Asymptotic bias in the linear mixed effects model under non-ignorable missing data mechanisms

Summary.  In longitudinal studies, missingness of data is often an unavoidable problem. Estimators from the linear mixed effects model assume that missing data are missing at random. However, estimators are biased when this assumption is not met. In the paper, theoretical results for the asymptotic bias are established under non-ignorable drop-out, drop-in and other missing data patterns. The asymptotic bias is large when the drop-out subjects have only one or no observation, especially for slope-related parameters of the linear mixed effects model. In the drop-in case, intercept-related parameter estimators show substantial asymptotic bias when subjects enter late in the study. Eight other missing data patterns are considered and these produce asymptotic biases of a variety of magnitudes.     

Parents’ income and children’s school drop-out at 16 in England and Wales: evidence from the 1970 British Cohort Study

This paper investigates the effect of parents’ income on children’s drop-out from school at age 16 using data from the 1970 British Cohort Study (BCS70). Unlike previous papers using the same data set, we use a continuous measure of income derived from the grouped income variable available in the BCS70, we employ instrumental variable techniques to address the issue of endogeneity of family income and take account of the potential endogeneity of income response with respect to a child’s education by jointly modelling the school drop-out decision and response to the family income question. Our estimates show the exogeneity of response to the income question with a child’s education and are in line with the previous literature finding a statistically significant small negative effect of family income on school drop-out at 16. On the contrary, other non-pecuniary parental effects, such as parental education and social class, turn out to be both significant and of a sizeable magnitude. Early versions of this paper benefited from presentations at the University of Warwick, the ZEW Summer Workshop 2002 on Human Capital, the European Society for Population Economics 2002 Conference and the European Economic Association 2002 Conference and comments by Martin Andrews, Lorenzo Cappellari, Charlotte Lauer, Derek Leslie, Jeremy Smith, Mark Stewart, and two anonymous referees. The BCS70 data were kindly provided by, and used with permission of, the UK Data Archive (UKDA, University of Essex). Funding from the ESRC is gratefully acknowledged. The usual disclaimer applies.     

A hazard model of the probability of medical school drop-out in the UK

Summary.  From individual level longitudinal data for two entire cohorts of medical students in UK universities, we use multilevel models to analyse the probability that an individual student will drop out of medical school. We find that academic preparedness—both in terms of previous subjects studied and levels of attainment therein—is the major influence on withdrawal by medical students. Additionally, males and more mature students are more likely to withdraw than females or younger students respectively. We find evidence that the factors influencing the decision to transfer course differ from those affecting the decision to drop out for other reasons.     

Joint analysis of longitudinal data comprising repeated measures and times to events

In biomedical and public health research, both repeated measures of biomarkers Y as well as times T to key clinical events are often collected for a subject. The scientific question is how the distribution of the responses [ T , Y | X ] changes with covariates X . [ T | X ] may be the focus of the estimation where Y can be used as a surrogate for T . Alternatively, T may be the time to drop-out in a study in which [ Y | X ] is the target for estimation. Also, the focus of a study might be on the effects of covariates X on both T and Y or on some underlying latent variable which is thought to be manifested in the observable outcomes. In this paper, we present a general model for the joint analysis of [ T , Y | X ] and apply the model to estimate [ T | X ] and other related functionals by using the relevant information in both T and Y . We adopt a latent variable formulation like that of Fawcett and Thomas and use it to estimate several quantities of clinical relevance to determine the efficacy of a treatment in a clinical trial setting. We use a Markov chain Monte Carlo algorithm to estimate the model's parameters. We illustrate the methodology with an analysis of data from a clinical trial comparing risperidone with a placebo for the treatment of schizophrenia.     

Anthropological field survey on basic education development in the Tibetan nomadic community of Maqu,Gansu, China

This study takes a thorough look at basic education in some Tibetan nomadic communities. It is carried out by a senior Tibetan scholar who was born in eastern Tibet and has wide experience in working with governments, international organisations, academic institutions and private foundations. The paper provides a detailed examination of the main factors affecting the drop-out rate of students in Tibetan nomadic areas. (Ed.)     

