Generalized Estimating Equations Approach Research Articles

Predictors of initial stability of orthodontic miniscrew implants

The purpose of this retrospective study was to elucidate potential confounding factors affecting initial stability of miniscrews inserted to enhance orthodontic anchorage. Four hundred and seven miniscrews inserted in 168 patients treated by 17 orthodontic residents were analysed in a consecutive chart review. The outcome variable was the stability of the miniscrew, measured as a dichotomous variable, 0 if the miniscrew loosened during a 1 week period after insertion to the time of orthodontic force application and a value of 1 otherwise. Potential confounding variables examined were gender, age, jaw, insertion site, tissue type, length and diameter of the miniscrew, and number of previous insertions. Generalized estimating equations (GEE) methods were used to estimate the influence of each factor on stability for the correlated binary outcomes of each patient. A weighted analysis for the GEE approach was also performed for the convergence calculation of the estimation procedure due to a value of 0 in one of the cells. Crude odds ratio (cOR) and adjusted odds ratio (aOR) and their 95 per cent confidence intervals (CI) were calculated for this purpose. The overall success rate after 1 week was 93.1 per cent (379/407). The screws inserted by more experienced clinicians (more than 20 miniscrews) were found to have approximately a 3.6-fold higher success rate of initial stability compared with those inserted by less experienced clinicians after adjusting for the insertion site (aOR = 3.63, P = 0.015). The results of the present study suggest that the initial stability depends on insertion site and clinician experience.

Statistical Methods to Study Timing of Vulnerability with Sparsely Sampled Data on Environmental Toxicants

Statistical Methods to Study Timing of Vulnerability with Sparsely Sampled Data on Environmental Toxicants

Learning From Data

Learning From Data

Lagged temperature effect with mosquito transmission potential explains dengue variability in southern Taiwan: Insights from a statistical analysis

The purpose of this study was to link meteorological factors and mosquito ( Aedes aegypti) abundance to examine the potential effects of climate variations on patterns of dengue epidemiology in Taiwan during 2001–2008. Spearman's rank correlation tests with and without time-lag were performed to investigate the overall correlation between dengue incidence rates and meteorological variables (i.e., minimum, mean, and maximum temperatures, relative humidity (RH), and rainfall) and percentage Breteau index (BI) level > 2 in Taipei and Kaohsiung of northern and southern Taiwan, respectively. A Poisson regression analysis was performed by using a generalized estimating equations (GEE) approach. The most parsimonious model was selected based on the quasi-likelihood based information criterion (QICu). Spearman's rank correlation tests revealed marginally positive trends in the weekly mean ( ρ = 0.28, p < 0.0001), maximum ( ρ = 0.26, p < 0.0001), and minimum ( ρ = 0.30, p < 0.0001) temperatures in Taipei. However, in Kaohsiung, all negative trends were found in the weekly mean ( ρ = − 0.32, p < 0.0001), maximum ( ρ = − 0.30, p < 0.0001), and minimum ( ρ = − 0.32, p < 0.0001) temperatures. This study concluded that based on the GEE approach, rainfall, minimum temperature, and RH, all with 3-month lag, and 1-month lag of percentage BI level > 2 are the significant predictors of dengue incidence in Kaohsiung (QICu = − 277.77). This study suggested that warmer temperature with 3-month lag, elevated humidity with high mosquito density increased the transmission rate of human dengue fever infection in southern Taiwan.

Analyzing family data: A GEE approach for substance use researchers

Introduction Analyzing data that arises from correlated observations such as husband–wife pairs, siblings, or repeated assessments of the same individuals over time requires more specialized analytic tools. Additionally, outcomes that are not normally distributed such as count data, (e.g., number of symptoms or number of problems endorsed) also require specialized analytic tools. Generalized estimating equations (GEE) are a very flexible tool for dealing with correlated data (such as data derived from related individuals such as families). The objective of this report was to compare traditional ordinary least squares regression (OLS) to a GEE approach for analyzing family data. Methods Using data from an ongoing five-wave longitudinal study of newlywed couples, we examined a subset of 173 families with children between the ages of 4 and 11 at two data collection points. The relation between parental risk factors (e.g., heavy drinking, aggression, marital quality) and child internalizing symptoms was examined within the context of two regression-based models: traditional OLS regression and a GEE approach. Results Overall, the GEE approach allowed a more complete use of the available data, provided more robust findings, and produced more reliable parameter estimates. Conclusion GEE models are a flexible regression-based approach for dealing with related data that arises from correlated data such as family data. Further, given the availability of the models in common statistical programs, family researchers should consider these models for their work.

