Generalized Estimating Equations Method Research Articles

Assessing the use of GEE methods for analyzing binary outcomes in family studies: the Strong Heart Family Study

ABSTRACT The generalized estimating equations method (GEE) is commonly applied to analyze data obtained from family studies. GEE is well known for its robustness on misspecification of correlation structure. However, the unbalanced distribution of family sizes and complicated genetic relatedness structure within each family may challenge GEE performance. We focused our research on binary outcomes. To evaluate the performance of GEE, we conducted a series of simulations, on data generated adopting the kinship matrix (correlation structure within each family) from the Strong Heart Family Study (SHFS). We performed a fivefold cross-validation to further evaluate the GEE predictive power on data from the SHFS. A Bayesian modeling approach, with direct integration of the kinship matrix, was also included to contrast with GEE. Our simulation studies revealed that GEE performs well on a binary outcome from families having a relatively simple kinship structure. However, data with a binary outcome generated from families with complex kinship structures, especially with a large genetic variance, can challenge the performance of GEE.

The Effect of Simulated Obstructive Apneas on Mechanical Characteristics of Lower Airways in Individuals with Asthma.

Increased negative intrathoracic pressure that occurs during pharyngeal obstruction can increase thoracic fluid volume that may contribute to lower airway narrowing in individuals with obstructive sleep apnea (OSA) and asthma. Our previous study showed that fluid accumulation in the thorax induced by simulated OSA can increase total respiratory resistance. However, the effect of fluid shift on lower airway narrowing has not been investigated. To examine the effect of fluid accumulation in the thorax on the resistance of the lower airway. Non-asthma participants and individuals with (un)controlled asthma were recruited and underwent a single-day experiment. A catheter with six pressure sensors was inserted through the nose to continuously measure pressure at different sites of the airway, while a pneumotachograph was attached to a mouthpiece to record airflow. To simulate obstructive apneas, participants performed 25 Mueller maneuvers (MMs) while lying supine. Using the recordings of pressure sensor and airflow, total respiratory (RT), lower respiratory components (RL), and upper airway (RUA) resistances were calculated before and after MMs. Generalized estimation equation method was used to find the predictors of RL among variables including age, sex, body mass index, and the effect of MMs and asthma. Eighteen participants were included. Performing MMs significantly increased RT (2.23 ± 2.08 cmH2O/L/s, p = 0.003) and RL (1.52 ± 2.00 cmH2O/L/s, p = 0.023) in participants with asthma, while only RL was increased in non-asthma group (1.96 ± 1.73 cmH2O/L/s, p = 0.039). We found the model with age, and the effect of MMs and asthma severity generated the highest correlation (R2 = 0.69, p < 0.001). We provide evidence that fluid accumulation in the thorax caused by excessive intrathoracic pressure increases RL in both non-asthma and asthma groups. The changes in RL were related to age, having asthma and the effect of simulated OSA. This can explain the interrelationship between OSA and asthma.

Power calculation for detecting interaction effect in cross-sectional stepped-wedge cluster randomized trials: an important tool for disparity research

