Statistical methods for the analysis of longitudinal data from school-based smoking prevention studies

The features which make longitudinal data obtained from school-based smoking prevention studies well-suited for efficient analysis by survival analysis methods are discussed. Survival analysis methods, in particular relative risk regression models, are described and illustrated through an example involving data from the Waterloo Smoking Prevention Project--Study 1. Indications of some of the possible applications for these techniques in the evaluation of interventions to prevent smoking and the study of the smoking onset process are provided.     

Application of a two-stage random effects model to longitudinal pulmonary function data from sarcoidosis patients

We applied a two-stage random effects model to pulmonary function data from 31 sarcoidosis patients to illustrate its usefulness in analysing unbalanced longitudinal data. For the first stage, repeated measurements of percentage of predicted forced vital capacity (FVC%) from an individual were modelled as a function of time since initial clinical assessment. At the second stage, parameters of this function were modelled as a function of certain patient characteristics. We used three methods for estimating the model parameters: maximum likelihood; empirical Bayes; and a two-step least-squares procedure. Similar results were obtained from each, but we recommend the empirical Bayes, since it provides unbiased estimates of variance components. Results indicated that deterioration in FVC% is associated with a higher initial FVC% value and large numbers of both total cells and eosinophils in bronchoalveolar lavage at the initial assessment. Improvement is associated with higher values of pulmonary Gallium uptake at initial assessment and race. Blacks are more likely to improve than whites.     

广义估计方程与多水平logistic回归模型在临床纵向数据分析中的应用及比较

目的探讨广义估计方程和多水平模型的应用与临床纵向研究以解决个体重复观测数据内部的相关性问题。方法根据临床纵向实例数据的特点,拟合因变量为二分类的广义估计方程和多水平模型,并与一般logistic模型比较。结果广义估计方程和多水平模型的分析结果与一般logistic模型不同。由于未能考虑个体内重复观测数据的相关性,一般logistic模型错误显示临床分期与近期疗效相关,而广义估计方程和多水平模型分析结果则显示相关无统计学意义。经分层分析也未发现临床分期与近期疗效的关联。结论广义估计方程和多水平模型都能有效地考虑重复观测数据内部相关性并能处理有缺失值的资料。与多水平模型相比,广义估计方程的参数估计较为稳定,可有效的估计各解释变量的效应。     

A regression model for multivariate random length data

Multivariate random length data occur when we observe multiple measurements of a quantitative variable and the variable number of these measurements is also an observed outcome for each experimental unit. For example, for a patient with coronary artery disease, we may observe a number of lesions in that patient's coronary arteries, along with percentage of blockage of each lesion. Barnhart and Sampson first proposed the multiple population model to analyse multivariate random length data without covariates. This paper extends their approach to deal with multiple covariates. We propose a new multiple population regression model with covariates, and discuss the estimation issues. We analyse data from the TYPE II coronary intervention study to illustrate the methodology.     

Fifteen-month follow-up results of a school-based life-skills approach to smoking prevention

The life-skills approach to smoking prevention was tested in this study. In total, 1024 pupils (mean age 11.4 years, SD = 0.90) from Austria, Denmark, Luxembourg and Germany were recruited as an experimental group, and a sample of 834 matched pupils served as a control group. While the pupils from the control group received no specific intervention, the pupils in the experimental group participated in an intervention programme which was based on the life-skills approach and consisted of 21 sessions. The aims of the programme were to promote fundamental social competencies and coping skills. In addition, specific information on cigarette smoking was given and skills for resisting social influences to smoke were rehearsed. The programme was conducted by trained school teachers during a course of 4 months. Anonymous questionnaires were administrated (1) before the programme was implemented and (2) 15 months after the programme had started. Teachers as well as pupils showed a high level of satisfaction with the programme idea and the materials. With regard to the outcome variables, the programme had no differential effect on current smoking (4-week prevalence). The programme showed a weak effect (P < 0.1) on lifetime smoking prevalence and experimental smoking. There was also an effect of the programme on smoking knowledge, on the social competences of the pupils as well as on the classroom climate. No effects were found on susceptibility to smoking among never-smokers, attitudes towards smoking and the perceived positive consequences of smoking. The results indicate that prevention programmes that are run for only a few months can have a positive impact on variables considered to be protective with regard to smoking uptake.     