Validation of an algorithm for categorizing the severity of hospital emergency department visits.

Differentiating between appropriate and inappropriate resource use represents a critical challenge in health services research. The New York University Emergency Department (NYU ED) visit severity algorithm attempts to classify visits to the ED based on diagnosis, but it has not been formally validated. To assess the validity of the NYU algorithm. A longitudinal study in a single integrated delivery system from January 1999 to December 2001. A total of 2,257,445 commercial and 261,091 Medicare members of an integrated delivery system. ED visits were classified as emergent, nonemergent, or intermediate severity, using the NYU ED algorithm. We examined the relationship between visit-severity and the probability of future hospitalizations and death using a logistic model with a general estimating equation approach. Among commercially insured subjects, ED visits categorized as emergent were significantly more likely to result in a hospitalization within 1-day (odds ratio = 3.37, 95% CI: 3.31-3.44) or death within 30-days (odds ratio = 2.81, 95% CI: 2.62-3.00) than visits categorized as nonemergent. We found similar results in Medicare patients and in sensitivity analyses using different probability thresholds. ED overuse for nonemergent conditions was not related to socio-economic status or insurance type. The evidence presented supports the validity of the NYU ED visit severity algorithm for differentiating ED visits based on need for hospitalization and/or mortality risk; therefore, it can contribute to evidence-based policies aimed at reducing the use of the ED for nonemergencies.

Longitudinal Data Analysis for Generalized Linear Models Under Participant-Driven Informative Follow-up: An Application in Maternal Health Epidemiology

It is common in longitudinal studies for scheduled visits to be accompanied by as-needed visits due to medical events occurring between scheduled visits. If the timing of these as-needed visits is related to factors that are associated with the outcome but are not among the regression model covariates, naively including these as-needed visits in the model yields biased estimates. In this paper, the authors illustrate and discuss the key issues pertaining to inverse intensity rate ratio (IIRR)-weighted generalized estimating equations (GEE) methods in the context of a study of Kenyan mothers infected with human immunodeficiency virus type 1 (1999-2005). The authors estimated prevalences and prevalence ratios for morbid conditions affecting the women during a 1-year postpartum follow-up period. Of the 484 women under study, 62% had at least 1 as-needed visit. Use of a standard GEE model including both scheduled and unscheduled visits predicted a pneumonia prevalence of 2.9% (95% confidence interval: 2.3%, 3.5%), while use of the IIRR-weighted GEE predicted a prevalence of 1.5% (95% confidence interval: 1.2%, 1.8%). The estimate obtained using the IIRR-weighted GEE approach was compatible with estimates derived using scheduled visits only. These results highlight the importance of properly accounting for informative follow-up in these studies.

Independent Risk Factors for Infection in Tissue Expander Breast Reconstruction

Postoperative infection in tissue expander breast reconstruction causes increased morbidity, cost, and suboptimal patient outcomes. To improve outcomes, it is important to preoperatively identify factors that might predispose to infection and minimize them when possible. It is hypothesized that certain patient characteristics are associated with an increased infection rate. A retrospective, 6-year, single-institution review of patient records was performed from 413 tissue expanders placed in 300 women for postmastectomy breast reconstruction. Infection was defined as any case where antibiotics were given in response to clinical signs of infection. Fourteen potential risk factors were analyzed. A generalized estimation equations approach was used to perform univariable and multivariable analyses. Antibiotics were given to treat clinical infection in 68 of 413 expanders (16.5 percent), with a median time to diagnosis of 6.5 weeks (range, 1 to 52 weeks). Univariable analysis showed significant association with breast size larger than C cup (p < 0.001), previous irradiation (p = 0.007), repeated implant (p = 0.008), and delayed reconstruction (p = 0.04). All variables except delayed reconstruction remained significant (p < 0.002 for all) in a multivariable model. Additional significant covariates in this model included one surgical oncologist (p = 0.003) and contralateral surgery (p = 0.046). Given infection, one surgical oncologist was associated with an increased rate of mastectomy flap necrosis (p = 0.01). Certain patient characteristics are associated with increased infection in tissue expansion breast reconstruction. Understanding how these predispose to infection requires additional study. Patients identified with these characteristics should be educated about these risks and other reconstructive options to optimize the success of their breast reconstruction.