网络教育学生流失情况的分析与对策

在我国,远程教育普遍存在着学生流失率高的现象,这不仅影响办学单位的经济效益,更影响远程教育机构的社会信任度,在一定程度上阻碍了远程教育的长远发展。为了找出学生辍学的个中原因,以北京邮电大学网络教育学院2004--2006年秋季入学的远程教育学生为研究对象,通过采用查阅学生档案、分析数据等方法,研究学生流失的规律和特点,从而提出一些有针对性的解决措施,对远程教育机构学生工作的开展有一定的借鉴意义。     

云南边境民族地区学生辍学的现状、原因及对策

调查发现,近年来云南边境民族地区义务教育阶段的"因贫辍学"现象逐渐减少,"非贫辍学"现象却逐年增多。具体来说,辍学呈现非贫辍学日渐凸显、隐性辍学比例增大以及地域、性别、学段特征明显等特点。辍学对学生身心发展及民族地区经济社会发展、社会治安等带来消极影响。造成辍学新问题的原因涉及社会环境、家庭环境、政府管理、学校教育及学生自身等诸多方面。对此,应通过夯实主体责任、加强教育精准扶贫、提高基础教育质量等方式,确保"控辍保学"目标的有效实现,为云南边境民族地区学生成长和家庭幸福打下坚实的教育基础。     

Factors associated with phosphodiesterase type 5 inhibitor treatment satisfactions: results of patient interrogation

Introduction. Phosphodiesterase type 5 (PDE5) inhibitor therapy is an efficacious means of treatment for erectile dysfunction (ED). PDE5 inhibitors supply penile erection by inhibiting the hydrolysis of cGMP and therefore relaxing the corpus cavernosum. In this study, retrospective evaluation of those patients who were admitted to our clinic with the complaint of ED and who were recommended on PDE5 inhibitor treatment in terms of follow-up results and patient satisfaction were aimed.

Method. The patients were called by phone and after informing about the study and taking the informed consent, patient satisfaction with the treatment, purposes of withdrawal, treatment alterations and partner satisfaction were investigated.

Results. Interviews were made with 345 patients, who accepted to enroll in the study and the mean patient age was 56 ± 11.2 years. Of the patients 66.4% were learned to be satisfied with the treatment. It was determined that 10.7% of the patients have never used the medication and 50% could not continue because of high drug cost. It was recognised that 50.2% of the patients who are not satisfied with the treatment tried another PDE5 inhibitor. The success rate of the treatment was found to be higher in the followed-up group than those losses to follow-up.

Conclusion. Therapy with PDE5 inhibitors is an effective means of ED treatment. The importance of doctor-patient communication should be considered, and the patient should be advised for adaptation to follow-up program. High drug cost is a significant predictor of patient compliance to treatment continuation.     

Multilevel models for longitudinal variables prognostic for survival

The issue of modelling the joint distribution of survival time and of prognostic variables measured periodically has recently become of interest in the AIDS literature but is of relevance in other applications. The focus of this paper is on clinical trials where follow-up measurements of potentially prognostic variables are often collected but not routinely used. These measurements can be used to study the biological evolution of the disease of interest; in particular the effect of an active treatment can be examined by comparing the time profiles of patients in the active and placebo group. It is proposed to use multilevel regression analysis to model the individual repeated observations as function of time and, possibly, treatment. To address the problem of informative drop-out—which may arise if deaths (or any other censoring events) are related to the unobserved values of the prognostic variables—we analyse sequentially overlapping portions of the follow-up information. An example arising from a randomized clinical trial for the treatment of primary biliary cirrhosis is examined in detail.     

Bayesian binary quantile regression for the analysis of Bachelor-to-Master transition

The multi-cycle organization of modern university systems stimulates the interest in studying the progression to higher level degree courses during the academic career. In particular, after the achievement of the first level qualification (Bachelor degree), students have to decide whether to continue their university studies, by enrolling in a second level (Master) programme, or to conclude their training experience. In this work we propose a binary quantile regression (BQR) approach to analyse the Bachelor-to-Master transition phenomenon with the adoption of the Bayesian inferential perspective. In addition to the traditional predictors of academic outcomes, such as the personal characteristics and the field of study, different aspects of student's performance are considered. Moreover, the role of a new contextual variable, representing the type of university regulations experienced during the academic path, is investigated. The utility of the Bayesian BQR to characterize the non-continuation decision after the first cycle studies is illustrated with an application to administrative data of Bachelor graduates at the School of Economics of Sapienza University of Rome. The method favourably compares with more conventional model specifications concerning the conditional mean of the binary response.