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Ecological momentary assessment and other modern data collection technologies facilitate research on both within-subject and between-subject variability of health outcomes and behaviors. For such intensively measured longitudinal data, Hedeker et al extended the usual two-level mixed-effects model to a two-level mixed-effects location scale (MELS) model to accommodate covariates' influence as well as random subject effects on both mean (location) and variability (scale) of the outcome. However, there is a lack of existing standardized effect size measures for the MELS model. To fill this gap, our study extends Rights and Sterba's framework of

We address the issue of (non-) responsivity of self-initiated assessments in Ecological Momentary Assessment (EMA) or other mobile health (mHealth) studies, where subjects are instructed to self-initiate reports when experiencing defined events, for example, smoking. Since such reports are self-initiated, the frequency and determinants of nonresponse to these event reports is usually unknown, however it may be suspected that nonresponse of such self-initiated reports is not random. In this case, existing methods for missing data may be insufficient in the modeling of these observed self-initiated reports. In certain EMA studies, random prompts, distinct from the self-initiated reports, may be converted to event reports. For example, such a conversion can occur if during a random prompt a subject is assessed about the event (eg, smoking) and it is determined that the subject is engaging in the event at the time of the prompt. Such converted prompts can provide some information about the subject's non-responsivity of event reporting. Furthermore, such non-responsivity can be associated with the primary longitudinal EMA outcome (eg, mood) in which case a joint modeling of the non-responsivity and the mood outcome is possible. Here, we propose a shared-parameter location-scale model to link the primary outcome model for mood and a model for subjects' non-responsivity by shared random effects which characterize a subject's mood level, mood change pattern, and mood variability. Via simulations and real data analysis, our proposed model is shown to be more informative, have better coverage of parameters, and provide better fit to the data than more conventional models.

This study investigates trajectories of racial discrimination, racial and ethnic socialization (RES), and their interaction effects with social positions (nativity and gender) on mental health. A longitudinal study of 786 Filipino American and Korean American youth from the Midwestern U.S. (M(age.Wave1) = 15) confirmed that discrimination increased and significantly contributed to the upward trend of mental health distress, whereas the impact of RES differed by its type and by ethnicity. For example, promotion of mistrust and ethnic-heritage socialization were protective among U.S.-born Filipino American youth, but for Korean American youth, preparation for bias was protective regardless of nativity and gender. This study highlights the importance of considering social positions to better understand the role of RES in youth psychological adjustment.

We use a multivariate multilevel model to study the links between physical fitness (PF) and gross motor coordination (GMC) and investigate the influence of predictors affecting their levels across age. We sampled 7918 Peruvians, aged 6-15 years, from sea-level, Amazon region and high-altitude. Composite markers of GMC and PF were derived (GMCz and PFz , respectively). BMI, biological maturation, and stunting were assessed. School characteristics were obtained via an objective audit. School contexts explained 35% of the associations between PFz and GMCz , whereas children's characteristics explained 65% of the total variation. On average, with increasing age, there was a greater increase in GMCz (β = 0.79 ± 0.04, P

Despite the need for sensitivity analysis to nonignorable missingness in intensive longitudinal data (ILD), such analysis is greatly hindered by novel ILD features, such as large data volume and complex nonmonotonic missing-data patterns. Likelihood of alternative models permitting nonignorable missingness often involves very high-dimensional integrals, causing curse of dimensionality and rendering solutions computationally prohibitive to obtain. We aim to overcome this challenge by developing a computationally feasible method, nonlinear indexes of local sensitivity to nonignorability (NISNI). We use linear mixed effects models for the incomplete outcome and covariates. We use Markov multinomial models to describe complex missing-data patterns and mechanisms in ILD, thereby permitting missingness probabilities to depend directly on missing data. Using a second-order Taylor series to approximate likelihood under nonignorability, we develop formulas and closed-form expressions for NISNI. Our approach permits the outcome and covariates to be missing simultaneously, as is often the case in ILD, and can capture U-shaped impact of nonignorability in the neighborhood of the missing at random model without fitting alternative models or evaluating integrals. We evaluate performance of this method using simulated data and real ILD collected by the ecological momentary assessment method.

