for censoring. A positive genetic trend of PL was observed. These results may contribute to the development of a routine genetic evaluation necessary to improve PL of Brazilian Holsteins.
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Survival analysis of productive life in Brazilian Holstein using a Weibull Proportional Hazard model
2015Co-Authors: Elisandra Lurdes Kern, J.a. Cobuci, C.n. Costa, Vincent DucrocqAbstract:Survival analysis of productive life in Brazilian Holstein using a Weibull Proportional Hazard model. 66. Annual Meeting of the European Federation of Animal Science (EAAP)
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heritability reliability of genetic evaluations and response to selection in Proportional Hazard models
Journal of Dairy Science, 2002Co-Authors: M H Yazdi, Vincent Ducrocq, Peter M Visscher, R ThompsonAbstract:The purposes of this study were 1) to investigate the heritability, reliability, and selection response for survival traits following a Weibull frailty Proportional Hazard model; and 2) to examine the relationship between genetic parameters from a Weibull model, a discrete Proportional Hazard model, and a binary data analysis using a linear model. Both analytical methods and Monte Carlo simulations were used to achieve these aims. Data were simulated using the Weibull frailty model with two different shapes of the Weibull distribution. Breeding values of 100 unrelated sires with 50 to 100 progeny (with different levels of censoring) were generated from a normal distribution and two different sire variances. For analysis of longevity data on the discrete scale, simulated data were transformed to a discrete scale using arbitrary ends of discrete intervals of 400, 800, or 1200 d. For binary data analysis, an individual's longevity was either 0 (when longevity was less than the end of interval) or 1 (when longevity was equal or greater than the end of interval). Three different statistical models were investigated in this study: a Weibull model, a discrete-time model (a Proportional Hazard model assuming that the survival data are measured on a discrete scale with few classes), and a linear model based upon binary data. An alternative derivation using basic expressions of reliabilities in sire models suggests a simple equation for the heritability on the original scale (effective heritability) that is not dependent on the Weibull parameters. The predictions of reliabilities using the proposed formulae in this study are in very good agreement with reliabilities observed from simulations. In general, the estimates of reliability from either the discrete model or the binary data analysis were close to estimates from the Weibull model for a given number of uncensored records in this simplified case of a balanced design. Although selection response from the binary data analysis depends on the end of interval point, there is a relatively good agreement between selection responses in the Weibull model and the binary data analysis. In general, when the underlying survival data is from a Weibull distribution, it appears that the method of analyzing data does not greatly affect the results in terms of sire ranking or response to selection, at least for the simplified context considered in this study.
Xuchao Bai - One of the best experts on this subject based on the ideXlab platform.
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reliability inference of stress strength model for the truncated Proportional Hazard rate distribution under progressively type ii censored samples
Applied Mathematical Modelling, 2019Co-Authors: Xuchao Bai, Yimin Shi, Yiming Liu, Bin LiuAbstract:Abstract This paper considers the reliability inference for the truncated Proportional Hazard rate stress–strength model based on progressively Type-II censoring scheme. When the stress and strength variables follow the truncated Proportional Hazard rate distributions, the maximum likelihood estimation and the pivotal quantity estimation of stress–strength reliability are derived. Based on the percentile bootstrap sampling technique, the 95% confidence interval of stress–strength reliability is obtained, as well as the related coverage percentage. Moreover, based on the Fisher Z transformation and the modified generalized pivotal quantity, the 95% modified generalized confidence interval for the stress–strength reliability is obtained. The performance of the proposed method is evaluated by the Monte Carlo simulation. The numerical results show that the pivotal quantity estimators performs better than the maximum likelihood estimators. At last, two real datasets are analyzed by the proposed methodology for illustrative purpose. The results of real example analysis show that our model can be applied to the practical problem, the truncated Proportional Hazard rate distribution can fit the failure data better than other distributions, and the algorithms in this paper are suitable to handle the small sample data.
Henry Brodaty - One of the best experts on this subject based on the ideXlab platform.
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Proportional Hazard model estimation under dependent censoring using copulas and penalized likelihood
Statistics in Medicine, 2018Co-Authors: Michael H Connors, Henry BrodatyAbstract:This paper considers Cox Proportional Hazard models estimation under informative right censored data using maximum penalized likelihood, where dependence between censoring and event times are modelled by a copula function and a roughness penalty function is used to restrain the baseline Hazard as a smooth function. Since the baseline Hazard is nonnegative, we propose a special algorithm where each iteration involves updating regression coefficients by the Newton algorithm and baseline Hazard by the multiplicative iterative algorithm. The asymptotic properties for both regression coefficients and baseline Hazard estimates are developed. The simulation study investigates the performance of our method and also compares it with an existing maximum likelihood method. We apply the proposed method to a dementia patients dataset.
