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Hunter, David R.; Lange, Kenneth

doi:10.1023/a:1016126007531

Cited by 19 publications

(3 citation statements)

References 17 publications

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“…, β * G 's α/2 and 1 − α/2 separately. Tables 9 and 10 present the estimation result of two MM algorithms, where the standard estimated error (SE) is defined by Equation ( 13) and the 95% confidence interval (CI1) is defined by Equation (12). Moreover, the 95% confidence interval (CI2) is defined by Equation ( 14).…”

Section: Real Data Analysismentioning

confidence: 99%

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Efficient Estimation and Inference in the Proportional Odds Model for Survival Data

et al. 2022

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In modeling time-to-event data with long-term survivors, the proportional hazards model is widely used for its easy and direct interpretation as well as the flexibility to accommodate the past information and allow time-varying predictors. This becomes most relevant when the mortality of individuals converges with time, and the estimation and inference based upon the proportional odds model can often yield more accurate and reasonable results than the classical Cox’s proportional hazards model. Along with the fast development of the data science technologies, computational challenges for survival data with increasing sample size and diverging parameter dimension exist. Currently, existing methods for analyzing such data are computationally inconvenient. In this paper, we propose efficient computational methods for analyzing survival data in the proportional odds model, where the nonparametric maximum likelihood approach is combined with the minorization-maximization (MM) algorithm and the regularization scheme to yield fast and accurate estimation and inferential procedures. The illustration of the methodology using extensive simulation studies and then the application to the Veterans’ Administration lung cancer data is also given.

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Section: Real Data Analysismentioning

confidence: 99%

“…As for the improvement of the parameter estimation efficiency, ref. [12] proposed the minorization-maximization (MM) algorithm for the proportional odds model and this algorithm performswell given high-dimensional data. Ref.…”

Section: Introductionmentioning

confidence: 99%

Efficient Estimation and Inference in the Proportional Odds Model for Survival Data

et al. 2022

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“…Thus far, the MM algorithm has been widely used in many statistical optimization problems. We can find applications of MM principle in a broad range of statistical contexts, including the Bradley-Terry model [18], quantile regression [19], variable selection [20,21], the proportional odds model [22], the shared frailty model [23], distance majorization [24] and so on.…”

Section: Introductionmentioning

confidence: 99%

Mixture Modeling of Time-to-Event Data in the Proportional Odds Model

Huang

Xiong

et al. 2022

Mathematics

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Subgroup analysis with survival data are most essential for detailed assessment of the risks of medical products in heterogeneous population subgroups. In this paper, we developed a semiparametric mixture modeling strategy in the proportional odds model for simultaneous subgroup identification and regression analysis of survival data that flexibly allows the covariate effects to differ among several subgroups. Neither the membership or the subgroup-specific covariate effects are known a priori. The nonparametric maximum likelihood method together with a pair of MM algorithms with monotone ascent property are proposed to carry out the estimation procedures. Then, we conducted two series of simulation studies to examine the finite sample performance of the proposed estimation procedure. An empirical analysis of German breast cancer data is further provided for illustrating the proposed methodology.

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Nonconvex Optimization via MM Algorithms: Convergence Theory

Lange

Won

Landeros

et al. 2021

Wiley StatsRef: Statistics Reference Online

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The majorization-minimization (MM) principle is an extremely general framework for deriving optimization algorithms. It includes the expectation-maximization (EM) algorithm, proximal gradient algorithm, concave-convex procedure, quadratic lower bound algorithm, and proximal distance algorithm as special cases. Besides numerous applications in statistics, optimization, and imaging, the MM principle finds wide applications in large scale machine learning problems such as matrix completion, discriminant analysis, and nonnegative matrix factorizations. When applied to nonconvex optimization problems, MM algorithms enjoy the advantages of convexifying the objective function, separating variables, numerical stability, and ease of implementation. However, compared to the large body of literature on other optimization algorithms, the convergence analysis of MM algorithms is scattered and problem specific. This survey presents a unified treatment of the convergence of MM algorithms. With modern applications in mind, the results encompass non-smooth objective functions and nonasymptotic analysis.

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Cited by 19 publications

References 17 publications

Efficient Estimation and Inference in the Proportional Odds Model for Survival Data

Efficient Estimation and Inference in the Proportional Odds Model for Survival Data

Mixture Modeling of Time-to-Event Data in the Proportional Odds Model

Nonconvex Optimization via MM Algorithms: Convergence Theory

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