We consider partially linear models of the form Y = X^Tβ + ν(Z) + ɛ when the response variable Y is sometimes missing with missingness probability π depending on (X, Z), and the covariate X is measured with error, where ν(z) is an unspecified smooth function. The missingness structure is therefore missing not at random, rather than the usual missing at random. We propose a class of semiparametric estimators for the parameter of interest β, as well as for the population mean E(Y). The resulting estimators are shown to be consistent and asymptotically normal under general assumptions. To construct a confidence region for β, we also propose an empirical-likelihood-based statistic, which is shown to have a chi-squared distribution asymptotically. The proposed methods are applied to an AIDS clinical trial dataset. A simulation study is also reported.

Active commuting to school (ACS) may increase children’s daily physical activity and help them maintain a healthy weight. Previous studies have identified various perceived barriers related to children’s ACS. However, it is not clear whether and how these studies were methodologically sound and theoretically grounded. The purpose of this review was to critically assess the current literature on perceived barriers to children’s ACS and provide recommendations for future studies. Empirically based literature on perceived barriers to ACS was systematically searched from six databases. A methodological quality scale (MQS) and a theory utilization quality scale (TQS) were created based on previously established instruments and tailored for the current review. Among the 39 studies that met the inclusion criteria, 19 (48.7%) reported statistically significant perceived barriers to child’s ACS. The methodological and theory utilization qualities of reviewed studies varied, with MQS scores ranging between 7 and 20 (Mean =12.95, SD =2.95) and TQS scores from 1 to 7 (Mean =3.62, SD =1.74). A detailed appraisal of the literature suggests several empirical, methodological, and theoretical recommendations for future studies on perceived barriers to ACS. Empirically, increasing the diversity of study regions and samples should be a high priority, particularly in Asian and European countries, and among rural residents; more prospective and interventions studies are needed to determine the causal mechanism liking the perceived factors and ACS; future researchers should include policy-related barriers into their inquiries. Methodologically, the conceptualization of ACS should be standardized or at least well rationalized in future studies to ensure the comparability of results; researchers’ awareness need to be increased for improving the methodological rigor of studies, especially in regard to appropriate statistical analysis techniques, control variable estimation, multicollinearity testing, and reliability and validity reporting. Theoretically, future researchers need to first ground their investigations in theoretical foundations; efforts should be devoted to make sure theories are used thoroughly and correctly; important theoretical constructs, in particular, need to be conceptualized and operationalized appropriately to ensure accurate measurement. By reviewing what has been achieved, this review offered insights for more sophisticated ACS studies in the future.

Efficient estimation of parameters is a major objective in analyzing longitudinal data. We propose two generalized empirical likelihood-based methods that take into consideration within-subject correlations. A nonparametric version of the Wilks theorem for the limiting distributions of the empirical likelihood ratios is derived. It is shown that one of the proposed methods is locally efficient among a class of within-subject variance-covariance matrices. A simulation study is conducted to investigate the finite sample properties of the proposed methods and compares them with the block empirical likelihood method by You et al. (2006) and the normal approximation with a correctly estimated variance-covariance. The results suggest that the proposed methods are generally more efficient than existing methods that ignore the correlation structure, and are better in coverage compared to the normal approximation with correctly specified within-subject correlation. An application illustrating our methods and supporting the simulation study results is presented.

Patient-Centered Innovations, Education and Technology for Cancer Care and Cancer Research

Active commuting to school (ACS) can promote children’s physical activity and may help prevent childhood obesity. Previous researchers in various disciplines, e.g., health, urban planning, and transportation, have identified various predictors of ACS. However, little research has been carried out into investigating the effect of self-efficacy on ACS. The purpose of this study is to investigate the roles of children’s and parents’ self-efficacy in children’s ACS, controlling for sociodemographic and objective environmental characteristics. This study is part of the Texas Childhood Obesity Prevention Policy Evaluation (T-COPPE) project, which includes data from 857 parent/child pairs from 74 schools who lived within two miles of school in Texas. Measures included children’s usual modes of commuting to school, participants’ sociodemographics, perceived self-efficacy toward ACS, sources of children’s self-efficacy, school settings, and objective environmental constraints. Multilevel structural equation modeling (SEM) was employed to test the hypothesized pathways using Mplus 7.0. Around 18% of the children were active commuters. Two sources of children’s self-efficacy were identified, i.e., emotional states (β = 0.36, p < 0.001) and social modeling (β = 0.28, p < 0.01). Compared with children’s self-efficacy (β = 0.16, p < 0.001), parents’ self-efficacy (β = 0.63, p < 0.001) had a stronger influence on children’s ACS. Participants’ social economic disadvantage (β = 0.40, p < 0.001), environmental constraints (β = −0.49, p < 0.001), and school setting (β = −0.17, p = 0.029) all had statistically significant direct effects on children’s ACS. Future initiatives should consider both parents’ and children’s self-efficacy in developing strategies for promoting children’s ACS. Social disadvantage and environmental constraints also need to be addressed for effective interventions. The work reported here provides support for the continuing exploration of the role of self-efficacy in children’s ACS.