BackgroundThe stepped-wedge cluster randomized trial (SW-CRT) design has become popular in healthcare research. It is an appealing alternative to traditional cluster randomized trials (CRTs) since the burden of logistical issues and ethical problems can be reduced. Several approaches for sample size determination for the overall treatment effect in the SW-CRT have been proposed. However, in certain situations we are interested in examining the heterogeneity in treatment effect (HTE) between groups instead. This is equivalent to testing the interaction effect. An important example includes the aim to reduce racial disparities through healthcare delivery interventions, where the focus is the interaction between the intervention and race. Sample size determination and power calculation for detecting an interaction effect between the intervention status variable and a key covariate in the SW-CRT study has not been proposed yet for binary outcomes.MethodsWe utilize the generalized estimating equation (GEE) method for detecting the heterogeneity in treatment effect (HTE). The variance of the estimated interaction effect is approximated based on the GEE method for the marginal models. The power is calculated based on the two-sided Wald test. The Kauermann and Carroll (KC) and the Mancl and DeRouen (MD) methods along with GEE (GEE-KC and GEE-MD) are considered as bias-correction methods.ResultsAmong three approaches, GEE has the largest simulated power and GEE-MD has the smallest simulated power. Given cluster size of 120, GEE has over 80% statistical power. When we have a balanced binary covariate (50%), simulated power increases compared to an unbalanced binary covariate (30%). With intermediate effect size of HTE, only cluster sizes of 100 and 120 have more than 80% power using GEE for both correlation structures. With large effect size of HTE, when cluster size is at least 60, all three approaches have more than 80% power. When we compare an increase in cluster size and increase in the number of clusters based on simulated power, the latter has a slight gain in power. When the cluster size changes from 20 to 40 with 20 clusters, power increases from 53.1% to 82.1% for GEE; 50.6% to 79.7% for GEE-KC; and 48.1% to 77.1% for GEE-MD. When the number of clusters changes from 20 to 40 with cluster size of 20, power increases from 53.1% to 82.1% for GEE; 50.6% to 81% for GEE-KC; and 48.1% to 79.8% for GEE-MD.ConclusionsWe propose three approaches for cluster size determination given the number of clusters for detecting the interaction effect in SW-CRT. GEE and GEE-KC have reasonable operating characteristics for both intermediate and large effect size of HTE.

Effects of an integrated ambulatory care program on healthcare utilization and costs in older patients with multimorbidity: a propensity score-matched cohort study

BackgroundPopulation aging has increased the prevalence of multimorbidity, jeopardizing the sustainability and efficiency of healthcare systems. This study aimed to evaluate the effects of an integrated ambulatory care program (IACP) on healthcare utilization and costs among older patients with multimorbidity while accounting for the confounding effects of frailty.MethodsA retrospective cohort study using propensity matching including patients aged 65 or older with two or more chronic conditions attending the outpatient clinic at our hospital between June 1 and December 31, 2019, was conducted. Exposure was defined as receipt of IACP care. Patients not undergoing the IACP comprised the unexposed group and were matched at a ratio of 1:4 to patients undergoing the IACP group according to sex, age, Charlson Comorbidity Index score, multimorbidity frailty index score, and number of outpatient visits within 6 months before the index date. Outcomes were changes in healthcare utilization and related costs between 6 months before and after receiving IACP care. Multivariate regression analyses were used for data analysis and the Generalized Estimation Equation method was used to fit the regression models.ResultsA total of 166 (IACP) and 664 (non-exposed) patients were analyzed. The mean participant baseline ages were 77.15 ± 7.77 (IACP) and 77.28 ± 7.90 years (unexposed). In univariate analyses, the IACP group demonstrated greater reductions than the unexposed group in the frequency of outpatient visits (-3.16 vs. -1.36, p < 0.001), number of physicians visited (-0.99 vs. -0.17, p < 0.001), diagnostic fees (-1300 New Taiwan Dollar [NTD] vs. -520 NTD, p < 0.001), drug prescription fees (-250 NTD vs. -70 NTD, p < 0.001), and examination fees (-1620 NTD vs. -700 NTD, p = 0.014). Multivariate analyses demonstrated that patients in the IACP group experienced significant reduction in the frequency of outpatient visits (95% CI: -0.357 to -0.181, p < 0.001), number of physicians visited (95% CI: -0.334 to -0.199, p < 0.001), and overall outpatient costs (95% CI: -0.082 to -0.011, p = 0.01). However, emergency department utilization, hospitalization, and costs did not differ significantly.ConclusionsExpanding IACPs may help patients with multimorbidity reduce their use of outpatient clinics at the 6-month follow-up, reduce care fragmentation, and promote sustainability of the healthcare system.

Compare the marginal effects for environmental exposure and biomonitoring data with repeated measurements and values below the limit of detection.