Ecological Momentary Assessment data present some new modeling opportunities. Typically, there are sufficient data to explicitly model the within-subject (WS) variance, and in many applications, it is of interest to allow the WS variance to depend on covariates as well as random subject effects. We describe a model that allows multiple random effects per subject in the mean model (eg, random location intercept and slopes), as well as random scale in the error variance model. We present an example of the use of this model on a real dataset and a simulation study that shows the benefit of this model, relative to simpler approaches.

Women who inherit a BRCA1 or BRCA2 mutation have an increased risk of breast cancer. Preliminary evidence suggests they may also have defects in bone marrow function. To test this hypothesis, we conducted a multicenter, retrospective, matched cohort study, comparing women with localized breast cancer requiring cytotoxic chemotherapy who carried an inherited BRCA1 or BRCA2 mutation to similar wild‐type patients treated between 1995 and 2017 and matched based on age, race, site, and chemotherapy regimen. The proportion who developed specific hematologic toxicities, timing of these toxicities, and patterns of blood count fluctuations over time were compared among BRCA1 carriers vs matched wild‐type patients and among BRCA2 carriers vs matched wild‐type patients. 88 BRCA1 carriers and 75 BRCA2 carriers were matched to 226 and 242 wild‐type patients, respectively. The proportions and timing of experiencing any grade or grade 3/4 cytopenias during chemotherapy were not significantly different for BRCA1 carriers or BRCA2 carriers vs matched wild‐type patients. Proportions requiring treatment modifications and time to first modification were also similar. Patterns of blood count fluctuations over time in mutation carriers mirrored those in wild‐type patients overall and by the most common regimens. Women with an inherited mutation in BRCA1 or BRCA2 experience similar frequency, severity, and timing of hematologic toxicities during curative intent breast cancer chemotherapy as matched wild‐type patients. Our findings suggest that BRCA1 or BRCA2 haploinsufficiency is sufficient for adequate bone marrow reserve in the face of short‐term repetitive hematopoietic stressors., In this multicenter, retrospective, matched cohort study, we investigated whether women with an inherited mutation in BRCA1 or BRCA2 experience more severe hematologic toxicities during curative intent chemotherapy for breast cancer than similar women without a mutation. We found that the frequency, severity, and timing of toxicities were similar in these two groups. This study is reassuring that women with an inherited mutation are able to tolerate the repetitive bone marrow stress of modern chemotherapy regimens with usual supportive care measures as well as those without a mutation.

Latent trait shared-parameter mixed models for ecological momentary assessment (EMA) data containing missing values are developed in which data are collected in an intermittent manner. In such studies, data are often missing due to unanswered prompts. Using item response theory models, a latent trait is used to represent the missing prompts and modeled jointly with a mixed model for bivariate longitudinal outcomes. Both one- and two-parameter latent trait shared-parameter mixed models are presented. These new models offer a unique way to analyze missing EMA data with many response patterns. Here, the proposed models represent missingness via a latent trait that corresponds to the students' "ability" to respond to the prompting device. Data containing more than 10 300 observations from an EMA study involving high school students' positive and negative affects are presented. The latent trait representing missingness was a significant predictor of both positive affect and negative affect outcomes. The models are compared to a missing at random mixed model. A simulation study indicates that the proposed models can provide lower bias and increased efficiency compared to the standard missing at random approach commonly used with intermittent missing longitudinal data.

Ecological momentary assessment studies usually produce intensively measured longitudinal data with large numbers of observations per unit, and research interest is often centered around understanding the changes in variation of people's thoughts, emotions and behaviors. Hedeker et al developed a 2-level mixed effects location scale model that allows observed covariates as well as unobserved variables to influence both the mean and the within-subjects variance, for a 2-level data structure where observations are nested within subjects. In some ecological momentary assessment studies, subjects are measured at multiple waves, and within each wave, subjects are measured over time. Li and Hedeker extended the original 2-level model to a 3-level data structure where observations are nested within days and days are then nested within subjects, by including a random location and scale intercept at the intermediate wave level. However, the 3-level random intercept model assumes constant response change rate for both the mean and variance. To account for changes in variance across waves, as well as clustering attributable to waves, we propose a more comprehensive location scale model that allows subject heterogeneity at baseline as well as across different waves, for a 3-level data structure where observations are nested within waves and waves are then further nested within subjects. The model parameters are estimated using Markov chain Monte Carlo methods. We provide details on the Bayesian estimation approach and demonstrate how the Stan statistical software can be used to sample from the desired distributions and achieve consistent estimates. The proposed model is validated via a series of simulation studies. Data from an adolescent smoking study are analyzed to demonstrate this approach. The analyses clearly favor the proposed model and show significant subject heterogeneity at baseline as well as change over time, for both mood mean and variance. The proposed 3-level location scale model can be widely applied to areas of research where the interest lies in the consistency in addition to the mean level of the responses.

