Sieve Maximum Likelihood Estimation Research Articles

Copula-based analysis of dependent current status data with semiparametric linear transformation model.

This paper discusses regression analysis of current status data with dependent censoring, a problem that often occurs in many areas such as cross-sectional studies, epidemiological investigations and tumorigenicity experiments. Copula model-based methods are commonly employed to tackle this issue. However, these methods often face challenges in terms of model and parameter identification. The primary aim of this paper is to propose a copula-based analysis for dependent current status data, where the association parameter is left unspecified. Our method is based on a general class of semiparametric linear transformation models and parametric copulas. We demonstrate that the proposed semiparametric model is identifiable under certain regularity conditions from the distribution of the observed data. For inference, we develop a sieve maximum likelihood estimation method, using Bernstein polynomials to approximate the nonparametric functions involved. The asymptotic consistency and normality of the proposed estimators are established. Finally, to demonstrate the effectiveness and practical applicability of our method, we conduct an extensive simulation study and apply the proposed method to a real data example.

Simple closed-form estimation of a binary latent variable model

Abstract This paper develops a closed-form nonparametric estimator of the conditional distribution function for a binary outcome variable given an unobserved latent variable. This type of function is commonly used in models that involve measurement error and dynamic models with agent-specific unobserved heterogeneity. This paper presents a consistent extremum sieve estimator with the following advantages: i) it has a closed-form expression for all the sieve coefficients; ii) it is computationally straightforward, equivalent to computing eigenvalues and eigenvectors of matrices without the use of iterative optimization algorithms. While as flexible as the sieve maximum likelihood estimator (MLE) previously proposed for this model, our estimator proves computationally simpler. The finite sample properties of the estimator are investigated through a Monte Carlo study, and the developed estimator is applied to a probit model to assess the targeting performance of a social welfare program.

Regression analysis of group-tested current status data

Summary Group testing is an effective way to reduce the time and cost associated with conducting large-scale screening for infectious diseases. Benefits are realized through testing pools formed by combining specimens, such as blood or urine, from different individuals. In some studies, individuals are assessed only once and a time-to-event endpoint is recorded, for example, the time until infection. Combining group testing with this type of endpoint results in group-tested current status data (Petito & Jewell, 2016). To analyse these complex data, we propose methods that estimate a proportional hazard regression model based on test outcomes from measuring the pools. A sieve maximum likelihood estimation approach is developed that approximates the cumulative baseline hazard function with a piecewise constant function. To identify the sieve estimator, a computationally efficient expectation-maximization algorithm is derived by using data augmentation. Asymptotic properties of both the parametric and nonparametric components of the sieve estimator are then established by applying modern empirical process theory. Numerical results from simulation studies show that our proposed method performs nominally and has advantages over the corresponding estimation method based on individual testing results. We illustrate our work by analysing a chlamydia dataset collected by the State Hygienic Laboratory at the University of Iowa.

Efficient estimation of Cox model with random change point.

In clinical studies, the risk of a disease may dramatically change when some biological indexes of the human body exceed some thresholds. Furthermore, the differences in individual characteristics of patients such as physical and psychological experience may lead to subject-specific thresholds or change points. Although a large literature has been established for regression analysis of failure time data with change points, most of the existing methods assume the same, fixed change point for all study subjects. In this paper, we consider the situation where there exists a subject-specific change point and two Cox type models are presented. The proposed models also offer a framework for subgroup analysis. For inference, a sieve maximum likelihood estimation procedure is proposed and the asymptotic properties of the resulting estimators are established. An extensive simulation study is conducted to assess the empirical performance of the proposed method and indicates that it works well in practical situations. Finally the proposed approach is applied to a set of breast cancer data.