Environmental exposure and biomonitoring data with repeated measurements from environmental and occupational studies are commonly right-skewed and in the presence of limits of detection (LOD). However, existing model has not been discussed for small-sample properties and highly skewed data with non-detects and repeated measurements. Marginal modeling provides an alternative to analyzing longitudinal and cluster data, in which the parameter interpretations are with respect to marginal or population-averaged means. We outlined the theories of three marginal models, i.e., generalized estimating equations (GEE), quadratic inference functions (QIF), and generalized method of moments (GMM). With these approaches, we proposed to incorporate the fill-in methods, including single and multiple value imputation techniques, such that any measurements less than the limit of detection are assigned values. We demonstrated that the GEE method works well in terms of estimating the regression parameters in small sample sizes, while the QIF and GMM outperform in large-sample settings, as parameter estimates are consistent and have relatively smaller mean squared error. No specific fill-in method can be deemed superior as each has its own merits. Marginal modeling is firstly employed to analyze repeated measures data with non-detects, in which only the mean structure needs to be correctly provided to obtain consistent parameter estimates. After replacing non-detects through substitution methods and utilizing small-sample bias corrections, in a simulation study we found that the estimating approaches used in the marginal models have corresponding advantages under a wide range of sample sizes. We also applied the models to longitudinal and cluster working examples.

Modeling Longitudinal Outcomes in a Small Matched-Pair Sample Motivated by Cardiovascular Data: A Simulation Study

Introduction: In cardiovascular research, matched pairs with longitudinal outcomes are used to assess time and treatment effects on relevant cardiovascular parameters of interest. Generalized estimating equations (GEE) with independent working correlation are commonly employed for unbiased estimation, but their consistency depends on large sample properties. This study investigates the validity of independent GEE for small sample matched pair data under various working correlations, comparing the results with quasi-least squares (QLS) estimates through simulation. Methods: We simulate a hospital cohort with longitudinal outcomes for two exposure groups and individual random effects. After obtaining the propensity score-matched sample, we performed different simulation scenarios across various mortality rates and the random effect. We compare results from GEE and QLS methods under independence, exchangeable, and AR1 working correlation structures. Results: The independence structure often yields a wider range of relative biases and higher standard errors when there is considerable drop-out. Conversely, the exchangeable structure appears as the true correlation structure, providing more accurate and reliable estimates. No significant discrepancies are observed between the results generated by GEE and QLS methods in this study, and the performance of both approaches is significantly influenced by mortality rates and the standard deviation of the random intercept. Conclusion: Our findings suggest that GEE with an independent working correlation structure is misspecified due to incorrect correlation assumptions and is less efficient. Therefore, correctly specifying the working correlation structure is important for small sample data.

Assessing the Use of GEE Methods for Analyzing Continuous Outcomes from Family Studies: Strong Heart Family Study

Background: Because of its convenience and robustness, the generalized estimating equations (GEE) method has been commonly used to fit marginal models of continuous outcomes in family studies. However, unbalanced family sizes and complex pedigree structures within each family may challenge the GEE method, which treats families as clusters with the same correlation structure. The appropriateness of using the GEE method to analyze continuous outcomes in family studies remains unclear. In this paper, we performed simulation studies to evaluate the performance of GEE in the analysis of family study data.&#x0D; Methods: In simulation studies, we generated data from a linear mixed effects model with individual random effects. The random effects covariance matrix is specified as twice that of the pedigree matrix from the Strong Heart Family Study (SHFS) and other hypothetical pedigree structures. A Bayesian approach that utilizes the pedigree matrix was also conducted as a benchmark to compare with GEE methods with either independent or exchangeable correlation structures. Finally, analysis with a real data example was included.&#x0D; Results: Our simulation results showed that GEE with independent correlation structure worked well for family data with continuous outcomes. Real data analysis revealed that all GEE and Bayesian approaches produced similar results.&#x0D; Conclusion: GEE model performs well on continuous outcome in family studies, and it yields estimated coefficients similar to a Bayesian model, which takes genetic relationship into account. Overall, GEE is robust to misspecification of genetic relationships among family members.

Cash flow management and its effect on firm performance: Empirical evidence on non-financial firms of China.