Objective To determine the effects on weight loss of three abbreviated behavioral weight loss interventions with and without coaching and mobile technology. Methods A randomized controlled efficacy study of three 6-month weight loss treatments was conducted in 96 adults with obesity: 1) self-guided (SELF), 2) standard (STND), or 3) technology-supported (TECH). STND and TECH received eight in-person group treatment sessions. SELF and STND used paper diaries to self-monitor diet, activity, and weight; TECH used a smartphone application with social networking features and wireless accelerometer. Results Weight loss was greater for TECH and STND than SELF at 6 months (−5.7 kg [95% confidence interval: −7.2 to −4.1] vs. −2.7 kg [95% confidence interval: −5.1 to −0.3], P

This article discusses marginalization of the regression parameters in mixed models for correlated binary outcomes. As is well known, the regression parameters in such models have the "subject-specific" (SS) or conditional interpretation, in contrast to the "population-averaged" (PA) or marginal estimates that represent the unconditional covariate effects. We describe an approach using numerical quadrature to obtain PA estimates from their SS counterparts in models with multiple random effects. Standard errors for the PA estimates are derived using the delta method. We illustrate our proposed method using data from a smoking cessation study in which a binary outcome (smoking, Y/N) was measured longitudinally. We compare our estimates to those obtained using GEE and marginalized multilevel models, and present results from a simulation study.

There is often a need to assess the dependence of standard analyses on the strong untestable assumption of ignorable missingness. To tackle this problem, past research developed simple sensitivity index measures assuming a linear impact of nonignorability and missingness in outcomes only. These restrictions limit their applicability for studies with missingness in both outcome and covariates. Nonignorable missingness in this setting poses significant new analytic challenges and calls for more general and flexible methods that are also computationally tractable even for large datasets. In this paper, we relax the restrictions of extant linear sensitivity index methods and develop nonlinear sensitivity indices that maintain computational simplicity and perform equally well when the impact of nonignorability is locally linear. On the other hand, they can substantially improve the effectiveness of local sensitivity analysis when regression outcomes and covariates are subject to concurrent missingness. In this situation, the local linear sensitivity analysis fails to detect the impact of nonignorability while the proposed nonlinear sensitivity measures can. Because the new sensitivity indices avoid fitting complicated nonignorable models, they are computationally tractable (i.e., scalable) for use in large datasets. We develop general formula for nonlinear sensitivity index measures, and evaluate the new measures in simulated data and a real dataset collected using the ecological momentary assessment method. Copyright © 2016 John Wiley & Sons, Ltd.

Background and aims The neuropsychological correlates of simultaneous marijuana and tobacco use are largely unknown, which is surprising as both substances have similar neural substrates and have opposing influences on working memory (WM). This study examined the effects of marijuana alone, tobacco alone and simultaneous marijuana and tobacco use on WM. Design Primary aims were tested using a within-subject design, controlling for multiple subject- and momentary-level confounds via ecological momentary assessment (EMA). Setting Data collection occurred in the Chicago, USA area in participants' natural environments. Participants Participants were 287 community young adults from a larger natural history study, oversampled for ever smoking, all of whom event-recorded at least one substance use occasion during the study week. Measurements Momentary tobacco, marijuana and alcohol use were recorded during multiple EMA across 1 week of data capture. WM was assessed at the end of each EMA assessment. Contextual variables that may influence WM were recorded via EMA. Findings There were main effects for marijuana and tobacco: WM was poorer with marijuana [odds ratio (OR) = 0.91, 95% confidence interval (CI) = 0.84-0.99] and better with tobacco (OR = 1.11, 95% CI = 1.04-1.18). These effects were not qualified by an interaction (OR = 1.03, 95% CI = 0.84-1.26). Alcohol also reduced WM (OR = 0.87, 95% CI = 0.79-0.95), and the tobacco × alcohol interaction was significant (OR = 0.81, 95% CI = 0.66-0.99), indicating that the facilitative effect of tobacco disappeared with concurrent alcohol use. Conclusions Relative to when individuals did not use these substances, working memory decreased with acute marijuana and alcohol use and increased with acute tobacco use. However, the putative effect of marijuana on working memory and the facilitative effect of tobacco on working memory were no longer present when used simultaneously with tobacco and alcohol, respectively. Data suggest that tobacco use may compensate for working memory decrements from marijuana among young adults and highlight the importance of investigating further the negative impact of alcohol use on cognition.

