Ross Boylan

Type I and type II error under random-effects misspecification in generalized linear mixed models

Generalized linear mixed models (GLMMs) have become a frequently used tool for the analysis of non-Gaussian longitudinal data. Estimation is based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. Recent research is showing that the results obtained from these models are not always robust against departures from the assumptions on which these models are based. In the present work we have used simulations with a logistic random-intercept model to study the impact of misspecifying the random-effects distribution on the type I and II errors of the tests for the mean structure in GLMMs. We found that the misspecification can either increase or decrease the power of the tests, depending on the shape of the underlying random-effects distribution, and it can considerably inflate the type I error rate. Additionally, we have found a theoretical result which states that whenever a subset of fixed-effects parameters, not included in the random-effects structure equals zero, the corresponding maximum likelihood estimator will consistently estimate zero. This implies that under certain conditions a significant effect could be considered as a reliable result, even if the random-effects distribution is misspecified.

Experiences of Discrimination and Their Impact on the Mental Health among African American, Asian and Pacific Islander, and Latino Men Who Have Sex with Men

OBJECTIVES We examined the associations between specific types and sources of discrimination and mental health outcomes among US racial/ethnic minority men who have sex with men (MSM) and how these associations varied by race/ethnicity. METHODS A chain-referral sample of 403 African American, 393 Asian and Pacific Islander (API), and 400 Latino MSM recruited in Los Angeles County, California completed a standardized questionnaire. Data were obtained from the Ethnic Minority Mens Health Study from May 2008 to October 2009. RESULTS Past-year experiences of racism within the general community and perceived homophobia among heterosexual friends were positively associated with depression and anxiety. Past-year homophobia experienced within the general community was also positively associated with anxiety. These statistically significant associations did not vary across racial/ethnic groups. The positive association of perceived racism within the gay community with anxiety differed by race/ethnicity, and was statistically significant only for APIs. Perceived homophobia within the family was not associated with either depression or anxiety. CONCLUSIONS Higher levels of experiences of discrimination were associated with psychological distress among MSM of color. However, specific types and sources of discrimination were differentially linked to negative mental health outcomes among African American, API, and Latino MSM.

Fibrosis Progression in African Americans and Caucasian Americans With Chronic Hepatitis C

BACKGROUND & AIMS Prior studies suggest the rate of liver fibrosis progression is slower in African Americans (AAs) than Caucasian Americans (CAs) with chronic HCV infection. METHODS With a multi-state Markov model, fibrosis progression was evaluated in a well-characterized cohort of 143 AA and 157 CA adults with untreated chronic HCV genotype 1 infection. In subjects with a history of injection drug use, duration of infection was imputed from a fitted risk model rather than assumed to be the reported first year of use. RESULTS The distribution of Ishak fibrosis stages was 0 (8.7%), 1/2 (55.7%), 3/4 (29.3%), and 5/6 (6.3%) and was similar in AAs and CAs (P = .22). After adjusting for biopsy adequacy, AAs had a 10% lower rate of fibrosis progression than did CAs, but the difference was not statistically significant (hazard ratio, 0.90; 95% confidence interval, 0.72-1.12). The overall 20-year estimates of probabilities of progression from stage 0 to stages 1/2, 3/4, and 5/6 were 59.3%, 28.8%, and 4.7%, respectively. The estimated median time from no fibrosis to cirrhosis was 79 years for the entire cohort and 74 and 83 years for CAs and AAs, respectively. In 3-variable models including race and biopsy adequacy, the factors significantly associated with fibrosis progression were age when infected, steatosis, ALT level, and necroinflammatory score. CONCLUSIONS The rates of fibrosis progression were slow and did not appear to differ substantially between AAs and CAs.

Estimation of covariate effects in generalized linear mixed models with a misspecified distribution of random intercepts and slopes

Generalized linear mixed models with random intercepts and slopes provide useful analyses of clustered and longitudinal data and typically require the specification of the distribution of the random effects. Previous work for models with only random intercepts has shown that misspecifying the shape of this distribution may bias estimates of the intercept, but typically leads to little bias in estimates of covariate effects. Very few papers have examined the effects of misspecifying the joint distribution of random intercepts and slopes. However, simulation results in a recent paper suggest that misspecifying the shape of the random slope distribution can yield severely biased estimates of all model parameters. Using analytic results, simulation studies and fits to example data, this paper examines the bias in parameter estimates due to misspecification of the shape of the joint distribution of random intercepts and slopes. Consistent with results for models with only random intercepts, and contrary to the claims of severe bias in a recent paper, we show that misspecification of the joint distribution typically yields little bias in estimates of covariate effects and is restricted to covariates associated with the misspecified random effects distributions. We also show that misspecification of the distribution of random effects has little effect on confidence interval performance. Coverage rates based on the model-based standard errors from fitted likelihoods were generally quite close to nominal.