The main purpose of this research is to investigate the impact of changes in cash flow measures and metrics on firm financial performance. The study uses generalized estimating equations (GEEs) methodology to analyze longitudinal data for sample of 20288 listed Chinese non-financial firms from the period 2018:q2-2020:q1. The main advantage of GEEs method over other estimation techniques is its ability to robustly estimate the variances of regression coefficients for data samples that display high correlation between repeated measurements. The findings of study show that the decline in cash flow measures and metrics bring significant positive improvements in the financial performance of firms. The empirical evidence suggests that performance improvement levers (i.e. cash flow measures and metrics) are more pronounced in low leverage firms, suggesting that changes in cash flow measures and metrics bring more positive changes in low leverage firms' financial performance relatively to high leveraged firms. The results hold after mitigating endogeneity based on dynamic panel system generalized method of moments (GMM) and sensitivity analysis considering the robustness of main findings. The paper makes significant contribution to the literature related to cash flow management and working capital management. Since, this paper is among few to empirically study, how cash flow measures and metrics are related to firm performance from dynamic stand point especially from the context of Chinese non-financial firms.

A comparison of bias-adjusted generalized estimating equations for sparse binary data in small-sample longitudinal studies.

Using a generalized estimating equation (GEE) can lead to a bias in regression coefficients for a small sample or sparse data. The bias-corrected GEE (BCGEE) and penalized GEE (PGEE) were proposed to resolve the small-sample bias. Moreover, the standard sandwich covariance estimator leads to a bias of standard error for small samples; several modified covariance estimators have been proposed to address this issue. We review the modified GEEs and modified covariance estimators, and evaluate their performance in sparse binary data from small-sample longitudinal studies. The simulation results showed that GEE and BCGEE often failed to achieve convergence, whereas the convergence proportion for PGEE was quite high. The bias for the regression coefficients was generally in the ascending order of PGEE BCGEE GEE. However, PGEE and BCGEE did not sufficiently remove the bias involving 20-30 subjects with unequal exposure levels with a 5% response rate. The coverage probability (CP) of the confidence interval for BCGEE was relatively poor compared with GEE and PGEE. The CP with the sandwich covariance estimator deteriorated regardless of the GEE methods under the small sample size and low response rate, whereas the CP with the modified covariance estimators-such as Morel's method-was relatively acceptable. PGEE will be the reasonable way for analyzing sparse binary data in small-sample studies. Instead of using the standard sandwich covariance estimator, one should always apply the modified covariance estimators for analyzing these data.

A toolbox of different approaches to analyze and present PRO-CTCAE data in oncology studies.

The patient-reported outcomes version of the Common Terminology Criteria for Adverse Events (PRO-CTCAE) is used to assess symptomatic adverse events in oncology trials. Currently, no standard for PRO-CTCAE analysis exists. Key methods of descriptive analysis and longitudinal modeling using PRO-CTCAE data from an oncology clinical trial, DRiving Excellence in Approaches to Multiple Myeloma-2 (DREAMM-2), a phase II trial of belantamab mafodotin in multiple myeloma (NCT03525678), were explored. Descriptive methods included maximum postbaseline ratings, mean change over time, ratings above a predefined cutoff, line graphs, and stacked bar charts to illustrate patient-reported adverse events at one timepoint or dynamics over time. Analysis methods involving modeling over time included toxicity over time (ToxT) (repeated measurement model, time-to-event, area under the curve analyses), generalized estimating equations (GEE), and ordinal log-linear models (OLLMs). Visualizations of PRO-CTCAE data highlighted different aspects of the data. Selection of the appropriate visualization will depend on the audience and message to be conveyed. Consistent results were obtained by all modeling approaches; no difference was found between dose groups of the DREAMM-2 study in any PRO-CTCAE item by the ToxT approach or the more sophisticated GEE and OLLM methods. Interpretation of GEE results was the most challenging. OLLM supported the interval nature of the PRO-CTCAE response scale in the DREAMM-2 study. All modeling approaches account for multiple testing (driven by the number of items). Descriptive analyses and longitudinal modeling approaches are complementary approaches to presenting PRO-CTCAE data. In modeling, the ToxT approach may be a good compromise compared with more sophisticated analyses.

