A generalized linear mixed model for longitudinal binary data with a marginal logit link function

Longitudinal studies of a binary outcome are common in the health, social, and behavioral sciences. In general, a feature of random effects logistic regression models for longitudinal binary data is that the marginal functional form, when integrated over the distribution of the random effects, is no longer of logistic form. Recently, Wang and Louis [Biometrika 90 (2003) 765--775] proposed a random intercept model in the clustered binary data setting where the marginal model has a logistic form. An acknowledged limitation of their model is that it allows only a single random effect that varies from cluster to cluster. In this paper we propose a modification of their model to handle longitudinal data, allowing separate, but correlated, random intercepts at each measurement occasion. The proposed model allows for a flexible correlation structure among the random intercepts, where the correlations can be interpreted in terms of Kendall's $\tau$. For example, the marginal correlations among the repeated binary outcomes can decline with increasing time separation, while the model retains the property of having matching conditional and marginal logit link functions. Finally, the proposed method is used to analyze data from a longitudinal study designed to monitor cardiac abnormalities in children born to HIV-infected women.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS390 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Development of an integrated cognitive behavioral therapy for anxiety and opioid use disorder: Study protocol and methods

Opioid use disorder is a highly disabling psychiatric disorder, and is associated with both significant functional disruption and risk for negative health outcomes such as infectious disease and fatal overdose. Even among those who receive evidence-based pharmacotherapy for opioid use disorder, many drop out of treatment or relapse, highlighting the importance of novel treatment strategies for this population. Over 60% of those with opioid use disorder also meet diagnostic criteria for an anxiety disorder; however, efficacious treatments for this common co-occurrence have not be established. This manuscript describes the rationale and methods for a behavioral treatment development study designed to develop and test an integrated cognitive-behavioral therapy for those with co-occurring opioid use disorder and anxiety disorders. The aims of the study are (1) to develop and pilot test a new manualized cognitive behavioral therapy for co-occurring opioid use disorder and anxiety disorders, (2) to test the efficacy of this treatment relative to an active comparison treatment that targets opioid use disorder alone, and (3) to investigate the role of stress reactivity in both prognosis and recovery from opioid use disorder and anxiety disorders. Our overarching aim is to investigate whether this new treatment improves both anxiety and opioid use disorder outcomes relative to standard treatment. Identifying optimal treatment strategies for this population are needed to improve outcomes among those with this highly disabling and life-threatening disorder.This study was funded by NIDA grant DA035297. The funding source had no involvement in the study design, analysis and interpretation of data, writing of the report, or the decision to submit the article for publication. (DA035297 - NIDA)Accepted manuscrip

Simple Methods of Determining Confidence Intervals for Functions of Estimates in Published Results

Often, the reader of a published paper is interested in a comparison of parameters that has not been presented. It is not possible to make inferences beyond point estimation since the standard error for the contrast of the estimated parameters depends upon the (unreported) correlation. This study explores approaches to obtain valid confidence intervals when the correlation is unknown. We illustrate three proposed approaches using data from the National Health Interview Survey. The three approaches include the Bonferroni method and the standard confidence interval assuming (most conservative) or (when the correlation is known to be non-negative). The Bonferroni approach is found to be the most conservative. For the difference in two estimated parameter, the standard confidence interval assuming yields a 95% confidence interval that is approximately 12.5% narrower than the Bonferroni confidence interval; when the correlation is known to be positive, the standard 95% confidence interval assuming is approximately 38% narrower than the Bonferroni. In summary, this article demonstrates simple methods to determine confidence intervals for unreported comparisons. We suggest use of the standard confidence interval assuming if no information is available or if the correlation is known to be non-negative

Economic inequalities in the effectiveness of a primary care intervention for depression and suicidal ideation.

BACKGROUND: Economic disadvantage is associated with depression and suicide. We sought to determine whether economic disadvantage reduces the effectiveness of depression treatments received in primary care. METHODS: We conducted differential-effects analyses of the Prevention of Suicide in Primary Care Elderly: Collaborative Trial, a primary-care-based randomized, controlled trial for late-life depression and suicidal ideation conducted between 1999 and 2001, which included 514 patients with major depression or clinically significant minor depression. RESULTS: The intervention effect, defined as change in depressive symptoms from baseline, was stronger among persons reporting financial strain at baseline (differential effect size = -4.5 Hamilton Depression Rating Scale points across the study period [95% confidence interval = -8.6 to -0.3]). We found similar evidence for effect modification by neighborhood poverty, although the intervention effect weakened after the initial 4 months of the trial for participants residing in poor neighborhoods. There was no evidence of substantial differences in the effectiveness of the intervention on suicidal ideation and depression remission by economic disadvantage. CONCLUSIONS: Economic conditions moderated the effectiveness of primary-care-based treatment for late-life depression. Financially strained individuals benefited more from the intervention; we speculate this was because of the enhanced treatment management protocol, which led to a greater improvement in the care received by these persons. People living in poor neighborhoods experienced only temporary benefit from the intervention. Thus, multiple aspects of economic disadvantage affect depression treatment outcomes; additional work is needed to understand the underlying mechanisms

Association of Regional Variation in Primary Care Physicians’ Colorectal Cancer Screening Recommendations with Individual Use of Colorectal Cancer Screening