Protective effect of copy number polymorphism of glutathione S-transferase T1 gene on melanoma risk in presence of CDKN2A mutations, MC1R variants and host-related phenotypes

The effect of CDKN2A, the major high-risk melanoma susceptibility gene, has been shown to be modified by host-related phenotypes and variants of MC1R gene. The glutathione S-transferase (GSTs) genes, implicated in detoxification of metabolites after UV exposure, are candidates for modulating CDKN2A penetrance. Few case-control studies have investigated the effect of GSTs on melanoma risk, and have led to controversial results while these genes have not yet been studied in CDKN2A melanoma-prone families. We examined the effect of GSTP1, GSTM1 and GSTT1 genotypes on melanoma risk in 25 multi-generational melanoma-prone families with CDKN2A mutations, in presence of MC1R gene variants, sun exposure, and host-related phenotypes. These data included 195 genotyped subjects for all studied genes. We applied the GEE (Generalized Estimating Equations) approach to test for the effect of GSTs while adjusting for age, sex and CDKN2A mutation status and including successively MC1R, sun exposure and host factors in the model. No significant effect of null GSTM1 allele and GSTP1 variants (p.I105V, p.A114V) on melanoma risk was found. However, a significant protective effect of carrying >or=1 null GSTT1 allele was shown: OR(adjusted for age,sex,CDKN2A ) = 0.41 (0.18-0.94) and OR(adjusted for age,sex,CDKN2A,MC1R ) = 0.24 (0.15-0.58). Altogether, the factors modifying significantly the melanoma risk associated with CDKN2A mutations (stepwise procedure) were: MC1R and dysplastic nevi (increasing the risk) and GSTT1 (decreasing the risk). This study shows that even when a high-risk gene (CDKN2A) has been identified, multiple genetic modifiers influence melanoma risk.

Effect of Second Pregnancy on Maternal Carriage and Outcome of High-Risk Human Papillomavirus (HPV)

Objectives: The effect of second pregnancy on human papillomavirus (HPV) carriage and outcome is modelled in longitudinal setting covering two subsequent pregnancies. Study Design: Among 329 (baseline pregnant) women prospectively followed up inthe Finnish Family HPV Study, two subcohorts were compiled: (i) 78 women (Group B) who became pregnant for the second time during the follow-up, and (ii) 100 women (Group A) who did not develop 2nd pregnancy. The effect of pregnancy on high-risk HPV (HR-HPV) carriage and outcome was analysed using Kaplan-Meier and Cox survival analyses and generalized estimating equation (GEE) modelling of the longitudinal data. Results: Women in the two groups were similar in their baseline HR-HPV status but significantly different in several known risk factors of HR-HPV infection. Group A women showed higher point prevalence of cervical and oral HR-HPV at the 36-month (p = 0.015) and 6-month (p = 0.024) follow-up visit, respectively. Among Group B women, prevalence of both cervical and oral HR-HPV significantly decreased during 2nd pregnancy (p = 0.005 and p = 0.002) as compared with inter-pregnancy period, but increased again after 2nd pregnancy. There was no difference in acquisition or clearance of cervical or oral HR-HPV between the two groups in univariate (Kaplan-Meier) or multivariate (Cox) survival analysis. In the GEE approach, 2nd pregnancy was not significantly associated with cervical or oral HR-HPV carriage or persistence when adjusted for all other covariates. Conclusions: Second pregnancy is of little impact on carriage and persistence of oral and cervical HR-HPV infections in a longitudinal setting over time.

A cluster randomized trial to improve adherence to evidence-based guidelines on diabetes and reduce clinical inertia in primary care physicians in Belgium: study protocol [NTR 1369

