Survival data including potentially cured subjects are common in clinical studies and mixture cure rate models are often used for analysis. The non-cured probabilities are often predicted by non-parametric, high-dimen...
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Survival data including potentially cured subjects are common in clinical studies and mixture cure rate models are often used for analysis. The non-cured probabilities are often predicted by non-parametric, high-dimensional, or even unstructured (e.g. image) predictors, which is a challenging task for traditional nonparametric methods such as spline and local kernel. We propose to use the neural network to model the nonparametric or unstructured predictors' effect in cure rate models and retain the proportional hazards structure due to its explanatory ability. We estimate the parameters by Expectation-Maximization algorithm. Estimators are showed to be consistent. Simulation studies show good performance in both prediction and estimation. Finally, we analyze Open Access Series of Imaging Studies data to illustrate the practical use of our methods.
In biomedical studies, the causal mediation effect might be heterogeneous across individuals in the study population due to each study subject's unique characteristics. While individuals' mediation effects may...
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In biomedical studies, the causal mediation effect might be heterogeneous across individuals in the study population due to each study subject's unique characteristics. While individuals' mediation effects may differ from each other, it is often reasonable and more interpretable to assume that individuals belong to several distinct latent subgroups with similar attributes. In this article, we first show that the subgroup-specific mediation effect can be identified under the group-specific sequential ignorability assumptions. Then, we propose a simple mixture modeling approach to account for the latent subgroup structure where each mixture component corresponds to one latent subgroup in the linear structural equation model framework. Model parameters can be estimated using the standard expectation-maximization (em) algorithm. Each individual's subgroup membership can be inferred based on the posterior probability. We propose to use the singular Bayesian information criterion to consistently select the number of latent subgroups by recognizing that the Fisher information matrix for mixture models might be singular. We then propose to use nonparametric bootstrap method to compute standard errors and confidence intervals. We conducted simulation studies to evaluate the empirical performance of our proposed method named iMed. Finally, we reanalyzed a DNA methylation data set from the Normative Aging Study and found that the mediation effects of two well-documented DNA methylation CpG sites are heterogeneous across two latent subgroups in the causal pathway from smoking behavior to lung function. We also developed an R package iMed for public use.
Multivariate circular observations, i.e. points on a torus arise frequently in fields where instruments such as compass, protractor, weather vane, sextant or theodolite are used. Multivariate wrapped models are often ...
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Multivariate circular observations, i.e. points on a torus arise frequently in fields where instruments such as compass, protractor, weather vane, sextant or theodolite are used. Multivariate wrapped models are often appropriate to describe data points scattered onp-dimensional torus. However, the statistical inference based on such models is quite complicated since each contribution in the log-likelihood function involves an infinite sum of indices in Z(p), wherepis the dimension of the data. To overcome this problem, for moderate dimensionp, we propose two estimation procedures based on Expectation-Maximisation and Classification Expectation-Maximisation algorithms. We study the performance of the proposed techniques on a Monte Carlo simulation and further illustrate the advantages of the new procedures on three real-world data sets.
Mixture models are promising statistical tools aiming to modeling and clustering data arisen from a heterogeneous population. This paper presents a mixture model based on the assumption that the mixing components foll...
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Mixture models are promising statistical tools aiming to modeling and clustering data arisen from a heterogeneous population. This paper presents a mixture model based on the assumption that the mixing components follow the multivariate restricted skew-normal scale mixture of Birnbaum-Saunders (SNBS) distributions. A computationally feasible expectation-maximization algorithm is developed to carry out maximum likelihood estimation of the new model. Simulation studies are carried out to check the clustering performance and classification accuracy. Finally, illustrative example is presented by analyzing a real-world data set.
With advancements in medical research, broader range of diseases may be curable, which indicates some patients may not die owing to the disease of interest. The mixture cure model, which can capture patients being cur...
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With advancements in medical research, broader range of diseases may be curable, which indicates some patients may not die owing to the disease of interest. The mixture cure model, which can capture patients being cured, has received an increasing attention in practice. However, the existing mixture cure models only focus on major events with potential cures while ignoring the potential risks posed by other non-curable competing events, which are commonly observed in the real world. The main purpose of this article is to propose a new mixture cure model allowing non-curable competing risk. A semiparametric estimation method is developed via an em algorithm, the asymptotic properties of parametric estimators are provided and its performance is demonstrated through comprehensive simulation studies. Finally, the proposed method is applied to a prostate cancer clinical trial dataset. (C) 2020 Elsevier B.V. All rights reserved.
Mixed-effects models, with modifications to accommodate censored observations (LMEC/NLMEC), are routinely used to analyze measurements, collected irregularly over time, which are often subject to some upper and lower ...