Social network characteristics and HIV risk among African American, Asian/Pacific Islander, and Latino men who have sex with men.

Objectives:To examine how social networks influence HIV risk among US racial/ethnic minority men who have sex with men (MSM) and whether the associations of social network characteristics with risk vary by race/ethnicity. Methods:A chain-referral sample of 403 African American, 393 Asian/Pacific Islander, and 400 Latino MSM recruited in Los Angeles County, California, completed a questionnaire, which asked about their egocentric social networks, safer sex peer norms, and male anal intercourse partners. HIV-nonconcordant partnerships were those reported by respondents as serodisconcordant or where self and/or partner serostatus was unknown. Results:Overall, 26% of the sample reported HIV-nonconcordant unprotected anal intercourse (UAI) with a nonprimary male partner in the previous 6 months. In a generalized estimating equation (GEE) logistic model that controlled for race/ethnicity, age, nativity, incarceration history, and HIV status, being in a more dense network was associated with less HIV-nonconcordant UAI [adjusted odds ratio (AOR) = 0.92, 95% confidence interval (CI): 0.86 to 0.99, P = 0.0467]. In addition, the effect of safer sex peer norms on HIV-nonconcordant UAI was moderated by ego-alter closeness (P = 0.0021). Safer sex peer norms were protective among those reporting “medium” or “high” ego-alter closeness (AOR = 0.70, 95% CI: 0.52 to 0.95, P = 0.0213 and AOR = 0.48, 95% CI: 0.35 to 0.66, P < 0.0001, respectively), but not among those reporting “low” ego-alter closeness (AOR = 0.96, 95% CI: 0.63 to 1.46, P = 0.8333). The effects of density, closeness, and norms on HIV-nonconcordant UAI did not differ by race/ethnicity. Conclusions:The significant association of social network characteristics with UAI point to network-level factors as important loci for both ongoing research and HIV prevention interventions among US MSM of color.

Substance Use and Experienced Stigmatization Among Ethnic Minority Men Who Have Sex with Men in the United States

Research has documented deleterious effects of racism among ethnic minorities and of homophobia among men who have sex with men (MSM). Less is known about the impact of multiple forms of stigmatization on ethnic minority MSM. This study examined substance use by African American, Asian/Pacific Islander and Latino MSM, and the associations of experienced racism and homophobia from various sources with polydrug use and stimulant drug use. Experienced racism within the general community was associated with higher levels of use; other forms of discrimination were either not associated with polydrug or stimulant use or had more complex relationships with use. Implications for further research and interventions are discussed.

Progression of Biopsy-Measured Liver Fibrosis in Untreated Patients with Hepatitis C Infection: Non-Markov Multistate Model Analysis

Background Fibrosis stages from liver biopsies reflect liver damage from hepatitis C infection, but analysis is challenging due to their ordered but non-numeric nature, infrequent measurement, misclassification, and unknown infection times. Methods We used a non-Markov multistate model, accounting for misclassification, with multiple imputation of unknown infection times, applied to 1062 participants of whom 159 had multiple biopsies. Odds ratios (OR) quantified the estimated effects of covariates on progression risk at any given time. Results Models estimated that progression risk decreased the more time participants had already spent in the current stage, African American race was protective (OR 0.75, 95% confidence interval 0.60 to 0.95, p = 0.018), and older current age increased risk (OR 1.33 per decade, 95% confidence interval 1.15 to 1.54, p = 0.0002). When controlled for current age, older age at infection did not appear to increase risk (OR 0.92 per decade, 95% confidence interval 0.47 to 1.79, p = 0.80). There was a suggestion that co-infection with human immunodeficiency virus increased risk of progression in the era of highly active antiretroviral treatment beginning in 1996 (OR 2.1, 95% confidence interval 0.97 to 4.4, p = 0.059). Other examined risk factors may influence progression risk, but evidence for or against this was weak due to wide confidence intervals. The main results were essentially unchanged using different assumed misclassification rates or imputation of age of infection. Discussion The analysis avoided problems inherent in simpler methods, supported the previously suspected protective effect of African American race, and suggested that current age rather than age of infection increases risk. Decreasing risk of progression with longer time already spent in a stage was also previously found for post-transplant progression. This could reflect varying disease activity, with recent progression indicating active disease and high risk, while longer time already spent in a stage indicates quiescent disease and low risk.