BackgroundMost quality improvement programs in diabetes care incorporate aspects of clinician education, performance feedback, patient education, care management, and diabetes care teams to support primary care physicians. Few studies have applied all of these dimensions to address clinical inertia.AimTo evaluate interventions to improve adherence to evidence-based guidelines for diabetes and reduce clinical inertia in primary care physicians.DesignTwo-arm cluster randomized controlled trial.ParticipantsPrimary care physicians in Belgium.InterventionsPrimary care physicians will be randomly allocated to 'Usual' (UQIP) or 'Advanced' (AQIP) Quality Improvement Programs. Physicians in the UQIP will receive interventions addressing the main physician, patient, and office system factors that contribute to clinical inertia. Physicians in the AQIP will receive additional interventions that focus on sustainable behavior changes in patients and providers.OutcomesPrimary endpoints are the proportions of patients within targets for three clinical outcomes: 1) glycosylated hemoglobin < 7%; 2) systolic blood pressure differences ≤130 mmHg; and 3) low density lipoprotein/cholesterol < 100 mg/dl. Secondary endpoints are individual improvements in 12 validated parameters: glycosylated hemoglobin, low and high density lipoprotein/cholesterol, total cholesterol, systolic blood pressure, diastolic blood pressure, weight, physical exercise, healthy diet, smoking status, and statin and anti-platelet therapy.Primary and secondary analysisStatistical analyses will be performed using an intent-to-treat approach with a multilevel model. Linear and generalized linear mixed models will be used to account for the clustered nature of the data, i.e., patients clustered withinimary care physicians, and repeated assessments clustered within patients. To compare patient characteristics at baseline and between the intervention arms, the generalized estimating equations (GEE) approach will be used, taking the clustered nature of the data within physicians into account. We will also use the GEE approach to test for differences in evolution of the primary and secondary endpoints for all patients, and for patients in the two interventions arms, accounting for within-patient clustering.Trial Registrationnumber: NTR 1369.

Model diagnostic plots for repeated measures data using the generalized estimating equations approach

The generalized estimating equations (GEE) approach has been widely used to analyze repeated measures data. However, in the absence of likelihood ratio tests, model diagnostic checking tools are not well established for the GEE approach, whereas they are for other likelihood-based approaches. Diagnostic checking tools are essential for determining a model’s goodness of fit, especially for non-normal data. In this paper, we propose simple residual plots to investigate the goodness of fit of the model based on the GEE approach for discrete data. The proposed residual plots are based on the quantile–quantile ( Q – Q ) plots of a χ 2 -distribution, and are particularly useful for comparing several models simultaneously.

Impact of androgen deprivation therapy (ADT) on bone, cardiovascular, and endocrine outcomes: A propensity-matched analysis of 20,000 patients

5012 Background: Several studies have suggested an increased risk of fragility fractures, acute myocardial infarction (AMI), and diabetes mellitus with continuous use of ADT in men with prostate cancer (PC). Published studies have generally been small and have been unable to adjust for other comorbidities, medications, and indications for ADT. Methods: Using linked administrative databases, we performed an observational study of men age 66 or older with PC in Ontario, Canada. The treated group (n=19,709) consisted of men who started continuous ADT for at least 6 months or underwent bilateral orchiectomy. The non-treated group also had PC, but had not received ADT. Treated and untreated groups were hard-matched on age, prior PC treatment, and year of diagnosis, and propensity-matched on comorbidities, medications, cardiovascular risk factors, prior fractures, and socioeconomic variables. Primary outcomes were development of a fragility fracture, AMI, diabetes, and hypercholesterolemia. Cox proportional hazards models were used with a frailty term to accommodate the matched design. Analyses were also done using a logistic regression model with generalized estimating equation (GEE) methods for a matched design. Results: The cohort was followed for a mean of 6.47 y. In time-to-event analyses, ADT use was associated with an increased risk of fragility fracture (hazard ratio (HR) 1.65, 95% confidence interval (CI) 1.53, 1.77) and diabetes (HR 1.16, 95% CI 1.11, 1.21) but a decreased risk of AMI (HR 0.91, 95% CI 0.84, 1.00) and hypercholesterolemia (HR 0.91, 95% CI 0.89, 0.94). Similar results were found using the logistic GEE approach. The absolute excess risk of fracture and diabetes was 3.11% (8.88% vs. 5.77%) and 2.65% (22.30% vs. 19.65%), respectively. Conclusions: Continuous ADT use for at least 6 months in men age 66 or older with PC is associated with an increased risk of fragility fracture and diabetes but not AMI or hypercholesterolemia. No significant financial relationships to disclose.