Influence of target industry growth on premiums in cross-border acquisitions

PurposeIn this paper, the knowledge-based view of the firm is applied to theoretically elucidate and empirically examine the influence of target industry growth on premium payments in cross-border acquisitions. This study aims to extend internally driven Mergers and Acquisitions research efforts of acquirers to industry contingencies of targets by analyzing cross-border acquirers located within the group of seven (G7) countries.Design/methodology/approachThis study’s investigation covers 209 cross-border acquisitions from 2012 to 2019 undertaken by firms located within the G7 countries. This paper used generalized estimation equations method to test the hypotheses applying Gaussian distribution for the dependent variable, an identity link function, exchangeable correlation structure and robust standard errors.FindingsThis study’s results reveal that target industry growth determines premiums. Furthermore, this study shows that acquirer industry growth, as well as acquirer slack, moderates this relationship. This study is built on the notion that industry contingencies influence premiums even when target firms are based in foreign countries.Originality/valueTo the best of the authors’ knowledge, unlike other studies, this is the first to explicitly focus on premiums for multiple cross-border acquisitions by hand selecting nine years of industry sale figures for 53 industries separately in each of the G7 nation countries (leading to 371 separate downloads of data samples). This study contends that industry growth of cross-border targets matters for premium payments.

Influence of Air Pollutants on the Disease Activity and Quality of Life in Rheumatoid Arthritis, an Iranian Observational Longitudinal Study.

Environmental exposures and genetic predisposition interactions may result in autoimmune rheumatic diseases. This study aimed to determine the effect of outdoor air pollutants on the activity of rheumatoid arthritis (RA) in a longitudinal follow-up. We longitudinally studied 50 patients with RA bimonthly over 6 months in Mashhad, one of the most polluted cities in Iran. Disease activity and health-related quality of life (HRQoL) were examined according to the disease activity score (DAS28ESR), health assessment questionnaires (HAQ), physical health component summary (PCS), and visual analogue scale (VAS) criteria. The outdoor air pollutant was measured by monitoring the average concentration of nitrogen oxide (NO), carbon monoxide (CO), O2 level, Sulfur dioxide (SO2), and some particles less than 10 and 2.5 micrometers in diameter (PM <10 µm, PM <2.5 µm). The temperature and humidity levels were also measured. The univariate and multivariate statistical analyses were used for data analysis and the role of confounding factors was determined using the generalized estimation equation method. Statistical analysis indicated a significant increase of the DAS28ESR (B = 0.04 [0.08]; P = 0.01) and VAS (B = 4.48 [1.73]; P = 0.01) by CO concentration. Moreover, a number of polluted days increased the VAS in patients. In addition, other air pollutants, temperature, and humidity were not affected significantly by the DAS28ESR and quality of life indexes by considering confounders such as medications, age, and job. Based on our findings, CO concentration was the only effective outdoor air pollutant that could increase RA disease activity. In addition, CO concentration and the number of polluted days make patients feel more ill. As the role of indoor air pollutants is highly important, further research on this critical topic is required to establish the role of air pollution on RA disease activity.

Idiopathic Hirsutism and Metabolic Status: A Population-based Prospective Cohort Study.

