Akio Suzukawa

Kullback-Leibler information consistent estimation for censored data

This paper is intended as an investigation of parametric estimation for the randomly right censored data. In parametric estimation, the Kullback-Leibler information is used as a measure of the divergence of a true distribution generating a data relative to a distribution in an assumed parametric model M. When the data is uncensored, maximum likelihood estimator (MLE) is a consistent estimator of minimizing the Kullback-Leibler information, even if the assumed model M does not contain the true distribution. We call this property minimum Kullback-Leibler information consistency (MKLI-consistency). However, the MLE obtained by maximizing the likelihood function based on the censored data is not MKLI-consistent. As an alternative to the MLE, Oakes (1986, Biometrics, 42, 177–182) proposed an estimator termed approximate maximum likelihood estimator (AMLE) due to its computational advantage and potential for robustness. We show MKLI-consistency and asymptotic normality of the AMLE under the misspecification of the parametric model. In a simulation study, we investigate mean square errors of these two estimators and an estimator which is obtained by treating a jackknife corrected Kaplan-Meier integral as the log-likelihood. On the basis of the simulation results and the asymptotic results, we discuss comparison among these estimators. We also derive information criteria for the MLE and the AMLE under censorship, and which can be used not only for selecting models but also for selecting estimation procedures.

A FORMULA FOR NORMALIZING TRANSFORMATION OF SOME STATISTICS

ABSTRACT On the basis of Konishis study of a normalizing transformation (Konishi [1]), a concrete normalizing transformation is derived. Some applications of the proposed normalizing transformation are shown, and performance of the transformation in the applications is numerically investigated.

Semiparametric estimation based on parametric modeling of the cause-specific hazard ratios in competing risks

This paper is intended as an investigation of estimating cause-specific cumulative hazard and cumulative incidence functions in a competing risks model. The proportional model in which ratios of the cause-specific hazards to the overall hazard are assumed to be constant (independent of time) is a well-known semiparametric model. We are here concerned with relaxation of the proportionality assumption. The set C of all causes are decomposed into two disjoint subsets of causes as C - C1 ∪ C2. The relative risk of cause A in the sub-causes C1 can be represented as a function defined by ratic of the cause-specific hazard of cause A to the sum of cause-specific hazards in the sub-causes C1. We call this function the risk pattern function of cause A in C1, and consider a semiparametric model in which risk pattern functions in C1 are not constant (independent of time) but those functional forms, except for finite-dimensional parameters, are known. Based on this model, semiparametric estimators are obtained, and estimated variances of them are derived by delta methods. We investigate asymptotic properties of the semiparametric estimators and compare them with the nonparametric estimators. The semiparametric procedure is illustrated with the radiation-exposed mice data set, which represents lifetimes and causes of death of mice exposed to radiation in two different environments.

The mediator effect of personality traits on the relationship between childhood abuse and depressive symptoms in schizophrenia

Previous studies indicated that personality traits have a mediator effect on the relationship between childhood abuse and depressive symptoms in major depressive disorder and nonclinical general adult subjects. In the present study, we aimed to test the hypothesis that personality traits mediate the relationship between childhood abuse and depressive symptoms in schizophrenia. We used the following questionnaires to evaluate 255 outpatients with schizophrenia: the Child Abuse and Trauma Scale, temperament and character inventory, and Patients Health Questionnire-9. Univariate analysis, multiple regression analysis, and structured equation modeling (SEM) were used to analyze the data. The relationship between neglect and sexual abuse and the severity of depressive symptoms was mostly mediated by the personality traits of high harm avoidance, low self-directedness, and low cooperativeness. This finding was supported by the results of stepwise multiple regression analysis and the acceptable fit indices of SEM. Thus, our results suggest that personality traits mediate the relationship between childhood abuse and depressive symptoms in schizophrenia. The present study and our previous studies also suggest that this mediator effect could occur independent of the presence or type of mental disorder. Clinicians should routinely assess childhood abuse history, personality traits, and their effects in schizophrenia.

Redundancy Index in Canonical Correlation Analysis with Linear Constraints

The redundancy index proposed by Stewart and Love (1968) is an index to measure the degree to which one set of variables can predict another set of variables, and is associated with canonical correlation analysis. Yanai and Takane (1992) developed canonical correlation analysis with linear constraints (CCALC). In this paper we define a redundancy index in CCALC, which is based on the reformulation of CCALC by Suzukawa (1997). The index is a general measure to summarize redundancy between two sets of variables in the sense that various dependency measures can be obtained by choosing constraints suitably. The asymptotic distribution of the index is derived under normality.