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

Pankratz, V. Shane; Andrade, Mariza de; Therneau, Terry M.

doi:10.1002/gepi.20043

Cited by 109 publications

(134 citation statements)

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“…Finally, to further adjust for familial breast cancer history, we added a correlated frailty score derived from a mixed effects Cox proportional hazards model. 27 Briefly, a specific frailty score was obtained based on the degree of relationship (kinship) among the women in the family and the pattern of breast cancer in the pedigree. The median of the frailty scores was obtained and used as the cut point to classify a woman's frailty score as either high or low.…”

Section: Discussionmentioning

confidence: 99%

Alcohol intake in adolescence and mammographic density

Vachon

Sellers

Janney

et al. 2005

Intl Journal of Cancer

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Adolescent exposures may be important in the development of breast cancer later in life. We examined the association of adolescent alcohol consumption and adult mammographic density, a strong risk factor for breast cancer. Women within the Minnesota Breast Cancer Family Cohort with detailed mammogram and risk factor information (n 5 1,893) formed our sample. Breast cancer cases were excluded. Adolescent alcohol consumption (before age 18) was solicited through a mailed questionnaire. Percent density (PD) was estimated using the computer-assisted thresholding program, Cumulus. Statistical analyses were performed using linear mixed effect models. Women who reported ever drinking alcohol before age 18 (n 5 390; 21%) had a higher unadjusted PD than women who never drank during adolescence (l unadj 5 26.5% vs. 22.2%), but this difference disappeared with adjustment for risk factors for mammographic density (l adj 5 21.0% vs. 21.2%, p 5 0.94). Adult PD was not associated with age at initiation, amount of alcohol consumed at one sitting or frequency of alcohol use before age 18. The lack of differences was seen across strata of menopausal status. There was suggestion of higher PD among heavy and more frequent drinkers (24.0%, 95% CI 21.1-26.8%) compared to lighter (21.3%, 95% CI 20.3-22.3%) and never drinkers (21.4%, 95% CI 20.9-21.9%) and also among regular adolescent drinkers who were daily or weekly adult drinkers (25.0%, 95% CI 23.0-27.0%) compared to less regular drinkers in these 2 time periods (23.0-23.4%). However, these associations were not statistically significant (p 5 0.27 and p 5 0.22, respectively). In summary, there was no evidence that adolescent alcohol use was associated with large and persistent effects on adult PD. ' 2005 Wiley-Liss, Inc.Key words: mammographic density; adolescent alcohol; breast cancerThe high number of cell divisions during adolescence and young adulthood may render the breast especially susceptible to carcinogenic influence and signify this as an especially critical time period.1 Usual adult alcohol consumption is a consistent risk factor for breast cancer, with a 7% (95% CI: 5.5-8.7%) increase in risk for each additional 10 g/day of alcohol (approximately 0.75-1 drink) compared to nondrinkers.2 However, the potential influence of alcohol consumption during adolescence on breast cancer remains unsettled. Epidemiologic evidence is inconsistent, with some studies finding an increased risk for breast cancer with age of initiation before age 25, 3-6 whereas others do not. 7-17 A recent review of the literature on adolescent alcohol consumption and breast cancer concluded that there is no clear association. 18One strategy to help resolve the inconsistency is to examine the association of alcohol use in adolescence with mammographic density, which is an established risk factor for breast cancer 19 and is a measurable phenotype closer in time to the exposure of interest.Women with percent mammographic density >50% have a 3-5-fold greater risk of breast cancer than women with low densit...