A limited number of studies have investigated the impact of idiopathic hirsutism (IH) on cardiometabolic parameters with contradictory and inconclusive results. This study aimed to explore the effect of IH on metabolic outcomes. In this population-based prospective study, 334 women with IH and 1226 women as healthy controls were selected from Tehran Lipid and Glucose Study. The generalized estimation equations method was applied to investigate the secular longitudinal trends of metabolic indices, including fasting blood sugar (FBS), high-density lipoprotein cholesterol (HDL-C), low-density lipoprotein cholesterol (LDL), non-HDL, triglyceride (TG), systolic blood pressure (SBP), diastolic blood pressure (DBP), and waist circumference (WC) in both groups. Unadjusted and adjusted Cox regression models were applied to assess the hazard ratios (HR) and 95% CIs for the association between IH and metabolic disorders. Potential confounding factors such as age, body mass index, smoking, physical activity, history of hypertension (HTN), and family history of diabetes were included in the adjusted model. This study showed that compared with healthy controls, women with IH had lower SHBG and higher total testosterone (median [interquartile ratio; IQR]: 0.37 [0.16-0.70] vs 0.33 [0.14-0.58]; P = 0.01), free androgen index (median [IQR]: 0.85 [0.38-1.54] vs 0.54 [0.26-0.97]; P = 0.001), androstenedione (median [IQR]: 1.60 [1.00-2.25] vs 1.10 [0.90-1.70]; P = 0.001), and dehydroepiandrosterone sulfate (median [IQR]: 168.5 [91.1-227.8] vs 125.2 [66.3-181]; P = 0.001). Over time, mean changes of FBS, HDL-C, LDL-C, non-HDL-C, TG, SBP, DBP, and WC were not significantly different in women with IH, compared with healthy controls. According to the unadjusted Cox regression model, except for type 2 diabetes mellitus (T2DM) (HR [95% CI]: 1.45 [1.00-2.11]) P = 0.05; there was no statistically significant difference in hazard of metabolic disorders (ie, HTN, pre-HTN, pre-T2DM, and metabolic syndrome) in IH, compared with healthy controls. Besides, the adjusted Cox regression model showed no significant differences in the hazard of these outcomes. This study showed no significant difference in overtime mean changes of metabolic risk factors and cardiometabolic outcomes in women with IH, compared with the healthy control group, except marginally significant difference on T2DM, which disappeared after further adjustment for potential confounders. Accordingly, routine screening of women for these metabolic outcomes should not recommend.

Poster 268: Allogeneic, Off The Shelf, Bone Marrow derived, Pooled, Mesenchymal Stromal Cells – A Potential Break through Therapy for Grade II &amp; III Osteoarthritis Knee Management

Poster 268: Allogeneic, Off The Shelf, Bone Marrow derived, Pooled, Mesenchymal Stromal Cells – A Potential Break through Therapy for Grade II &amp; III Osteoarthritis Knee Management

Analytical methods for evaluating reliability and validity of mobile audiometry tools.

Statistical approaches that could be used as standardized methodology for evaluating reliability and validity of data obtained using remote audiometry are proposed. Using data from the Nurses' Health Study II (n = 31), the approaches to evaluate the reliability and validity of hearing threshold measurements obtained by a self-administered iPhone-based hearing assessment application (Decibel Therapeutics, Inc., Boston, MA) compared with measurements obtained by clinical (soundbooth) audiometry are described. These approaches use mixed-effects models to account for multilevel correlations, intraclass correlation coefficients (ICCs) of single and averaged measurements, and regression techniques with the generalized estimating equations (GEEs) to account for between-ear correlations. Threshold measurements obtained using the iPhone application were moderately reliable. The reliability was improved substantially by averaging repeated measurements; good reliability was achieved by averaging three repeated measurements. In the linear regression analyses that assessed validity, the range of intercepts (2.3-8.4) and range of slopes (0.4-0.7) indicated that the measurements from the application were likely biased from those obtained by clinical audiometry. When evaluating alternative hearing assessment tools, it is recommended to assess reliability through mixed-effects models and use ICCs to determine the number of repeated assessments needed to achieve satisfactory reliability. When evaluating validity, GEE methods are recommended to estimate regression coefficients.

Effects of a WeChat-based individualized post-discharge rehabilitation program on patients with lumbar fusion surgery.

Exercise training after lumbar fusion surgery (LFS) is important for regaining the strength in the spinal muscles, pain management, and minimizing dysfunction. It may be prudent to evaluate technologies such as web-based chat and social media apps for increasing the efficacy of post-surgery interventions in LFS patients. To explore the effectiveness of a WeChat-based individualized post-discharge rehabilitation program in patients with LFS. Seventy-two eligible discharged LFS patients were enrolled from October 2018 to February 2019. The experimental group (36 cases) received a 10-week WeChat-based individualized rehabilitation program, while the control group (36 cases) received routine follow-up guidance. The outcomes were measured using the Exercise Compliance Questionnaire, Numerical Rating Scale, Oswestry Disability Index and Chinese version of the self-efficacy for exercise scale. The analysis using generalized estimation equations method shows significant differences in the interaction effect of group*time in exercise compliance (Wald c2= 7.459, P< 0.05), group effect in pain (Wald c2= 5.811, P< 0.05) and self-efficacy (Wald c2= 16.383, P< 0.05). However, there was no significant difference between the experimental and control groups in the group effect in dysfunction improvement (Wald c2= 2.289, P> 0.05). The WeChat-based rehabilitation intervention can improve exercise compliance and self-efficacy, and help achieve greater pain relief compared to the routine intervention. However, the WeChat-based intervention did not offer better improvement in the self-dysfunction in the post-discharge LFS patients.