Sieve maximum likelihood estimation for generalized linear mixed models with an unknown link function

Sieve maximum likelihood estimation for generalized linear mixed models with an unknown link function

Regression Analysis of Dependent Current Status Data with Left Truncation

Current status data are encountered in a wide range of applications, including tumorigenic experiments and demographic studies. In this case, each subject has one observation, and the only information obtained is whether the event of interest happened at the moment of observation. In addition to censoring, truncating is also very common in practice. This paper examines the regression analysis of current status data with informative censoring times, considering the presence of left truncation. In addition, we propose an inference approach based on sieve maximum likelihood estimation (SMLE). A copula-based approach is used to describe the relationship between the failure time of interest and the censoring time. The spline function is employed to approximate the unknown nonparametric function. We have established the asymptotic properties of the proposed estimator. Simulation studies suggest that the developed procedure works well in practice. We also applied the developed method to a real dataset derived from an AIDS cohort research.

Semiparametric estimation of latent variable asset pricing models

This paper studies semiparametric identification and estimation of consumption-based asset pricing models with latent state variables. First, we measure how consumption, dividends, and prices depend on Markovian state variables describing aggregate output growth. Subsequently, we identify state-dependent components in the stochastic discount factor using the Euler equation. We develop tractable algorithms for filtering, smoothing, and sieve maximum likelihood estimation, and establish its consistency. Empirically, we find sizable nonlinearities in the impact of expected growth and volatility on the price–dividend ratio and discount factor.

Group variable selection for the Cox model with interval-censored failure time data.

Group variable selection is often required in many areas, and for this many methods have been developed under various situations. Unlike the individual variable selection, the group variable selection can select the variables in groups, and it is more efficient to identify both important and unimportant variables or factors by taking into account the existing group structure. In this paper, we consider the situation where one only observes interval-censored failure time data arising from the Cox model, for which there does not seem to exist an established method. More specifically, a penalized sieve maximum likelihood variable selection and estimation procedure is proposed and the oracle property of the proposed method is established. Also, an extensive simulation study is performed and suggests that the proposed approach works well in practical situations. An application of the method to a set of real data isprovided.

Partially Linear Additive Hazards Regression for Bivariate Interval-Censored Data

In this paper, we discuss regression analysis of bivariate interval-censored failure time data that often occur in biomedical and epidemiological studies. To solve this problem, we propose a kind of general and flexible copula-based semiparametric partly linear additive hazards models that can allow for both time-dependent covariates and possible nonlinear effects. For inference, a sieve maximum likelihood estimation approach based on Bernstein polynomials is proposed to estimate the baseline hazard functions and nonlinear covariate effects. The resulting estimators of regression parameters are shown to be consistent, asymptotically efficient and normal. A simulation study is conducted to assess the finite-sample performance of this method and the results show that it is effective in practice. Moreover, an illustration is provided.

Semiparametric copula method for semi-competing risks data subject to interval censoring and left truncation: Application to disability in elderly.

We aim to evaluate the marginal effects of covariates on time-to-disability in the elderly under the semi-competing risks framework, as death dependently censors disability, not vice versa. It becomes particularly challenging when time-to-disability is subject to interval censoring due to intermittent assessments. A left truncation issue arises when the age time scale is applied. We develop a flexible two-parameter copula-based semiparametric transformation model for semi-competing risks data subject to interval censoring and left truncation. The two-parameter copula quantifies both upper and lower tail dependence between two margins. The semiparametric transformation models incorporate proportional hazards and proportional odds models in both margins. We propose a two-step sieve maximum likelihood estimation procedure and study the sieve estimators' asymptotic properties. Simulations show that the proposed method corrects biases in the marginal method. We demonstrate the proposed method in a large-scale Chinese Longitudinal Healthy Longevity Study and provide new insights into preventing disability in the elderly. The proposed method could be applied to the general semi-competing risks data with intermittently assessed disease status.