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Mixed-effects models, with modifications to accommodate censored observations (LMEC/NLMEC), are routinely used to analyze measurements, collected irregularly over time, which are often subject to some upper and lower detection limits. This paper presents a likelihood-based approach for fitting LMEC/NLMEC models with autoregressive of order dependence of the error term. An em-type algorithm is developed for computing the maximum likelihood estimates, obtaining as a byproduct the standard errors of the fixed effects and the likelihood value. Moreover, the constraints on the parameter space that arise from the stationarity conditions for the autoregressive parameters in the em algorithm are handled by a reparameterization scheme, as discussed in Lin and Lee (2007). To examine the performance of the proposed method, we present some simulation studies and analyze a real AIDS case study. The proposed algorithm and methods are implemented in the new R package ARpLMEC.
The mixture cure model has been widely applied to survival data in which a fraction of the observations never experience the event of interest, despite long-term follow-up. In this paper, we study the Cox proportional...
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The mixture cure model has been widely applied to survival data in which a fraction of the observations never experience the event of interest, despite long-term follow-up. In this paper, we study the Cox proportional hazards mixture cure model where the covariate effects on the distribution of uncured subjects' failure time may jump when a covariate exceeds a change point. The nonparametric maximum likelihood estimation is used to obtain the semiparametric estimates. We employ a two-step computational procedure involving the Expectation-Maximization algorithm to implement the estimation. The consistency, convergence rate and asymptotic distributions of the estimators are carefully established under technical conditions and we show that the change point estimator is n consistency. The m out of n bootstrap and the Louis algorithm are used to obtain the standard errors of the estimated change point and other regression parameter estimates, respectively. We also contribute a test procedure to check the existence of the change point. The finite sample performance of the proposed method is demonstrated via simulation studies and real data examples.
Mixture model-based clustering has become an increasingly popular data analysis technique since its introduction over fifty years ago, and is now commonly utilized within a family setting. Families of mixture models a...
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Mixture model-based clustering has become an increasingly popular data analysis technique since its introduction over fifty years ago, and is now commonly utilized within a family setting. Families of mixture models arise when the component parameters, usually the component covariance (or scale) matrices, are decomposed and a number of constraints are imposed. Within the family setting, model selection involves choosing the member of the family, i.e., the appropriate covariance structure, in addition to the number of mixture components. To date, the Bayesian information criterion (BIC) has proved most effective for model selection, and the expectation-maximization (em) algorithm is usually used for parameter estimation. In fact, this em-BIC rubric has virtually monopolized the literature on families of mixture models. Deviating from this rubric, variational Bayes approximations are developed for parameter estimation and the deviance information criteria (DIC) for model selection. The variational Bayes approach provides an alternate framework for parameter estimation by constructing a tight lower bound on the complex marginal likelihood and maximizing this lower bound by minimizing the associated Kullback-Leibler divergence. The framework introduced, which we refer to as VB-DIC, is applied to the most commonly used family of Gaussian mixture models, and real and simulated data are used to compared with the em-BIC rubric.
Panel count data occur often in event history studies and in these situations, one observes only incomplete information, the number of events rather than the occurrence times of each event, about the point processes o...
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Panel count data occur often in event history studies and in these situations, one observes only incomplete information, the number of events rather than the occurrence times of each event, about the point processes of interest.(2) Sometimes one may have to face a more complicated type of panel count data, mixed panel count data in which instead of the number of events, one only knows if there is an occurrence of an event.(3) Furthermore, this may depend on the underlying point process of interest or in other words, the point process of interest and the observation type process may be related. To address this, a sieve maximum likelihood estimation approach is proposed with the use of Bernstein polynomials, and for the implementation, an em algorithm is developed. To assess the finite sample performance of the proposed approach, a simulation study is conducted and suggests that it works well for practical situations. The method is then applied to a motivating example about cancer survivors.
This article proposes an imputation procedure that uses the factors estimated from a tall block along with the re-rotated loadings estimated from a wide block to impute missing values in a panel of data. Assuming that...
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This article proposes an imputation procedure that uses the factors estimated from a tall block along with the re-rotated loadings estimated from a wide block to impute missing values in a panel of data. Assuming that a strong factor structure holds for the full panel of data and its sub-blocks, it is shown that the common component can be consistently estimated at four different rates of convergence without requiring regularization or iteration. An asymptotic analysis of the estimation error is obtained. An application of our analysis is estimation of counterfactuals when potential outcomes have a factor structure. We study the estimation of average and individual treatment effects on the treated and establish a normal distribution theory that can be useful for hypothesis testing.
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