Estimating Complex Multi-State Misclassification Rates for Biopsy-Measured Liver Fibrosis in Patients with Hepatitis C

For both clinical and research purposes, biopsies are used to classify liver damage known as fibrosis on an ordinal multi-state scale ranging from no damage to cirrhosis. Misclassification can arise from reading error (misreading of a specimen) or sampling error (the specimen does not accurately represent the liver). Studies of biopsy accuracy have not attempted to synthesize these two sources of error or to estimate actual misclassification rates from either source. Using data from two studies of reading error and two of sampling error, we find surprisingly large possible misclassification rates, including a greater than 50% chance of misclassification for one intermediate stage of fibrosis. We find that some readers tend to misclassify consistently low or consistently high, and some specimens tend to be misclassified low while others tend to be misclassified high. Non-invasive measures of liver fibrosis have generally been evaluated by comparison to simultaneous biopsy results, but biopsy appears to be too unreliable to be considered a gold standard. Non-invasive measures may therefore be more useful than such comparisons suggest. Both stochastic uncertainty and uncertainty about our model assumptions appear to be substantial. Improved studies of biopsy accuracy would include large numbers of both readers and specimens, greater effort to reduce or eliminate reading error in studies of sampling error, and careful estimation of misclassification rates rather than less useful quantities such as kappa statistics.

Enhanced liver fibrosis marker as a noninvasive predictor of mortality in HIV/hepatitis C virus-coinfected women from a multicenter study of women with or at risk for HIV

Objective:Coinfection with hepatitis C virus (HCV) is a major cause of morbidity and mortality among individuals with HIV. Our objective was to assess the prognostic performance of noninvasive measures of liver fibrosis in predicting all-cause mortality in women with HIV/HCV coinfection. Design:We studied HCV/HIV coinfected women enrolled in the prospective, multicenter Womens Interagency HIV Study. Aspartate aminotransferase to platelet ratio and FIB-4 were used to identify women without fibrosis at all visits and women who progressed to severe fibrosis. Methods:Enhanced liver fibrosis (ELF), which utilizes direct measures of fibrosis, hyaluronic acid, procollagen III aminoterminal peptide and tissue inhibitor of matrix metalloproteinase was performed. Results:Included were 381 women with 2296 ELF measurements, with mean follow-up 8.3 ± 3.3 years. There were 134 deaths (60% with severe liver fibrosis). Receiver operator characteristic curves at fixed time windows prior to death or at end of follow-up showed that ELF was best at predicting mortality when tested within a year of death (area under the curve for ELF 0.85 vs. APRI 0.69, P < 0.0001 and vs. FIB-4 0.75, P = 0.0036); and 1–3 years prior (ELF 0.71 vs. APRI 0.61, P = 0.005 and vs. FIB-4 0.65, P = 0.06). Use of all three measures did not improve on ELF alone. In multivariate logistic regression models controlling for CD4+ cell count, HIV viral load, antiretroviral use and age, ELF continued to perform better than APRI and FIB-4. Conclusion:ELF predicted all-cause mortality and was superior to APRI and FIB-4 in HIV/HCV coinfected women.

Likelihood-based analysis of longitudinal data from outcome-related sampling designs

Investigators commonly gather longitudinal data to assess changes in responses over time and to relate these changes to within-subject changes in predictors. With rare or expensive outcomes such as uncommon diseases and costly radiologic measurements, outcome-dependent, and more generally outcome-related, sampling plans can improve estimation efficiency and reduce cost. Longitudinal follow up of subjects gathered in an initial outcome-related sample can then be used to study the trajectories of responses over time and to assess the association of changes in predictors within subjects with change in response. In this article, we develop two likelihood-based approaches for fitting generalized linear mixed models (GLMMs) to longitudinal data from a wide variety of outcome-related sampling designs. The first is an extension of the semi-parametric maximum likelihood approach developed in Neuhaus, Scott and Wild (2002, Biometrika 89, 23-37) and Neuhaus, Scott and Wild (2006, Biometrics 62, 488-494) and applies quite generally. The second approach is an adaptation of standard conditional likelihood methods and is limited to random intercept models with a canonical link. Data from a study of attention deficit hyperactivity disorder in children motivates the work and illustrates the findings.