In the statistical literature, the methods to understand the relationship of explanatory variables on each individual outcome variable are well developed and widely applied. However, in most health-related studies given the technological advancement and sophisticated methods of obtaining and storing data, a need to perform joint analysis of multivariate outcomes while explaining the impact of predictors simultaneously and accounting for all the correlations is in high demand. In this manuscript, we propose a generalized approach within a Bayesian framework that models the changes in the variation in terms of explanatory variables and captures the correlations between the multivariate continuous outcomes by the inclusion of random effects at both the location and scale levels. We describe the use of a spherical transformation for the correlations between the random location and scale effects in order to apply separation strategy for prior elicitation while ensuring positive semi-definiteness of the covariance matrix. We present the details of our approach using an example from an ecological momentary assessment study on adolescents.

The true missing data mechanism is never known in practice. We present a method for generating multiple imputations for binary variables, which formally incorporates missing data mechanism uncertainty. Imputations are generated from a distribution of imputation models rather than a single model, with the distribution reflecting subjective notions of missing data mechanism uncertainty. Parameter estimates and standard errors are obtained using rules for nested multiple imputation. Using simulation, we investigate the impact of missing data mechanism uncertainty on post-imputation inferences and show that incorporating this uncertainty can increase the coverage of parameter estimates. We apply our method to a longitudinal smoking cessation trial where nonignorably missing data were a concern. Our method provides a simple approach for formalizing subjective notions regarding nonresponse and can be implemented using existing imputation software.

In a cluster randomized controlled trial (RCT), the number of randomized units is typically considerably smaller than in trials where the unit of randomization is the patient. If the number of randomized clusters is small, there is a reasonable chance of baseline imbalance between the experimental and control groups. This imbalance threatens the validity of inferences regarding post-treatment intervention effects unless an appropriate statistical adjustment is used. Here, we consider application of the propensity score adjustment for cluster RCTs. For the purpose of illustration, we apply the propensity adjustment to a cluster RCT that evaluated an intervention to reduce suicidal ideation and depression. This approach to adjusting imbalance had considerable bearing on the interpretation of results. A simulation study demonstrates that the propensity adjustment reduced well over 90% of the bias seen in unadjusted models for the specifications examined. Copyright © 2013 John Wiley & Sons, Ltd.

Ecological momentary assessment and/or experience sampling methods are increasingly used in health studies to study subjective experiences within changing environmental contexts. In these studies, up to 30 or 40 observations are often obtained for each subject. Because there are so many measurements per subject, one can characterize a subject's mean and variance and can specify models for both. In this article, we focus on an adolescent smoking study using ecological momentary assessment where interest is on characterizing changes in mood variation. We describe how covariates can influence the mood variances and also extend the statistical model by adding a subject-level random effect to the within-subject variance specification. This permits subjects to have influence on the mean, or location, and variability, or (square of the) scale, of their mood responses. These mixed-effects location scale models have useful applications in many research areas where interest centers on the joint modeling of the mean and variance structure.