Introduction: Studies show that the recommendations of a primary care physician for colorectal cancer screening may be one important influence on an individual's use of screening. However, another possible influence, the effect of regional differences in physicians' beliefs and recommendations on screening use, has not been assessed. Methods: We linked data from the National Health Interview Survey on the use of colorectal cancer screening by respondents aged 50 years or older, by hospital-referral region, with data from the Survey of Colorectal Cancer Screening Practices on the colorectal cancer screening recommendations of primary care physicians, by region. Our principal independent variables were the proportion of physicians in a region who recommended screening at age 50 and continuing screening at the recommended frequency. Results: On average, 53.3% of physicians in a region correctly recommended initiating colorectal cancer screening, and 64.8% advised screening at the recommended frequency. Of adults who lived in regions where less than 30% of physicians correctly recommended initiating screening, 47.3% had been screened, in contrast to 54.8% in areas where 70% or more of physicians made correct recommendations. Seventy-one percent of respondents living in regions where less than 30% of physicians advised screening at the recommended frequency were current on screening, in contrast to 79.9% of respondents living in regions where 70% or more of physicians made this recommendation. These differences were statistically significant after adjustment for individual characteristics. Conclusion: Strategies to improve colorectal cancer screening recommendations of primary care physicians may improve the use of screening for millions of Americans

Acute low back pain is marked by variability: An internet-based pilot study

<p>Abstract</p> <p>Background</p> <p>Pain variability in acute LBP has received limited study. The objectives of this pilot study were to characterize fluctuations in pain during acute LBP, to determine whether self-reported 'flares' of pain represent discrete periods of increased pain intensity, and to examine whether the frequency of flares was associated with back-related disability outcomes.</p> <p>Methods</p> <p>We conducted a cohort study of acute LBP patients utilizing frequent serial assessments and Internet-based data collection. Adults with acute LBP (lasting ≤3 months) completed questionnaires at the time of seeking care, and at both 3-day and 1-week intervals, for 6 weeks. Back pain was measured using a numerical pain rating scale (NPRS), and disability was measured using the Oswestry Disability Index (ODI). A pain flare was defined as 'a period of increased pain lasting at least 2 hours, when your pain intensity is distinctly worse than it has been recently'. We used mixed-effects linear regression to model longitudinal changes in pain intensity, and multivariate linear regression to model associations between flare frequency and disability outcomes.</p> <p>Results</p> <p>42 of 47 participants (89%) reported pain flares, and the average number of discrete flare periods per patient was 3.5 over 6 weeks of follow-up. More than half of flares were less than 4 hours in duration, and about 75% of flares were less than one day in duration. A model with a quadratic trend for time best characterized improvements in pain. Pain decreased rapidly during the first 14 days after seeking care, and leveled off after about 28 days. Patients who reported a pain flare experienced an almost 3-point greater current NPRS than those not reporting a flare (mean difference [SD] 2.70 [0.11]; p < 0.0001). Higher flare frequency was independently associated with a higher final ODI score (<it>ß </it>[SE} 0.28 (0.08); p = 0.002).</p> <p>Conclusions</p> <p>Acute LBP is characterized by variability. Patients with acute LBP report multiple distinct flares of pain, which correspond to discrete increases in pain intensity. A higher flare frequency is associated with worse disability outcomes.</p

Joint generalized estimating equations for multivariate longitudinal binary outcomes with missing data: an application to acquired immune deficiency syndrome data

In a large, prospective longitudinal study designed to monitor cardiac abnormalities in children born to HIV-infected women, instead of a single outcome variable, there are multiple binary outcomes (e.g., abnormal heart rate, abnormal blood pressure, abnormal heart wall thickness) considered as joint measures of heart function over time. In the presence of missing responses at some time points, longitudinal marginal models for these multiple outcomes can be estimated using generalized estimating equations (GEE) (Liang and Zeger, 1986), and consistent estimates can be obtained under the assumption of a missing completely at random (MCAR) mechanism. When the missing data mechanism is missing at random (MAR), that is the probability of missing a particular outcome at a time-point depends on observed values of that outcome and the remaining outcomes at other time points, we propose joint estimation of the marginal models using a single modified GEE based on an EM-type algorithm. The proposed method is motivated by the longitudinal study of cardiac abnormalities in children born to HIV-infected women and analyses of these data are presented to illustrate the application of the method. Further, in an asymptotic study of bias, we show that under an MAR mechanism in which missingness depends on all observed outcome variables, our joint estimation via the modified GEE produces almost unbiased estimates, provided the correlation model has been correctly specified, whereas estimates from standard GEE can lead to substantial bias

Testing for independence in J × K contingency tables with complex sample survey data

Summary: The test of independence of row and column variables in a (J × K) contingency table is a widely used statistical test in many areas of application. For complex survey samples, use of the standard Pearson chi-squared test is inappropriate due to correlation among units within the same cluster

A weighted combination of pseudo-likelihood estimators for longitudinal binary data subject to non-ignorable non-monotone missingness

For longitudinal binary data with non-monotone non-ignorably missing outcomes over time, a full likelihood approach is complicated algebraically, and with many follow-up times, maximum likelihood estimation can be computationally prohibitive. As alternatives, two pseudo-likelihood approaches have been proposed that use minimal parametric assumptions. One formulation requires specification of the marginal distributions of the outcome and missing data mechanism at each time point, but uses an “independence working assumption,” i.e., an assumption that observations are independent over time. Another method avoids having to estimate the missing data mechanism by formulating a “protective estimator.” In simulations, these two estimators can be very inefficient, both for estimating time trends in the first case and for estimating both time-varying and time-stationary effects in the second. In this paper, we propose use of the optimal weighted combination of these two estimators, and in simulations we show that the optimal weighted combination can be much more efficient than either estimator alone. Finally, the proposed method is used to analyze data from two longitudinal clinical trials of HIV-infected patients