Semiparametric lack-of-fit tests in an additive hazard regression model

In the semiparametric additive hazard regression model of McKeague and Sasieni (Biometrika 81: 501–514), the hazard contributions of some covariates are allowed to change over time, without parametric restrictions (Aalen model), while the contributions of other covariates are assumed to be constant. In this paper, we develop tests that help to decide which of the covariate contributions indeed change over time. The remaining covariates may be modelled with constant hazard coefficients, thus reducing the number of curves that have to be estimated nonparametrically. Several bootstrap tests are proposed. The behavior of the tests is investigated in a simulation study. In a practical example, the tests consistently identify covariates with constant and with changing hazard contributions.     

Semiparametric regression estimation for longitudinal data in models with martingale difference error's structure

An inherent characteristic of longitudinal data is the dependence among the observations within the same subject. For exhibiting dependencies among the observations within the same subject, this paper considers a semiparametric partially linear regression model for longitudinal data based on martingale difference error's structure. We establish a strong consistency for the least squares estimator of a parametric component and the estimator of a non-parametric function under some mild conditions. A simulation study shows the performance of the proposed estimator in finite samples.     

Semiparametric regression methods for temporal processes subject to multiple sources of censoring

Process regression methodology is underdeveloped relative to the frequency with which pertinent data arise. In this article, the response-190 is a binary indicator process representing the joint event of being alive and remaining in a specific state. The process is indexed by time (e.g., time since diagnosis) and observed continuously. Data of this sort occur frequently in the study of chronic disease. A general area of application involves a recurrent event with non-negligible duration (e.g., hospitalization and associated length of hospital stay) and subject to a terminating event (e.g., death). We propose a semiparametric multiplicative model for the process version of the probability of being alive and in the (transient) state of interest. Under the proposed methods, the regression parameter is estimated through a procedure that does not require estimating the baseline probability. Unlike the majority of process regression methods, the proposed methods accommodate multiple sources of censoring. In particular, we derive a computationally convenient variant of inverse probability of censoring weighting based on the additive hazards model. We show that the regression parameter estimator is asymptotically normal, and that the baseline probability function estimator converges to a Gaussian process. Simulations demonstrate that our estimators have good finite sample performance. We apply our method to national end-stage liver disease data. The Canadian Journal of Statistics 48: 222–237; 2020 © 2019 Statistical Society of Canada     

Semiparametric ROC surface estimation for continuous diagnostic tests via polytomous logistic regression procedures

In this paper, we propose a semiparametric method of estimating receiver operating characteristic (ROC) surfaces for continuous diagnostic tests under density ratio models. Implementation of our method is easy since the usual polytomous logistic regression procedures in many statistical software packages can be employed. A simulated example is provided to facilitate the implementation of our method. Simulation results show that the proposed semiparametric ROC surface estimator is more efficient than the nonparametric counterpart and the parametric counterpart whether the normality assumption of data holds or not. Moreover, some simulation results on the underlying semiparametric distribution function estimators are also reported. In addition, some discussions on the proposed method as well as analysis of a real data set are provided.     

Semiparametric Additive Accelerated Life Models

In this paper we investigate the asymptotic properties of estimators obtained for the semiparametric additive accelerated life model proposed by Bagdonavicius & Nikulin (1995). This model generalizes the well known additive hazards model of survival analysis and is close to the general transformation model (see Dabrowska & Doksum, 1988). Asymptotic properties of the estimator of the regression parameter and the estimator of the reliability function are given in the case of right censoring for discretized data and a numerical example illustrates these results.     

Checking a Semiparametric Additive Risk Model

McKeague and Sasieni [A partly parametric additive risk model. Biometrika 81 (1994) 501] propose a restriction of Aalen’s additive risk model by the additional hypothesis that some of the covariates have time-independent influence on the intensity of the observed counting process. We introduce goodness-of-fit tests for this semiparametric Aalen model. The asymptotic distribution properties of the test statistics are derived by means of martingale techniques. The tests can be adjusted to detect particular alternatives. As one of the most important alternatives we consider Cox’s proportional hazards model. We present simulation studies and an application to a real data set.     