Effectiveness of a school-based multi-component smoking prevention intervention: The LdP cluster randomized controlled trial

ObjectiveWe assessed the effectiveness of the Luoghi di Prevenzione-Prevention Grounds school-based smoking prevention programme.MethodsWe undertook a cluster randomized controlled trial of 989 students aged 14–15 years in 13 secondary schools located in Reggio Emilia, Italy. The intervention consisted of the “Smoking Prevention Tour” (SPT) out-of-school workshop, one in-depth lesson on one Smoking Prevention Tour topic, a life-skills peer-led intervention, and enforcement surveillance of school antismoking policy. Self-reported past 30-day smoking of ≥ 20 or 1–19 days of cigarette smoking (daily or frequent smoking, respectively) was recorded in 2 surveys administered immediately before and 18 months after the beginning of the programme. Analysis was by intention to treat. The effect of the intervention was evaluated using random effects logistic regression and propensity score-matching analyses.ResultsPast 30-day smoking and daily cigarette use at eighteen months follow-up were 31% and 46% lower, respectively, for intervention students compared to control students. Taking into account non-smokers at baseline only, daily smoking at eighteen months follow-up was 59% lower in intervention students than in controls. Past 30-day smoking in school areas was 62% lower in intervention students compared to controls.ConclusionsThe Luoghi di Prevenzione-Prevention Grounds programme was effective in reducing daily smokers and in reducing smoking in school areas.     

A linear mixed model for predicting a binary event from longitudinal data under random effects misspecification

The use of longitudinal data for predicting a subsequent binary event is often the focus of diagnostic studies. This is particularly important in obstetrics, where ultrasound measurements taken during fetal development may be useful for predicting various poor pregnancy outcomes. We propose a modeling framework for predicting a binary event from longitudinal measurements where a shared random effect links the two processes together. Under a Gaussian random effects assumption, the approach is simple to implement with standard statistical software. Using asymptotic and simulation results, we show that estimates of predictive accuracy under a Gaussian random effects distribution are robust to severe misspecification of this distribution. However, under some circumstances, estimates of individual risk may be sensitive to severe random effects misspecification. We illustrate the methodology with data from a longitudinal fetal growth study.     

Marginalized random effects models for multivariate longitudinal binary data

Generalized linear models with random effects are often used to explain the serial dependence of longitudinal categorical data. Marginalized random effects models (MREMs) permit likelihood‐based estimations of marginal mean parameters and also explain the serial dependence of longitudinal data. In this paper, we extend the MREM to accommodate multivariate longitudinal binary data using a new covariance matrix with a Kronecker decomposition, which easily explains both the serial dependence and time‐specific response correlation. A maximum marginal likelihood estimation is proposed utilizing a quasi‐Newton algorithm with quasi‐Monte Carlo integration of the random effects. Our approach is applied to analyze metabolic syndrome data from the Korean Genomic Epidemiology Study for Korean adults. Copyright © 2009 John Wiley & Sons, Ltd.     

Tweedie family of generalized linear models with distribution‐free random effects for skewed longitudinal data

Generalized linear mixed models have played an important role in the analysis of longitudinal data; however, traditional approaches have limited flexibility in accommodating skewness and complex correlation structures. In addition, the existing estimation approaches generally rely heavily on the specifications of random effects distributions; therefore, the corresponding inferences are sometimes sensitive to the choice of random effect distributions under certain circumstance. In this paper, we incorporate serially dependent distribution‐free random effects into Tweedie generalized linear models to accommodate a wide range of skewness and covariance structures for discrete and continuous longitudinal data. An optimal estimation of our model has been developed using the orthodox best linear unbiased predictors of random effects. Our approach unifies population‐averaged and subject‐specific inferences. Our method is illustrated through the analyses of patient‐controlled analgesia data and Framingham cholesterol data.     