A prospective study on the association between hay fever among children and incidence of asthma in East Germany

Aim of this study was to examine the effect of hay fever in childhood for asthma onset from childhood to adulthood in a prospective cohort of 3,199 asthma-free children, initially aged 5-13 years, which were followed for up to 12 years in East-Germany. Crude and adjusted incidence rate ratios (IRR) of asthma onset due to hay fever at baseline were calculated by a generalized estimation equation approach accounting for person years at risk, age at study entry, parental asthma, and gender. Overall 142 incident cases of asthma were observed. Prevalence of hay fever at baseline was 4%. Crude and adjusted IRR were essentially the same and showed overall and in each age group a substantial higher risk of asthma onset due to hay fever. The adjusted IRR was 4 overall and ranged between 3 and 5 within the three age groups. Restricting the analysis to those participants, who were 17-25 years of age at the end of follow-up resulted in similar IRR. Hay fever in childhood is a strong predictor of asthma onset later in life up to adulthood. The preventive potential of early and efficient treatment of allergic rhinitis to avoid asthma development needs to be investigated.

Local Influence in Generalized Estimating Equations

Abstract. We investigate the influence of subjects or observations on regression coefficients of generalized estimating equations (GEEs) using local influence. The GEE approach does not require the full multivariate distribution of the response vector. We extend the likelihood displacement to a quasi‐likelihood displacement, and propose local influence diagnostics under several perturbation schemes. An illustrative example in GEEs is given and we compare the results using the local influence and deletion methods.

Análisis experimental de tratamientos floculantes de residuos orgánicos derivados de la producción porcina

A.L. dos Santos, and F. Mora. 2007. Experimental analysis of fl occulant treatments of organic waste from swine production. Cien. Inv. Agr. 34(1):49-56. Swine production is an important part of the Brazilian agro-industry whose development depends in part on the environmental strategy adopted by the companies involved in the industry. This study examined organic waste treatment experiments from a swine agro-industry located in southern Brazil. Five experiments were conducted that independently considered the following fl occulants: Type-1: calcium hydroxide, Type-2: aluminum sulfate + calcium hydroxide, Type-3: calcium hydroxide + dolomite, Type-4: dolomite, and Type-5: aluminum sulfate. All experiments were conducted at the following doses: 0, 1.25, 2.5, 5, 10 and 20 mL. Total solids of the solid fraction (g⋅m -3 ) were analyzed in a longitudinal study. A parallel experiment was conducted to compare the treatments at a fi xed dose of 20 mL. The analysis was carried out using Generalized Linear Models (GLM) and Generalized Estimating Equations (GEE). These were used because the response variable did not follow a normal distribution; this was confi rmed by ShapiroWilk test. The Gamma distribution was considered in both GEE and GLM approaches. All equations evidenced a positive effect of the doses on fl occulation. Quantity of the total solids was dependent on fl occulant type, with values ranging from 8,444 to 21,070 g⋅m -3 , for Type-1 and Type-2, respectively. No signifi cant differences were evidenced between Type-2, Type-4 and Type-5 fl occulants; these all demonstrated higher total solid values. Type-1 and Type-3 fl occulants should not be considered for use due to ineffi ciency. The quantity of biofertilize feasible for production in this swine industry would be dependent on the fl occulant type used.

A comparison of the statistical power of different methods for the analysis of cluster randomization trials with binary outcomes

Cluster randomization trials are randomized controlled trials (RCTs) in which intact clusters of subjects are randomized to either the intervention or to the control. Cluster randomization trials require different statistical methods of analysis than do conventional randomized controlled trials due to the potential presence of within-cluster homogeneity in responses. A variety of statistical methods have been proposed in the literature for the analysis of cluster randomization trials with binary outcomes. However, little is known about the relative statistical power of these methods to detect a statistically significant intervention effect. We conducted a series of Monte Carlo simulations to examine the statistical power of three methods that compare cluster-specific response rates between arms of the trial: the t-test, the Wilcoxon rank sum test, and the permutation test; and three methods that compare subject-level response rates: an adjusted chi-square test, a logistic-normal random effects model, and a generalized estimating equations (GEE) method. In our simulations we allowed the number of clusters, the number of subjects per cluster, the intraclass correlation coefficient and the magnitude of the intervention effect to vary. We demonstrated that the GEE approach tended to have the highest power for detecting a statistically significant intervention effect. However, in most of the 240 scenarios examined, the differences between the competing statistical methods were negligible. The largest mean difference in power between any two different statistical methods across the 240 scenarios was 0.02. The largest observed difference in power between two different statistical methods across the 240 scenarios and 15 pair-wise comparisons of methods was 0.14.

