The mean residual life model for the right-censored data in the presence of covariate measurement errors.

In this article, we consider the mean residual life regression model in the presence of covariate measurement errors. In the whole cohort, the surrogate variable of the error-prone covariate is available for each subject, while the instrumental variable (IV), which is related to the underlying true covariates, is measured only for some subjects, the calibration sample. Without specifying distributions of measurement errors but assuming that the IV is missing at random, we develop two estimation methods, the IV calibration and cohort estimators, for the regression parameters by solving estimation equations (EEs) based on the calibration sample and cohort sample, respectively. To improve estimation efficiency, a synthetic estimator is derived by applying the generalized method of moment for all EEs. The large sample properties of the proposed estimators are established and their finite sample performance are evaluated via simulation studies. Simulation results show that the cohort and synthetic estimators outperform the IV calibration estimator and the relative efficiency of the cohort and synthetic estimators mainly depends on the missing rate of IV. In the case of low missing rate, the synthetic estimator is more efficient than the cohort estimator, while the result can be reversed when the missing rate is high. We illustrate the proposed method by application to data from the patients with stage 5 chronic kidney disease in Taiwan.

Comparison of two treatments on a covariate variable.

In clinical trials, the efficacy of treatment might be dependent on the value of a covariate variable. Therefore, it might be possible to detect the region over the covariate variable where the two treatments under investigation do not have significantly different efficacy or the region of superiority of one treatment. The non-significant region can be verified to be a confidence interval for the abscissa of the intersection point of two regression lines, and each of the complementary regions of the confidence interval corresponds to a region of superiority. In this study, we develop a method of constructing the confidence interval based on the concept of a generalized pivotal quantity, so as to perform the task of detecting the possible three regions for a clinical trial. Two real-world examples are given to illustrate the application of our proposed method, and a simulation study is conducted to evaluate its performance.

The subject-dependent, cumulative, and recency association of aerobic fitness with academic performance in Taiwanese junior high school students.

BACKGROUND: The objective of the current study was to examine whether the relation between aerobic fitness and academic achievement during adolescence is subject-dependent, and to investigate cumulative and recency effects. METHODS: This study made use of two nationwide datasets. The first was the aerobic fitness profile of junior high school students collected by the Ministry of Education in Taiwan. The second contained the scores on the Basic Competence Test for Junior High School Students (BCTJH). The sample consisted of 382,259 students who completed the BCTJH in the 5 years between 2009 and 2013. Data on each student's aerobic fitness during their three years of junior high school were matched with their exam results at the end of this period. RESULTS: The results revealed that students classified as highly-fit during at least one of the three years had higher BCTJH scores than those who never achieved this level, with the size of effect increasing with the length of time that fitness was maintained. Additionally, aerobic fitness in the final year was more closely linked to BCTJH scores than that in the earlier two years. Fitness was also more strongly associated with exam performance in math, science and social science, relative to language-related subjects. CONCLUSIONS: Our findings suggest that while aerobic fitness is positively related to academic achievement in Taiwanese junior high school students, the relationship depends on academic subject, as well as the length and time of being aerobically fit.

Polynomial regression with heteroscedastic measurement errors in both axes: Estimation and hypothesis testing.

This article investigates point estimation and hypothesis testing in a polynomial regression model with heteroscedastic measurement errors present in both response and regressor variables. For point estimation, the adjusted least squares method and its modifications are developed. These methods can treat both functional and structural models, and models with or without an equation error. For hypothesis testing, the Wald-type and score-type tests are discussed. Their performance is investigated in a simulation study. Applications of these methods are also illustrated with real datasets.

The Relations between 3-year Changes in Physical Fitness and Academic Performance in Nationally Representative Sample of Junior High School Students.

The objective of the current study was to examine the relationship between different components of physical fitness across 3 years of junior high school with academic performance assessed at the end of the period. Two nationwide representative datasets were used. The first was the physical fitness profile assessed at the beginning of each of the three school years. The second contained the scores on a standardized test administered at the end of the third year. All data were standardized by calculating percentile rank (PR). Students were classified as "High-fit" if their fitness scores ≧ top 25% PR on the age- and sex-adjusted norms. All other students were classified as "not high-fit". The relationships between fitness and exam performance were tested adjusting for sex, body mass index, and level of urbanization. Students who were in the high-fit group in both years 1 and 3 academically outperformed those who were outside this classification during both assessments. The degree of outperformance was greatest for those who were aerobically fit, followed by those who were high-fit in terms of muscular endurance, muscular strength, and flexibility, respectively. It is therefore concluded that the relationship between physical fitness and academic performance in Taiwanese junior high school students is strongest in the case of aerobic fitness.