Analysis of non-ignorable missing and left-censored longitudinal data using a weighted random effects tobit model

In a longitudinal study with response data collected during a hospital stay, observations may be missing because of the subject's discharge from the hospital prior to completion of the study or the death of the subject, resulting in non-ignorable missing data. In addition to non-ignorable missingness, there is left-censoring in the response measurements because of the inherent limit of detection. For analyzing non-ignorable missing and left-censored longitudinal data, we have proposed to extend the theory of random effects tobit regression model to weighted random effects tobit regression model. The weights are computed on the basis of inverse probability weighted augmented methodology. An extensive simulation study was performed to compare the performance of the proposed model with a number of competitive models. The simulation study shows that the estimates are consistent and that the root mean square errors of the estimates are minimal for the use of augmented inverse probability weights in the random effects tobit model. The proposed method is also applied to the non-ignorable missing and left-censored interleukin-6 biomarker data obtained from the Genetic and Inflammatory Markers of Sepsis study.     

Mixed linear regression model for longitudinal data: application to an unbalanced anthropometric data set

A longitudinal data set is characterized by a time sequence of two or more observations from each individual. In cohort studies, these data are usually not balanced. A data set related to longitudinal height measurements in children of HIV-infected mothers was recorded at the university hospital of the Federal University in Minas Gerais, Brazil. The objective was to assess the application of the mixed effect model to this unbalanced data set. At six months of age, on average boys were 1.8 cm taller than girls, and seroreverter infants were 2.9 cm taller than their HIV+ peers. At 12 months of age, on average boys were 2.4 cm taller than girls and seroreverter children were 3.5 cm taller than HIV+ ones. In addition to describing longitudinal height behavior, this model also includes the growth rate estimation for this infant population by gender and group.     

A meta-evaluation of 11 school-based smoking prevention programs

Eleven school-based smoking prevention programs were subjected to a meta-evaluation. Criteria for the meta-evaluation included: 1) adequacy of the research design, 2) evidence of reliability, 3) evidence of validity, 4) appropriate statistical analyses and interpretations, 5) reporting of effect sizes or practical significance, 6) accounting for attrition, and 7) tracking of fidelity to the program. A three-point rating scale was used ranging from 0-2. Criteria with the best ratings were research design and statistical analysis. The lowest ratings occurred for reliability and validity. The remainder of the criteria ranged between 1 and 2 with minor factors accounting for the difference in ratings. Recommendations include increasing the number of evaluations that included tests of reliability and validity and calculated effect size estimates.     

A random effects model for ordinal responses from a crossover trial

Crossover studies have been successfully conducted in the case of continuous responses. Existing procedures of analysis for ordinal responses, on the other hand, are rarely satisfactory unless strict, usually unrealistic, assumptions are made. In this paper we investigate a random effects model and show that the model is simple and general. Interpretation of parameters is easy, though with a complicated fitting procedure.     

Effects of a school-based smoking prevention program among subgroups of adolescents

In autumn 1995 The Norwegian Cancer Society in cooperation with The Research Center for Health Promotion, University of Bergen started a study of school-based interventions aiming at preventing smoking among pupils in Norwegian secondary schools. The study comprised a nationwide sample of 4441 students at 99 schools (195 classes). This panel of students is followed through annual data collections till they graduate in spring 1997. Written consensus from students and parents was obtained from 95%. Schools were systematically allocated to one of four groups: Group A, control; Group B, intervention, containing classroom program, involvement of parents and teacher courses; Group C, like B, but without teacher courses; Group D, like B, but without parental involvement. Baseline data were collected by questionnaires administered in class in November 1994 and the first follow-up survey was carried out in May 1995. At follow-up the proportion of smokers had increased by 8.3 percentage points in Group A (control) and by 1.9 percentage points in Group B (most extensive intervention). As expected, the recruitment of smokers was higher in Groups C and D than in the ideal intervention, but lower than in the control group. Effects of the most extensive program among subgroups of students were examined by comparing Groups A and B. Students are categorized as high risk or low risk based on scores on scales measuring sensation seeking, physical maturity, antisocial behavior and parental smoking. The effect of the program on recruitment of smokers seems to have been at least as strong or even stronger among 'high-risk' students than among other students.     

Maternal smoking during pregnancy and childhood growth trajectory: a random effects regression analysis

Background

Although maternal smoking during pregnancy has been reported to have an effect on childhood overweight/obesity, the impact of maternal smoking on the trajectory of the body mass of their offspring is not very clear. Previously, we investigated this effect by using a fixed-effect model. However, this analysis was limited because it rounded and categorized the age of the children. Therefore, we used a random-effects hierarchical linear regression model in the present study.