The implementation of Medicare Part D on January 1, 2006 provided a voluntary outpatient prescription drug benefit to 43 million Medicare beneficiaries for the first time since Medicare's inception (Doherty 2004). Following the implementation of Part D, Medicare's portion of national prescription drug spending increased from 2 percent (2005) to 18 percent (2006) (Kaiser Family Foundation 2008). Around 50–60 percent of Medicare beneficiaries without prior prescription drug coverage had Part D drug coverage in 2006 (Levy and Weir 2009). The estimated federal cost of Part D from 2007 through 2016 is U.S.$768 billion dollars (Kaiser Family Foundation 2006). Studies have found that Part D increased Medicare beneficiaries' prescription utilization and decreased their out-of-pocket costs (Lichtenberg and Sun 2007; Simoni-Wastila et al. 2008; Yin et al. 2008;). However, it is less clear whether the program has led to reductions, or offsets, in nonprescription utilization of health care services. Khan, Kaestner, and Lin (2008) used data from the 1992–2000 Medicare Current Beneficiary Survey and found that prescription drug insurance did not appear to reduce beneficiary's hospitalizations. In contrast, Hsu et al. (2006) analyzed Medicare Part C claims data from Kaiser Permanente–Northern California and concluded that increases in medication coverage resulted in reduced hospitalizations and lower health care expenditures. Similarly, Zhang et al. (2009) analyzed claims data from a Medicare Advantage plan for a Pennsylvania insurer 2 years before and 2 years after the implementation of Part D and found that the increased spending on prescription drugs was offset by lower nondrug medical spending among groups with limited or no previous drug coverage. We sought to study the overall policy impact of Part D on non-low-income Medicare beneficiaries using detailed health care utilization and expenditure data from a large, nationally representative sample of Medicare beneficiaries. This study hypothesized that Part D eligibility would be associated with an increase in Medicare beneficiaries' medication utilization and a reduction in their out-of-pocket costs for prescription drugs, emergency department use, and hospitalization rates (Gellad et al. 2006; Tjia and Schwartz 2006;) as well as improvement in Medicare beneficiaries' overall health measured by preference-based health utility.

A new quasi-imputation strategy for correlated ordinal responses is proposed by borrowing ideas from random number generation. The essential idea is collapsing ordinal levels to binary ones and converting correlated binary outcomes to multivariate normal outcomes in a sensible way so that re-conversion to the binary and then ordinal scale, after conducting multiple imputation, yields the original marginal distributions and correlations. This conversion process ensures that the correlations are transformed reasonably, which in turn allows us to take advantage of well-developed imputation techniques for Gaussian outcomes. We use the phrase 'quasi' because the original observations are not guaranteed to be preserved. We present an application using a data set from psychiatric research. We conclude that the proposed method may be a promising tool for handling incomplete longitudinal or clustered ordinal outcomes.

Aims Little is known about smoking during the transition to college. The current study examined trajectories of smoking among college freshmen, how trajectories predicted later smoking and the social context of smoking. Design Weekly assessments of daily smoking were collected via the web during the first year of college for a large cohort with a previous history of smoking. Participants and setting A total of 193 college freshmen from a large public university with a previous history of smoking who smoked frequently enough to be included in trajectory analysis.Measurements Measuresincludedweeklyreportsof dailysmoking,familysmoking,perceivedpeerattitudes and smoking, social norms and social smoking environment. Findings Seven trajectories were identified: one of low-level sporadic smoking, one of low-level smoking with a small increase during the year, two classes with a substantial decrease during the year, two classes with relatively small decreases and one class with a substantial increase in smoking. Trajectories of smoking in the freshman year predicted levels of sophomore year smoking, and some social context variables tended to change as smoking increased or decreased for a given trajectory class. Conclusions The transition into college is marked by changes in smoking, with smoking escalating for some students andcontinuingintothesophomoreyear.Shiftsinsocialcontextthatsupportsmokingwereassociatedwithtrajectories of smoking. Despite the focus of developmental models on smoking in early adolescence, the transition into college warrants further investigation as a dynamic period for smoking.

For longitudinal data, mixed models include random subject effects to indicate how subjects influence their responses over repeated assessments. The error variance and the variance of the random effects are usually considered to be homogeneous. These variance terms characterize the within-subjects (i.e., error variance) and between-subjects (i.e., random-effects variance) variation in the data. In studies using ecological momentary assessment (EMA), up to 30 or 40 observations are often obtained for each subject, and interest frequently centers around changes in the variances, both within and between subjects. In this article, we focus on an adolescent smoking study using EMA where interest is on characterizing changes in mood variation. We describe how covariates can influence the mood variances, and also extend the standard mixed model by adding a subject-level random effect to the within-subject variance specification. This permits subjects to have influence on the mean, or location, and variability, or (square of the) scale, of their mood responses. Additionally, we allow the location and scale random effects to be correlated. These mixed-effects location scale models have useful applications in many research areas where interest centers on the joint modeling of the mean and variance structure.

