Regression analysis for the proportional hazards model with parameter constraints under case-cohort design

Deng, Lifeng; Ding, Jieli; Liu, Yanyan; Cheng-dong, Wei

doi:10.1016/j.csda.2017.08.013

Cited by 6 publications

(3 citation statements)

References 34 publications

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“…In step 3, we apply the Lagrangian method based on Karush-Kuhn-Tucher (KKT) conditions (Deng et al 2018;Nocedal and Wright 1999) to accommodate inequality in constraints (3). Let = T , T T .…”

Section: Maximize Likelihood Function (2) Subject To the Constraints (3)mentioning

confidence: 99%

A constrained maximum likelihood approach to developing well-calibrated models for predicting binary outcomes

Cao,

Ma,

Zhao

et al. 2024

Lifetime Data Anal

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The added value of candidate predictors for risk modeling is routinely evaluated by comparing the performance of models with or without including candidate predictors. Such comparison is most meaningful when the estimated risk by the two models are both unbiased in the target population. Very often data for candidate predictors are sourced from nonrepresentative convenience samples. Updating the base model using the study data without acknowledging the discrepancy between the underlying distribution of the study data and that in the target population can lead to biased risk estimates and therefore an unfair evaluation of candidate predictors. To address this issue assuming access to a well-calibrated base model, we propose a semiparametric method for model fitting that enforces good calibration. The central idea is to calibrate the fitted model against the base model by enforcing suitable constraints in maximizing the likelihood function. This approach enables unbiased assessment of model improvement offered by candidate predictors without requiring a representative sample from the target population, thus overcoming a significant practical challenge. We study theoretical properties for model parameter estimates, and demonstrate improvement in model calibration via extensive simulation studies. Finally, we apply the proposed method to data extracted from Penn Medicine Biobank to inform the added value of breast density for breast cancer risk assessment in the Caucasian woman population.

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Section: Maximize Likelihood Function (2) Subject To the Constraints (3)mentioning

confidence: 99%

A constrained maximum likelihood approach to developing well-calibrated models for predicting binary outcomes

Cao,

Ma,

Zhao

et al. 2024

Lifetime Data Anal

View full text Add to dashboard Cite

show abstract

“…In this article, inspired by the idea of Ding et al [16] and Deng et al [17], we construct a surrogate function with a diagonal Hessian matrix by using the convexity of the exponential function and the negative logarithm function and then maximize this surrogate function with a diagonal Hessian matrix. is algorithm is minorization-maximization (MM) algorithm.…”

Section: Introductionmentioning

confidence: 99%

The Adjustment of Covariates in Cox’s Model under Case-Cohort Design

et al. 2020

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Case-cohort design is a biased sampling method. Due to its cost-effective and theoretical significance, this design has extensive application value in many large cohort studies. The case-cohort data includes a subcohort sampled randomly from the entire cohort and all the failed subjects outside the subcohort. In this paper, the adjustment for the distorted covariates is considered to case-cohort data in Cox’s model. According to the existing adjustable methods of distorted covariates for linear and nonlinear models, we propose estimating the distorting functions by nonparametrically regressing the distorted covariates on the distorting factors; then, the estimators for the parameters are obtained using the estimated covariates. The proof of consistency and being asymptotically normal is completed. For calculating the maximum likelihood estimates of the regression coefficients subject in Cox’s model, a minorization-maximization (MM) algorithm is developed. Simulation studies are performed to compare the estimations with the covariates undistorted, distorted, and adjusted to illustrate the proposed methods.

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“…[1][2][3][4][5][6] When the response is the failure time subject to censoring, the case-cohort design proposed by Prentice 7 have been widely used as a cost-effective design and the corresponding statistical methods have been extensively studied by many authors. [8][9][10][11][12][13] The aforementioned works are all based on the assumed models and infer unknown parameters of interest through the likelihood or estimating equation based approaches. However, the diagnostic methods for the assumed model have been less attended, which are important for the reliability of the proposed methods in practice.…”

Section: Introductionmentioning

confidence: 99%

A class of goodness‐of‐fit test for the additive hazards model with case‐cohort data

Cao

2020

Pharmaceutical Statistics

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The case-cohort design is commonly used in epidemiological studies due to its cost-effectiveness. The additive hazards model is widely used in survival analysis when the hazards difference is constant. In this article, we propose a class of goodness-of-fit test statistics for the assumption of the additive hazards model with case-cohort data through a class of asymptotically mean-zero multiparameter stochastic processes. We also establish the asymptotic theory of the proposed test statistics and a resampling scheme is adopted to approximate its asymptotic distribution. The performance of the proposed test statistics is evaluated through simulation studies and a real dataset is analyzed to illustrate the proposed method.

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Regression analysis for the proportional hazards model with parameter constraints under case-cohort design

Cited by 6 publications

References 34 publications

A constrained maximum likelihood approach to developing well-calibrated models for predicting binary outcomes

A constrained maximum likelihood approach to developing well-calibrated models for predicting binary outcomes

The Adjustment of Covariates in Cox’s Model under Case-Cohort Design

A class of goodness‐of‐fit test for the additive hazards model with case‐cohort data

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