Avaliação da introdução de tecnologias no sistema de produção de gado de corte no Pantanal

O desempenho produtivo de 1.075 matrizes e a estrutura etária do rebanho foram monitorados durante cinco anos (maio de 1994 a maio de 1999) em uma fazenda com sistema extensivo de cria de bovinos de corte na região do Pantanal. Nesse período, tecnologias foram introduzidas com o objetivo de modificar o sistema tradicional de produção da região e, conseqüentemente, melhorar o desempenho produtivo do rebanho de cria como um todo. As vacas foram numeradas e monitoradas durante a realização dos trabalhos de gado (TG), sendo classificadas como solteira ou parida e, conforme avaliação do desempenho reprodutivo ao longo dos trabalhos de gado, eram mantidas no rebanho ou descartadas. Os resultados foram modelados por meio de equações de estimação generalizadas (EEG) com a função de ligação logística e distribuição binomial. Utilizou-se o teste de Wald para análise do efeito das variáveis ao longo do tempo. O desempenho produtivo foi significativamente influenciado pelos efeitos das variáveis exploratórias invernada, ordem de trabalho, idade da vaca linear e quadrático. O descarte de matrizes foi influenciado de forma significativa pelos efeitos de invernada, ordem de trabalho de gado e idade da vaca linear. A introdução de tecnologias não representou tendência clara de aumento da probabilidade de as vacas serem classificadas como paridas. Após a introdução da estação de monta, a pressão de descarte foi maior, aumentando a probabilidade de descarte e diminuindo a probabilidade de permanência da matriz no rebanho nas idades mais avançadas, o que o tornou mais dinâmica a reposição das vacas.

Between-breed variability of stillbirth and its relationship with sow and piglet characteristics

Litter characteristics at birth were recorded in 4 genetic types of sows with differing maternal abilities. Eighty-two litters from F(1) Duroc x Large White sows, 651 litters from Large White sows, 63 litters from Meishan sows, and 173 litters from Laconie sows were considered. Statistical models included random effects of sow, litter, or both; fixed effects of sow genetic type, parity, birth assistance, and piglet sex, as well as gestation length, farrowing duration, piglet birth weight, and litter size as linear covariates. The quadratic components of the last 2 factors were also considered. For statistical analyses, GLM were first considered, assuming a binomial distribution of stillbirth. Hierarchical models were also fitted to the data to take into account correlations among piglets from the same litter. Model selection was performed based on deviance and deviance information criterion. Finally, standard and robust generalized estimating equations (GEE) procedures were applied to quantify the importance of each effect on a piglet's probability of stillbirth. The 5 most important factors involved were, in decreasing order (contribution of each effect to variance reduction): difference between piglet birth weight and the litter mean (2.36%), individual birth weight (2.25%), piglet sex (1.01%), farrowing duration (0.99%), and sow genetic type (0.94%). Probability of stillbirth was greater for lighter piglets, for male piglets, and for piglets from small or very large litters. Probability of stillbirth increased with sow parity number and with farrowing duration. Piglets born from Meishan sows had a lower risk of stillbirth (P < 0.0001) and were little affected by the sources of variation mentioned above compared with the 3 other sow genetic types. Standard and robust GEE approaches gave similar results despite some disequilibrium in the data set structure highlighted with the robust GEE approach.

Properties of analysis methods that account for clustering in volume–outcome studies when the primary predictor is cluster size

In recent years health services researchers have conducted 'volume-outcome' studies to evaluate whether providers (hospitals or surgeons) who treat many patients for a specialized condition have better outcomes than those that treat few patients. These studies and the inherent clustering of events by provider present an unusual statistical problem. The volume-outcome setting is unique in that 'volume' reflects both the primary factor under study and also the cluster size. Consequently, the assumptions inherent in the use of available methods that correct for clustering might be violated in this setting. To address this issue, we investigate via simulation the properties of three estimation procedures for the analysis of cluster correlated data, specifically in the context of volume-outcome studies. We examine and compare the validity and efficiency of widely-available statistical techniques that have been used in the context of volume-outcome studies: generalized estimating equations (GEE) using both the independence and exchangeable correlation structures; random effects models; and the weighted GEE approach proposed by Williamson et al. (Biometrics 2003; 59:36-42) to account for informative clustering. Using data generated either from an underlying true random effects model or a cluster correlated model we show that both the random effects and the GEE with an exchangeable correlation structure have generally good properties, with relatively low bias for estimating the volume parameter and its variance. By contrast, the cluster weighted GEE method is inefficient.