Interep: An R Package for High-Dimensional Interaction Analysis of the Repeated Measurement Data.

We introduce interep, an R package for interaction analysis of repeated measurement data with high-dimensional main and interaction effects. In G × E interaction studies, the forms of environmental factors play a critical role in determining how structured sparsity should be imposed in the high-dimensional scenario to identify important effects. Zhou et al. (2019) (PMID: 31816972) proposed a longitudinal penalization method to select main and interaction effects corresponding to the individual and group structure, respectively, which requires a mixture of individual and group level penalties. The R package interep implements generalized estimating equation (GEE)-based penalization methods with this sparsity assumption. Moreover, alternative methods have also been implemented in the package. These alternative methods merely select effects on an individual level and ignore the group-level interaction structure. In this software article, we first introduce the statistical methodology corresponding to the penalized GEE methods implemented in the package. Next, we present the usage of the core and supporting functions, which is followed by a simulation example with R codes and annotations. The R package interep is available at The Comprehensive R Archive Network (CRAN).

Do Gender or Major Influence the Performance in Programming Learning? Teaching Mode Decision Based on Exercise Series Analysis.

Both traditional teaching and online teaching advocate individualized education. One of the difficulties on exploring possible improvements of instructional design is the challenging process of data collection. Existing research mainly focuses on the exam score of students but pays little attention to students' daily practice. As an effective method to handle time-series dataset, the generalized estimating equations (GEE) have not been used in this research field. Considering above issues, we first propose an experimental paradigm of programming performance analysis based on the performance record of students' daily practice-exam and finish collecting a complete time-series dataset in one semester, including students' individual attributes, learning behavior, and learning performance. Then, we propose an approach that analyzes practice-exam time-series dataset based on GEE to study the influence of individual attributes and learning behavior on learning performance. It is the first time to apply the GEE method for ordinal multinomial responses in this research field, by which we conclude several results that gender or major does have a certain difference on the programming learning. The longer the answer time and the less the cost time, the better the students' performance. Regardless of gender, students tend to cram for the exam and perform a little worse in the daily exercise. Finally, targeting at two important individual attributes, we give corresponding teaching mode decisions that university should teach students programming by major and teacher should give different teaching methods to students of different genders at different time points.

Reviewing of Different Methods for Handling Longitudinal Count data

In this paper, we will review the methods that used to handle longitudinal data in the case of marginal models when inferences about the population average are the primary focus [1] or when future applications of the results require the expectation of the response as a function of the current covariates [7]. We will review the generalized estimating equations method (GEE), quadratic inference functions (QIF), generalized quasi likelihood (GQL) and the generalized method of moments (GMM). These methods will be reviewed by discussing its advantages and disadvantages in more details.

GEECORR: A SAS macro for regression models of correlated binary responses and within-cluster correlation using generalized estimating equations

Background and objectives: Generalized estimating equations (GEE) provide population-averaged model inference for longitudinal and clustered outcomes via a generalized linear model for the effect of explanatory variables on the marginal mean, while intra-cluster correlations are ordinarily treated as nuisance parameters. Software to richly parameterize and conduct inference for complex correlation structures in the marginal modeling framework is scarce.Methods: A SAS macro, GEECORR, has been developed for the analysis of clustered binary data based on GEE to include additional estimating equations for modeling pairwise correlation between binary variates as a function of covariates.Results: We illustrate the macro in a surveillance study with repeated measures, a longitudinal study, and a study with biological clustering.Conclusions: This article provides an overview of the GEE method consisting of a pair of estimating equations, describes the features and capabilities of the GEECORR macro including regression diagnostics and finite-sample bias-corrected covariance estimators, and demonstrates the macro usage for three studies.