Estimation of A Class of Nonparameteric Probit Models

In this paper, we consider a class of nonparametric probit models for binary dependent variables. We extend the standard parametric probit models to nonparametric models in which the parametric index function in the standard probit models is nonparametrically specified. Such a nonparametric specification for the index function in probit models allows us to consider a flexible functional form of the structural parameters. We propose to use a sieve maximum likelihood estimation approach to estimate the parameter and develop the asymptotic theory, including consistency, convergence rates, and asymptotic normality. 
 Our asymptotic normality results are applicable to a wide class of functionals of the parameter, regardless of whether the functional of interest is regular or irregular. The Monte Carlo simulation result shows that the proposed sieve maximum likelihood estimator performs well in finite samples in the sense that the proposed sieve maximum likelihood estimator has a small variance and negligible bias in finite samples.

Estimation of complier causal treatment effects under the additive hazards model with interval-censored data

Estimation of causal treatment effects has attracted a great deal of interest in many areas including social, biological and health science, and for this, instrumental variable (IV) has become a commonly used tool in the presence of unmeasured confounding. In particular, many IV methods have been developed for right-censored time-to-event outcomes. In this paper, we consider a much more complicated situation where one faces interval-censored time-to-event outcomes, which are ubiquitously present in studies with, for example, intermittent follow-up but are challenging to handle in terms of both theory and computation. A sieve maximum likelihood estimation procedure is proposed for estimating complier causal treatment effects under the additive hazards model, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is conducted to evaluate the finite sample performance of the proposed approach and suggests that it works well in practice. It is applied to a breast cancer screening study.

Efficient estimation for accelerated failure time model with interval-censored data in the presence of a cured subgroup

As the alternative of Cox model, the accelerated failure time (AFT) model, which simply regresses the logarithm of the survival time over the covariates, is commonly used in the analysis of interval-censored data. In this paper, we propose a novel two-component mixture-cure model for the interval-censored failure time data in the presence of a cure fraction. Specifically, the first component is a logistic regression model that describes the cure rate, and the second component is a semiparametric accelerated failure time model that describes the failure time of interest for the uncured subjects. An efficient semiparametric procedure is developed to estimate parameters in the considered model. We propose a penalized sieve maximum likelihood estimation approach with Bernstein polynomials to estimate the regression parameters quickly and accurately and the proposed procedure does not rely on the assumption of the distribution of the measurement error. The asymptotic properties of the resulting estimators are established. Extensive simulation studies conducted indicate that the proposed procedure works well for practical situations. In addition, AIDS data analysis is provided for illustration of the proposed method.

Semiparametric single-index models for optimal treatment regimens with censored outcomes.

There is a growing interest in precision medicine, where a potentially censored survival time is often the most important outcome of interest. To discover optimal treatment regimens for such an outcome, we propose a semiparametric proportional hazards model by incorporating the interaction between treatment and a single index of covariates through an unknown monotone link function. This model is flexible enough to allow non-linear treatment-covariate interactions and yet provides a clinically interpretable linear rule for treatment decision. We propose a sieve maximum likelihood estimation approach, under which the baseline hazard function is estimated nonparametrically and the unknown link function is estimated via monotone quadratic B-splines. We show that the resulting estimators are consistent and asymptotically normal with a covariance matrix that attains the semiparametric efficiency bound. The optimal treatment rule follows naturally as a linear combination of the maximum likelihood estimators of the model parameters. Through extensive simulation studies and an application to an AIDS clinical trial, we demonstrate that the treatment rule derived from the single-index model outperforms the treatment rule under the standard Cox proportional hazards model.

Survival Analysis via Ordinary Differential Equations

This article introduces an Ordinary Differential Equation (ODE) notion for survival analysis. The ODE notion not only provides a unified modeling framework, but more importantly, also enables the development of a widely applicable, scalable, and easy-to-implement procedure for estimation and inference. Specifically, the ODE modeling framework unifies many existing survival models, such as the proportional hazards model, the linear transformation model, the accelerated failure time model, and the time-varying coefficient model as special cases. The generality of the proposed framework serves as the foundation of a widely applicable estimation procedure. As an illustrative example, we develop a sieve maximum likelihood estimator for a general semiparametric class of ODE models. In comparison to existing estimation methods, the proposed procedure has advantages in terms of computational scalability and numerical stability. Moreover, to address unique theoretical challenges induced by the ODE notion, we establish a new general sieve M-theorem for bundled parameters and show that the proposed sieve estimator is consistent and asymptotically normal, and achieves the semiparametric efficiency bound. The finite sample performance of the proposed estimator is examined in simulation studies and a real-world data example. Supplementary materials for this article are available online.