Semiparametric additive isotonic regression

We consider the efficient estimation in the semiparametric additive isotonic regression model where each additive nonparametric component is assumed to be a monotone function. We show that the least-square estimator of the finite-dimensional regression coefficient is root-n$n$ consistent and asymptotically normal. Moreover, the isotonic estimator of each additive functional component is proved to have the oracle property, which means the additive component can be estimated with the highest asymptotic accuracy as if the other components were known. A fast algorithm is developed by iterating between a cyclic pool adjacent violators procedure and solving a standard ordinary least squares problem. Simulations are used to illustrate the performance of the proposed procedure and verify the oracle property.     

Maximum likelihood estimation for tied survival data under Cox regression model via EM-algorithm

We consider tied survival data based on Cox proportional regression model. The standard approaches are the Breslow and Efron approximations and various so called exact methods. All these methods lead to biased estimates when the true underlying model is in fact a Cox model. In this paper we review the methods and suggest a new method based on the missing-data principle using EM-algorithm that leads to a score equation that can be solved directly. This score has mean zero. We also show that all the considered methods have the same asymptotic properties and that there is no loss of asymptotic efficiency when the tie sizes are bounded or even converge to infinity at a given rate. A simulation study is conducted to compare the finite sample properties of the methods.     

Semiparametric Regression Smoothing of Non-linear Time Series

In this paper, we consider using a semiparametric regression approach to modelling non-linear autoregressive time series. Based on a finite series approximation to non-parametric components, an adaptive selection procedure for the number of summands in the series approximation is proposed. Meanwhile, a large sample study is detailed and a small sample simulation for the Mackey–Glass system is presented to support the large sample study.     

A method for checking regression models in survival analysis based on the risk score

We propose to perform model check for the Cox and Aalen regression models using martingale residual processes grouped after the risk score. Asymptotic distributions of the grouped martingale residual processes are deduced, so both formal and graphical model check can be performed. The method is validated by stochastic simulation. A data example with patients with primary biliary cirrhosis of the liver is discussed.     

Semiparametric test for multiple change-points based on empirical likelihood

In the dynamic financial market, the change of financial asset prices is always described as a certain random events which result in abrupt changes. The random time when the event occurs is called a change point. As the event happens, in order to mitigate property damage the government should increase the macro-control ability. As a result, we need to find a valid statistical model for change point problem to solve it effectively. This paper proposes a semiparametric model for detecting the change points. According to the research of empirical studies and hypothesis testing we acquire the maximum likelihood estimators of change points. We use the loglikelihood ratio to test the multiple change points. We obtain some asymptotic results. The estimated change point is more efficient than the non parametric one through simulation experiments. Real data application illustrates the usage of the model.     

Block empirical likelihood for longitudinal partially linear regression models

The authors propose a block empirical likelihood procedure to accommodate the within‐group correlation in longitudinal partially linear regression models. This leads them to prove a nonparametric version of the Wilks theorem. In comparison with normal approximations, their method does not require a consistent estimator for the asymptotic covariance matrix, which makes it easier to conduct inference on the parametric component of the model. An application to a longitudinal study on fluctuations of progesterone level in a menstrual cycle is used to illustrate the procedure developed here.     

Score test of homogeneity for survival data

If follow-up is made for subjects which are grouped into units, such as familial or spatial units then it may be interesting to test whether the groups are homogeneous (or independent for given explanatory variables). The effect of the groups is modelled as random and we consider a frailty proportional hazards model which allows to adjust for explanatory variables. We derive the score test of homogeneity from the marginal partial likelihood and it turns out to be the sum of a pairwise correlation term of martingale residuals and an overdispersion term. In the particular case where the sizes of the groups are equal to one, this statistic can be used for testing overdispersion. The asymptotic variance of this statistic is derived using counting process arguments. An extension to the case of several strata is given. The resulting test is computationally simple; its use is illustrated using both simulated and real data. In addition a decomposition of the score statistic is proposed as a sum of a pairwise correlation term and an overdispersion term. The pairwise correlation term can be used for constructing a statistic more robust to departure from the proportional hazard model, and the overdispesion term for constructing a test of fit of the proportional hazard model.     