There has been a growing interest regarding generalized classes ofdistributions in statistical theory and practice because of their flexibil-ityinmodelformation.Multipleimputationundersuchdistributionsthatspan a broader area in the symmetry–kurtosis plane appears to havethepotentialofbettercapturingrealincompletedatatrends.Inthisarti-cle, we impute continuous univariate data that exhibit varying charac-teristicsundertwowell-knowndistributions,assesstheextenttowhichthisprocedureworksproperly,makecomparisonswithnormalimputa-tion models in terms of commonly accepted bias and precision mea-sures, and discuss possible generalizations to the multivariate caseand to larger families of distributions.

Aims Analysis of binary outcomes with missing data is a challenging problem in substance abuse studies. We consider this problem in a simple two-group design where interest centers on comparing the groups in terms of the binary outcome at a single timepoint. Design We describe how the deterministic assumptions of missing = smoking and last observation carried forward (LOCF) can be relaxed by allowing missingness to be related imperfectly to the binary outcome, either stratified on past values of the outcome or not. We also describe use of multiple imputation to take into account the uncertainty inherent in the imputed data. Setting Data were analyzed from a published smoking cessation study evaluating the effectiveness of adding group-based treatment adjuncts to an intervention comprised of a television program and self-help materials. Participants Participants were 489 smokers who registered for the television-based program and who indicated an interest in attending group-based meetings. Measurements The measurement of the smoking outcome was conducted via telephone interviews at post-intervention and at 24 months. Findings and conclusions The significance of the group effect did vary as a function of the assumed relationship between missingness and smoking. The ‘conservative’ missing = smoking assumption suggested a beneficial group effect on smoking cessation, which was confirmed via a sensitivity analysis only if an extreme odds ratio of 5 between missingness and smoking was assumed. This type of sensitivity analysis is crucial in determining the role that missing data play in arriving at a study's conclusions.

This study examined grade and sex patterns in real-time measures of daily mood using Ecological Momentary Assessments via palmtop computers among 8th (N = 296) and 10th graders (N = 266) for 1 year using a three-wave longitudinal design. Participants responded to five to seven random prompts/day for 7 consecutive days; when prompted, participants rated eight mood adjectives assessing positive affect (PA) and negative affect (NA). Global depressed mood was also assessed via self-report questionnaire at every wave. Mixed-effects regression analyses indicated that PA modestly but significantly declined across Grade 8 to 11, but NA was relatively stable over time. Sex by time interactions showed that boys experienced greater declines in daily mood over time than did girls. In contrast, global depressed mood did not change over time, and girls reported higher depressed mood than boys. Findings suggest that normative mood declines in adolescence may be driven by deteriorations in PA, rather than increases in NA.

New quasi-imputation and expansion strategies for correlated binary responses are proposed by borrowing ideas from random number generation. The core idea is to convert correlated binary outcomes to multivariate normal outcomes in a sensible way so that re-conversion to the binary scale, after performing multiple imputation, yields the original specified marginal expectations and correlations. This conversion process ensures that the correlations are transformed reasonably which in turn allows us to take advantage of well-developed imputation techniques for Gaussian outcomes. We use the phrase 'quasi' because the original observations are not guaranteed to be preserved. We argue that if the inferential goals are well-defined, it is not necessary to strictly adhere to the established definition of multiple imputation. Our expansion scheme employs a similar strategy where imputation is used as an intermediate step. It leads to proportionally inflated observed patterns, forcing the data set to a complete rectangular format. The plausibility of the proposed methodology is examined by applying it to a wide range of simulated data sets that reflect alternative assumptions on complete data populations and missing-data mechanisms. We also present an application using a data set from obesity research. We conclude that the proposed method is a promising tool for handling incomplete longitudinal or clustered binary outcomes under ignorable non-response mechanisms.