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Section: Discussionmentioning

confidence: 99%

Alcohol intake in adolescence and mammographic density

Vachon

Sellers

Janney

et al. 2005

Intl Journal of Cancer

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“…The models based on continuous time used in the literature differ essentially in the form of the baseline hazard function λ 0 (·): the classical Cox model (with frailties) assumes the hazard function to be a smooth function (almost everywhere) imposing in this way almost no restriction on λ 0 (·) (see [19,26,28]); the piece-wise Weibull models (see [9]) assume λ 0 (·) to be a saw function (i.e. a piecewise linear function); while the piece-wise constant hazard models (as described here) assume λ 0 (·) to be a step function (i.e.…”

Section: Discussionmentioning

confidence: 99%

Multivariate survival mixed models for genetic analysis of longevity traits

Maia

Madsen

Labouriau

2013

Journal of Applied Statistics

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A class of multivariate mixed survival models for continuous and discrete time with a complex covariance structure is introduced in a context of quantitative genetic applications. The methods introduced can be used in many applications in quantitative genetics although the discussion presented concentrates on longevity studies. The framework presented allows to combine models based on continuous time with models based on discrete time in a joint analysis. The continuous time models are approximations of the frailty model in which the hazard function will be assumed to be piece-wise constant. The discrete time models used are multivariate variants of the discrete relative risk models. These models allow for regular parametric likelihood-based inference by exploring a coincidence of their likelihood functions and the likelihood functions of suitably defined multivariate generalized linear mixed models. The models include a dispersion parameter, which is essential for obtaining a decomposition of the variance of the trait of interest as a sum of parcels representing the additive genetic effects, environmental effects and unspecified sources of variability; as required in quantitative genetic applications. The methods presented are implemented in such a way that large and complex quantitative genetic data can be analyzed.

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“…Assuming that the random effects or frailties g followed a normal distribution, with mean 0 and the following variance and covariance matrix: (Equation 9) and assuming that censoring is independent and uninformative of g, the partial likelihood function for the Cox frailty model is given by the following equation (Pankratz et al, 2005;Giolo and Demétrio, 2011): ( Equation 10) where PL is the partial likelihood function for the usual Cox model. As the above integral does not provide a closed form, because according to Pankratz et al (2005), PL is a product of the ratio and the vector of random effects, g has dimension n. Ripatti and Palmgren (2000) used the Laplace approximation to obtain the logarithm of the likelihood function (1).…”

Section: Methodsmentioning

confidence: 99%

“…As the above integral does not provide a closed form, because according to Pankratz et al (2005), PL is a product of the ratio and the vector of random effects, g has dimension n. Ripatti and Palmgren (2000) used the Laplace approximation to obtain the logarithm of the likelihood function (1).…”

Section: Methodsmentioning

confidence: 99%

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Genomic selection for slaughter age in pigs using the Cox frailty model

Vs¹,

Filho²,

Resende³

et al. 2015

Genet. Mol. Res.

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ABSTRACT. The aim of this study was to compare genomic selection methodologies using a linear mixed model and the Cox survival model. We used data from an F2 population of pigs, in which the response variable was the time in days from birth to the culling of the animal and the covariates were 238 markers [237 single nucleotide polymorphism (SNP) plus the halothane gene]. The data were corrected for fixed effects, and the accuracy of the method was determined based on the correlation of the ranks of predicted genomic breeding values (GBVs) in both models with the corrected phenotypic values. The analysis was repeated with a subset of SNP markers with largest absolute effects. The results were in agreement with the GBV prediction and the estimation of marker effects for both models for uncensored data and for normality. However, when considering censored data, the Cox model with a normal random effect (S1) was more appropriate. Since there was no agreement between the linear mixed model and the imputed data (2015) (L2) for the prediction of genomic values and the estimation of marker effects, the model S1 was considered superior as it took into account the latent variable and the censored data. Marker selection increased correlations between the ranks of predicted GBVs by the linear and Cox frailty models and the corrected phenotypic values, and 120 markers were required to increase the predictive ability for the characteristic analyzed.

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

Cited by 109 publications

References 39 publications

Alcohol intake in adolescence and mammographic density

Alcohol intake in adolescence and mammographic density

Multivariate survival mixed models for genetic analysis of longevity traits

Genomic selection for slaughter age in pigs using the Cox frailty model

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