Semiparametric hidden Markov model with non-parametric regression

The hidden Markov model regression (HMMR) has been popularly used in many fields such as gene expression and activity recognition. However, the traditional HMMR requires the strong linearity assumption for the emission model. In this article, we propose a hidden Markov model with non-parametric regression (HMM-NR), where the mean and variance of emission model are unknown smooth functions. The new semiparametric model might greatly reduce the modeling bias and thus enhance the applicability of the traditional hidden Markov model regression. We propose an estimation procedure for the transition probability matrix and the non-parametric mean and variance functions by combining the ideas of the EM algorithm and the kernel regression. Simulation studies and a real data set application are used to demonstrate the effectiveness of the new estimation procedure.     

Semiparametric regression of clustered current status data

This paper discusses regression analysis of clustered current status data under semiparametric additive hazards models. In particular, we consider the situation when cluster sizes can be informative about correlated failure times from the same cluster. To address the problem, we present estimating equation-based estimation procedures and establish asymptotic properties of the resulting estimates. Finite sample performance of the proposed method is assessed through an extensive simulation study, which indicates the procedure works well. The method is applied to a motivating data set from a lung tumorigenicity study.     

Semiparametric Regression Analysis of Longitudinal Skewed Data

In this paper, we develop a semiparametric regression model for longitudinal skewed data. In the new model, we allow the transformation function and the baseline function to be unknown. The proposed model can provide a much broader class of models than the existing additive and multiplicative models. Our estimators for regression parameters, transformation function and baseline function are asymptotically normal. Particularly, the estimator for the transformation function converges to its true value at the rate n ^{? 1 ∕ 2}, the convergence rate that one could expect for a parametric model. In simulation studies, we demonstrate that the proposed semiparametric method is robust with little loss of efficiency. Finally, we apply the new method to a study on longitudinal health care costs.     

Semiparametric estimation of employment duration models

There are a variety of economic areas, such as studies of employment duration and of the durability of capital goods, in which data on important variables typically are censored. The standard techinques for estimating a model from censored data require the distributions of unobservable random components of the model to be specified a priori up to a finite set of parameters, and misspecification of these distributions usually leads to inconsistent parameter estimates. However, economic theory rarely gives guidance about distributions and the standard estimation techniques do not provide convenient methods for identifying distributions from censored data. Recently, several distribution-free or semiparametric methods for estimating censored regression models have been developed. This paper presents the results of using two such methods to estimate a model of employment duration. The paper reports the operating characteristics of the semiparametric estimators and compares the semiparametric estimates with those obtained from a standard parametric model.     

Semiparametric partially linear regression models for functional data

In the context of longitudinal data analysis, a random function typically represents a subject that is often observed at a small number of time point. For discarding this restricted condition of observation number of each subject, we consider the semiparametric partially linear regression models with mean function x^?β$x^{?}\beta$ + g(z), where x and z   are functional data. The estimations of β$\beta$ and g(z) are presented and some asymptotic results are given. It is shown that the estimator of the parametric component is asymptotically normal. The convergence rate of the estimator of the nonparametric component is also obtained. Here, the observation number of each subject is completely flexible. Some simulation study is conducted to investigate the finite sample performance of the proposed estimators.     

Semiparametric principal component poisson regression on clustered data

In modeling count data with multivariate predictors, we often encounter problems with clustering of observations and interdependency of predictors. We propose to use principal components of predictors to mitigate the multicollinearity problem and to abate information losses due to dimension reduction, a semiparametric link between the count dependent variable and the principal components is postulated. Clustering of observations is accounted into the model as a random component and the model is estimated via the backfitting algorithm. Simulation study illustrates the advantages of the proposed model over standard poisson regression in a wide range of scenarios.     

Semiparametric log-linear regression for longitudinal measurements subject to outcome-dependent follow-up

A common problem for longitudinal data analyses is that subjects follow-up is irregular, often related to the past outcome or other factors associated with the outcome measure that are not included in the regression model. Analyses unadjusted for outcome-dependent follow-up yield biased estimates. We propose a longitudinal data analysis that can provide consistent estimates in regression models that are subject to outcome-dependent follow-up. We focus on semiparametric marginal log-link regression with arbitrary unspecified baseline function. Based on estimating equations, the proposed class of estimators are root n consistent and asymptotically normal. We present simulation studies that assess the performance of the estimators under finite samples. We illustrate our approach using data from a health services research study.