The propensity adjustment is used to reduce bias in treatment effectiveness estimates from observational data. We show here that a mixed-effects implementation of the propensity adjustment can reduce bias in longitudinal studies of non-equivalent comparison groups. The strategy examined here involves two stages. Initially, a mixed-effects ordinal logistic regression model of propensity for treatment intensity includes variables that differentiate subjects who receive various doses of time-varying treatments. Second, a mixed-effects linear regression model compares the effectiveness of those ordinal doses on a continuous outcome over time. Here, a simulation study compares bias reduction that is achieved by implementing this propensity adjustment through various forms of stratification. The simulations demonstrate that bias decreased monotonically as the number of quantiles used for stratification increased from two to five. This was particularly pronounced with stronger effects of the confounding variables. The quartile and quintile strategies typically removed in excess of 80-90 per cent of the bias detected in unadjusted models; whereas a median-split approach removed from 20 to 45 per cent of bias. The approach is illustrated in an evaluation of the effectiveness of somatic treatments for major depression in a longitudinal, observational study of affective disorders.

A mixed-effects propensity adjustment is described that can reduce bias in longitudinal studies involving non-equivalent comparison groups. There are two stages in this data analytic strategy. First, a model of propensity for treatment intensity examines variables that distinguish among subjects who receive various ordered doses of treatment across time using mixed-effects ordinal logistic regression. Second, the effectiveness model examines multiple times until recurrence to compare the ordered doses using a mixed-effects grouped-time survival model. Effectiveness analyses are initially stratified by propensity quintile. Then the quintile-specific results are pooled, assuming that there is not a propensity x treatment interaction. A Monte Carlo simulation study compares bias reduction in fully specified propensity model relative to misspecified models. In addition, type I error rate and statistical power are examined. The approach is illustrated by applying it to a longitudinal, observational study of maintenance treatment of major depression.

Summary. A mixed-effects item response theory model that allows for three-level multivariate ordinal outcomes and accommodates multiple random subject effects is proposed for analysis of multivariate ordinal outcomes in longitudinal studies. This model allows for the estimation of different item factor loadings (item discrimination parameters) for the multiple outcomes. The covariates in the model do not have to follow the proportional odds assumption and can be at any level. Assuming either a probit or logistic response function, maximum marginal likelihood estimation is proposed utilizing multidimensional Gauss–Hermite quadrature for integration of the random effects. An iterative Fisher scoring solution, which provides standard errors for all model parameters, is used. An analysis of a longitudinal substance use data set, where four items of substance use behavior (cigarette use, alcohol use, marijuana use, and getting drunk or high) are repeatedly measured over time, is used to illustrate application of the proposed model.

Observational studies can be used to evaluate treatment effectiveness among patients with a broader range of illness severity than typically seen in randomized controlled clinical trials. However, there are several difficulties with observational evaluations including non-equivalent comparison groups, treatment doses and durations that vary widely, and, in longitudinal studies, multiple courses of treatment per subject. A mixed-effects approach to the propensity adjustment for non-equivalent comparison groups is described that can account for each of these perturbations. The strategy involves two stages. First, characteristics that distinguish among subjects who receive various levels of treatment are examined in a model of propensity for treatment intensity using mixed-effects ordinal logistic regression. Second, the propensity-stratified effectiveness of ordered categorical doses is compared in a mixed-effects grouped time survival model of time until recovery. The model is applied in a longitudinal, observational study of antidepressant effectiveness. Then a Monte Carlo simulation study indicates that the strategy has acceptable type I error rates and minimal bias in the estimates of treatment effectiveness. Statistical power exceeds 0.90 for an odds ratio of 1.5 with N = 250 and 500, and is acceptable for an odds ratio of 2.0 with N = 100. Nevertheless, with N = 100, the models that had high intraclass correlation coefficients had greater tendency towards non-convergence. This approach is a useful strategy for observational studies of treatment effectiveness. It is capable of adjusting for selection bias, incorporating multiple observations per subject, and comparing effectiveness of ordinal doses.

A mixed-effects multinomial logistic regression model is described for analysis of clustered or longitudinal nominal or ordinal response data. The model is parameterized to allow flexibility in the choice of contrasts used to represent comparisons across the response categories. Estimation is achieved using a maximum marginal likelihood (MML) solution that uses quadrature to numerically integrate over the distribution of random effects. An analysis of a psychiatric data set, in which homeless adults with serious mental illness are repeatedly classified in terms of their living arrangement, is used to illustrate features of the model.