A new approach to estimation of the proportional hazards model based on interval-censored data with missing covariates

This paper discusses the fitting of the proportional hazards model to interval-censored failure time data with missing covariates. Many authors have discussed the problem when complete covariate information is available or the missing is completely at random. In contrast to this, we will focus on the situation where the missing is at random. For the problem, a sieve maximum likelihood estimation approach is proposed with the use of I-spline functions to approximate the unknown cumulative baseline hazard function in the model. For the implementation of the proposed method, we develop an EM algorithm based on a two-stage data augmentation. Furthermore, we show that the proposed estimators of regression parameters are consistent and asymptotically normal. The proposed approach is then applied to a set of the data concerning Alzheimer Disease that motivated this study.

Semiparametric multiple inflation count model with application to a smoking cessation study.

Count data are observed by practitioners across various fields. Often, a substantially large proportion of one or some values causes extra variation and may lead to a particular case of mixed structured data. In these cases, a standard count model may lead to poor inference of the parameters involved because of its inability to account for extra variation. Furthermore, we hypothesize a possible nonlinear relationship of a continuous covariate with the logarithm of the mean count and with the probability of belonging to an inflated category. We propose a semiparametric multiple inflation Poisson (MIP) model that considers the two nonlinear link functions. We develop a sieve maximum likelihood estimator (sMLE) for the regression parameters of interest. We establish the asymptotic behavior of the sMLE. Simulations are conducted to evaluate the performance of the proposed sieve MIP (sMIP). Then, we illustrate the methodology on data from a smoking cessation study. Finally, some remarks and opportunities for future research conclude the article.

Efficient estimation of semiparametric varying-coefficient partially linear transformation model with current status data

We consider a varying-coefficient partially linear transformation model with current status data, which extends several semiparametric models for current status data in the literature. Sieve maximum likelihood estimation method is used to obtain an integrated estimate for both the parametric components and nonparametric components in the model, i.e. the linear regression coefficients, the varying-coefficient functions and the baseline survival function. Under some regularity conditions, the proposed parameter estimators are proved to be semiparametrically efficient and asymptotically normal, and the estimators for the nonparametric functions achieve the optimal rate of convergence. Simulation studies assure the theoretical results, and a real data is reanalysed using the proposed method and it yields new findings.

Efficient semiparametric copula estimation of regression models with endogeneity

An efficient sieve maximum likelihood estimation procedure for regression models with endogenous regressors using a copula-based approach is proposed. Specifically, the joint distribution of the endogenous regressor and the error term is characterized by a parametric copula function evaluated at the nonparametric marginal distributions. The asymptotic properties of the proposed estimator are derived, including semiparametrically efficient property. Monte Carlo simulations reveal that the proposed method performs well in finite samples comparing to other existing methods. An empirical application is presented to demonstrate the usefulness of the proposed approach.

Identification of nonparametric monotonic regression models with continuous nonclassical measurement errors

This paper provides sufficient conditions for identification of a nonparametric regression model with an unobserved continuous regressor subject to nonclassical measurement error. The measurement error may be directly correlated with the latent regressor in the model. Our identification strategy does not require the availability of additional data information, such as a secondary measurement, an instrumental variable, or an auxiliary sample. Our main assumptions for nonparametric identification include monotonicity of the regression function, independence of the regression error, and completeness of the measurement error distribution. We also propose a sieve maximum likelihood estimator and investigate its finite sample property through Monte Carlo simulations.