Methods

The study population comprised children born between 1 April 1991 and 31 March 1999 in Koshu City, Japan and their mothers. Maternal smoking during early pregnancy was the exposure studied. The body mass index (BMI) z-score trajectory of children born to smoking and non-smoking mothers, by gender, was used as the outcome. We modeled BMI trajectory using a 2-level random intercept and slope regression.

Results

The participating mothers delivered 1619 babies during the study period. For male children, there was very strong evidence that the effect of age in months on the increase in BMI z-score was enhanced by maternal smoking during pregnancy (P < 0.0001). In contrast, for female children, there was only weak evidence for an interaction between age in months and maternal smoking during pregnancy (P = 0.054), which suggests that the effect of maternal smoking during pregnancy on the early-life BMI trajectory of offspring differed by gender.

Conclusions

These results may be valuable for exploring the mechanism of fetal programming and might therefore be clinically important.Key words: body mass index, childhood growth, gender, multi-level analysis, pregnancy, smoking     

Modelling the random effects covariance matrix in longitudinal data

A common class of models for longitudinal data are random effects (mixed) models. In these models, the random effects covariance matrix is typically assumed constant across subject. However, in many situations this matrix may differ by measured covariates. In this paper, we propose an approach to model the random effects covariance matrix by using a special Cholesky decomposition of the matrix. In particular, we will allow the parameters that result from this decomposition to depend on subject-specific covariates and also explore ways to parsimoniously model these parameters. An advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix. In addition, the parameters resulting from this decomposition have a sensible interpretation. We propose fully Bayesian modelling for which a simple Gibbs sampler can be implemented to sample from the posterior distribution of the parameters. We illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects.     

Zero-inflated Poisson regression with random effects to evaluate an occupational injury prevention programme

This study presents a zero-inflated Poisson regression model with random effects to evaluate a manual handling injury prevention strategy trialled within the cleaning services department of a 600 bed public hospital between 1992 and 1995. The hospital had been experiencing high annual rates of compensable injuries of which over 60 per cent were attributed to manual handling. The strategy employed Workplace Risk Assessment Teams (WRATS) that utilized a workplace risk identification, assessment and control approach to manual handling injury hazard reduction. The WRATS programme was an intervention trial, covering the 1988-1995 financial years. In the course of compiling injury counts, it was found that the data exhibited an excess of zeros, in the context that the majority of cleaners did not suffer any injuries. This phenomenon is typical of data encountered in the occupational health discipline. We propose a zero-inflated random effects Poisson regression model to analyse such longitudinal count data with extra zeros. The WRATS intervention and other concomitant information on individual cleaners are considered as fixed effects in the model. The results provide statistical evidence showing the value of the WRATS programme. In addition, the methods can be applied to assess the effectiveness of intervention trials on populations at high risk of manual handling injury or indeed of injury from other hazards.     

随机系数发展模型与协方差模式模型在纵向数据分析中的应用及R实现

目的 应用随机系数发展模型与协方差模式模型分析社区卫生服务中心纵向数据,探讨纵向数据分析的问题,为社区随访数据处理提供科学方法.方法 使用R软件对社区卫生服务中心糖尿病重复测量数据分别拟合随机系数发展模型,协方差模式模型以及传统线性回归模型,并比较3种模型的分析结果.结果 随机系数发展模型和协方差模式模型的分析结果与传统线性回归模型不同,2模型较传统线性回归更多的考虑了数据的变异来源.随机系数发展模型与协方差模式模型变量的估计系数结果相近,2者在固定效应的估计上区别往往不是很大,2模型相比,信息标准统计相差也不大.随机系数发展模型倾向于解释组间随机效应,协方差模式模型更关注组内观测之间的联系.R软件nlme package相比于SAS proc mixed,其相应的结果比较与可视化的函数使用更为灵活方便,同时GLS函数提供更多的组内方差协方差模式以供选择.结论 随机系数发展模型与协方差模式模型都能较好的处理重复观测数据组内相关性的问题.2者处理组内相关性的出发点不同,如果强调组内观测之间的联系性,则选择协方差模式模型.相反,如果更关注组间的异质性,强调组间的随机效应,则选择随机系数发展模型.R软件nlme是比较完善的处理混合结构数据的分析包.