Objectives To investigate the relationships of biological, behavioral, familial, and environmental characteristics with siblings´ physical activity (PA) levels as well as the intrapair resemblance in PA. Methods The sample comprises 834 (390 females) biological siblings [brother-brother (BB), sister-sister (SS), brother-sister (BS)] aged 9 to 20 years. Total PA index (TPAI) was estimated by questionnaire. Information on potential behavioral, familial, and environmental correlates was obtained by self-report; body mass index (BMI), biological maturation, and physical fitness were measured. Multilevel models were used to analyze siblings´ clustered data, and sibling resemblance was estimated with the intraclass correlation (ρ). Results On average, younger sibs, those more physically fit, and those with more parental support had greater TPAI. Further, BB pairs had higher TPAI levels than SS or BS pairs, but also had greater within-pair variance. When adjusted for all covariates, SS pairs demonstrated greater resemblance in TPAI (ρ = 0.53, 95%CI = 0.38–0.68) than BS (ρ = 0.26, 95%CI = 0.14–0.43) or BB pairs (ρ = 0.18, 95%CI = 0.06–0.44). Conclusions Age, physical fitness, and parental support were the best predictors of TPAI levels. A moderate level of resemblance in TPAI was observed in SS pairs, while lower resemblance was found for BS and BB pairs. These findings may be due to differences in the roles of shared genetic factors, familial, and environmental characteristics across different sibling types.

The co-twin control design has been widely used in studying the effects of environmental factors on the development of diseases. For binary outcomes that arise from co-twin control studies, the conditional likelihood method is commonly used. This approach, however, does not readily extend to ordinal response data because the standard conditional likelihood does not exist for cumulative logit or proportional odds models. In this paper, we investigate the applicability of the random-effects and GEE approaches in analysing ordinal response data from co-twin control studies. Using both approaches, we re-analyse data from a co-twin control study of the impact of military services during the Vietnam era on post-traumatic stress disorders (PTSD). The ordinal models have considerably increased power in detecting the effects of exposure when compared to the analyses using a dichotomized response. We discuss the interpretation of the estimates from GEE and random-effects models in the context of the twin data. © 1998 John Wiley & Sons, Ltd.

This article describes and illustrates use of random-effects regression models (RRM) in relapse research. RRM are useful in longitudinal analysis of relapse data since they allow for the presence of missing data, time-varying or invariant covariates, and subjects measured at different timepoints. Thus, RRM can deal with "unbalanced" longitudinal relapse data, where a sample of subjects are not all measured at each and every timepoint. Also, recent work has extended RRM to handle dichotomous and ordinal outcomes, which are common in relapse research. Two examples are presented from a smoking cessation study to illustrate analysis using RRM. The first illustrates use of a random-effects ordinal logistic regression model, examining longitudinal changes in smoking status, treating status as an ordinal outcome. The second example focuses on changes in motivation scores prior to and following a first relapse to smoking. This latter example illustrates how RRM can be used to examine predictors and consequences of relapse, where relapse can occur at any study timepoint.

This research examines the relative importance of parental and friends' influences on adolescents' smoking behavior and changes in the effects of social influences during adolescence. Data were collected at 4 times from 7th to 9th grades. Random-effects ordinal regression models were employed to predict the repeated classification of adolescent smoking status using time effects, prior smoking status, friends' smoking, and parental smoking. In general, the effects of friends' smoking are stronger than those of parental smoking, and these differences increase over time. In addition, friends' smoking has greater effects on nonsmokers than smokers. Separate models for males and females disclose some gender differences. In particular, the effects of friends' smoking are stronger for females than for males, and the increasing trend of friends' influences is more noticeable for females than for males. Models for 4 ethnic groups also suggest differential susceptibility to social influences in different cultures.

This study describes the procedures used to establish videotaped inter-rater reliability in a multicenter study investigating the clinical efficacy of divalproex sodium for the treatment of acute mania. A total of 46 raters from 10 centers viewed and rated five videotaped diagnostic patients interviews using a modified SADS and SADS-C. Raters also viewed a follow-up videotaped interview at the midpoint of the study. Raters rated the quality of each interview for its teaching potential. Agreement among raters within study sites was estimated by the intraclass correlation coefficient. Results demonstrated significant agreement among raters within study centers at baseline and follow-up for both the SADS and SADS-C.