A study on the correlations of PRL levels with anxiety, depression, sleep, and self-efficacy in patients with prolactinoma

Purpose

The purpose of this study was to explore the factors influencing PRL levels in patients with prolactinoma and to investigate the correlations between anxiety, depression, sleep, self-efficacy, and PRL levels.

Methods

This retrospective study included 176 patients with prolactinoma who received outpatient treatment at the Affiliated Hospital of Zunyi Medical University from May 2017 to August 2022. The general information questionnaire, Hospital Anxiety and Depression Scale (HADS), Athens Insomnia Scale (AIS), and General Self-Efficacy Scale (GSES) were used for data collection. A generalized estimating equation (GEE) model was used to analyze the factors influencing PRL levels in patients with prolactinoma. GEE single-effect analysis was used to compare PRL levels at different time points between anxiety group and nonanxiety group, between insomnia group and normal group, and between low, medium, and high self-efficacy groups.

Results

The median baseline PRL level and the PRL levels at 1, 3, 6, and 12 months of follow-up were 268.50 ng/ml, 122.25 ng/ml, 21.20 ng/ml, 19.65 ng/ml, and 16.10 ng/ml, respectively. Among patients with prolactinoma, 59.10% had anxiety (HADS-A score = 7.35 ± 3.34) and 28.98% had depression (HADS-D score = 5.23 ± 3.87), 9.10% had sleep disorders (AIS score = 6.10 ± 4.31) and 54.55% had low self-efficacy (GSES score = 2.13 ± 0.83). Educational level, tumor size, number of visits, sleep quality, anxiety level, and self-efficacy level were found to be factors influencing PRL levels in patients with prolactinoma (P<0.05). Higher PRL levels were observed in the anxiety group compared to the non-anxiety group (P<0.001), in the insomnia group compared to the normal group (P<0.05), and in the low self-efficacy group compared to the medium and high self-efficacy groups (P<0.05).

Conclusion

PRL levels in patients with prolactinoma are related to education level, tumor size, number of visits, anxiety, self-efficacy, and sleep but not depression. PRL levels were higher in patients with anxiety, low self-efficacy, and sleep disorders.

Multivariate analysis of the effect of keratinized mucosa on peri-implant tissues with platform switching: A retrospective study

BACKGROUND

In recent years, platform switching implant treatment has been increasing, which is believed to minimize bone loss around the implant after placement. However, there have been no reports on the relationship between keratinized mucosa width (KMW) and bone loss and soft tissue recession in platform switching implants.

OBJECTIVE

We evaluated the effect of the KMW on the amount of bone loss and soft tissue recession around a platform switching implant retrospectively using multivariate analysis.

MATERIALS AND METHODS

This one-year retrospective study included 91 implants in 48 patients. Age, sex, a history of periodontitis, implant location, oral hygiene status, and the KMW were included as explanatory variables to evaluate bone loss (BL) and buccal gingival height (GH). Generalized estimating equations (GEEs) were used to evaluate the effect of the KMW on platform switching peri-implant tissues.

RESULTS

The mean bone loss on the mesial (ΔBLm), distal (ΔBLd), and buccal (ΔBLb) sides of the implant were 0.16 ± 0.27 mm, 0.19 ± 0.34 mm, and 0.24 ± 0.50 mm, respectively, at 1 year after superstructure placement. The mean amount of change of GH (ΔGH) on the buccal side was 0.30 ± 0.47 mm. After correcting for confounders using GEEs, the results suggested that KMW <1.5 mm was a significant factor (P < 0.001) for bone loss over time in ΔBLm, ΔBLd, and ΔBLb. In addition, for soft tissues on the buccal side, KMW <1.5 mm was a significant factor for ΔGH reduction over time (P < 0.001).

CONCLUSIONS

Keratinized mucosa width ≥1.5 mm was associated with a higher probability less hard and soft tissue recession around the platform switching implant after 1 year from superstructure placement.

Estimating average treatment effects for clustered RCTs with recruitment bias

In clustered randomized controlled trials (RCTs), sample recruitment is often conducted after cluster randomization. This timing can lead to recruitment bias if access to the intervention affects the composition of study-eligible cluster entrants and study consenters. This article develops a potential outcomes framework in such settings that yields a causal estimand that pertains to the always-recruited in either research condition. A consistent inverse probability weighting (IPW) estimator is developed using data on recruits only, and a generalized estimating equations approach is used to obtain robust clustered SE estimators that adjust for estimation error in the IPW weights. A simple data collection strategy is discussed to improve the predictive accuracy of the logit propensity score models. Simulations show that the IPW estimator achieves nominal confidence interval coverage under the assumed identification conditions. An empirical application demonstrates the methods using data from an RCT testing the effects of a behavioral health intervention in schools. An R program for estimation is available for download.

Homogeneity pursuit and variable selection in regression models for multivariate abundance data

When building regression models for multivariate abundance data in ecology, it is important to allow for the fact that the species are correlated with each other. Moreover, there is often evidence species exhibit some degree of homogeneity in their responses to each environmental predictor, and that most species are informed by only a subset of predictors. We propose a generalized estimating equation (GEE) approach for simultaneous homogeneity pursuit (ie, grouping species with similar coefficient values while allowing differing groups for different covariates) and variable selection in regression models for multivariate abundance data. Using GEEs allows us to straightforwardly account for between-response correlations through a (reduced-rank) working correlation matrix. We augment the GEE with both adaptive fused lasso- and adaptive lasso-type penalties, which aim to cluster the species-specific coefficients within each covariate and encourage differing levels of sparsity across the covariates, respectively. Numerical studies demonstrate the strong finite sample performance of the proposed method relative to several existing approaches for modeling multivariate abundance data. Applying the proposed method to presence-absence records collected along the Great Barrier Reef in Australia reveals both a substantial degree of homogeneity and sparsity in species-environmental relationships. We show this leads to a more parsimonious model for understanding the environmental drivers of seabed biodiversity, and results in stronger out-of-sample predictive performance relative to methods that do not accommodate such features.

Longitudinal varying coefficient single-index model with censored covariates

It is of interest to health policy research to estimate the population-averaged longitudinal medical cost trajectory from initial cancer diagnosis to death, and understand how the trajectory curve is affected by patient characteristics. This research question leads to a number of statistical challenges because the longitudinal cost data are often non-normally distributed with skewness, zero-inflation, and heteroscedasticity. The trajectory is nonlinear, and its length and shape depend on survival, which are subject to censoring. Modeling the association between multiple patient characteristics and nonlinear cost trajectory curves of varying lengths should take into consideration parsimony, flexibility, and interpretation. We propose a novel longitudinal varying coefficient single-index model. Multiple patient characteristics are summarized in a single-index, representing a patient's overall propensity for healthcare use. The effects of this index on various segments of the cost trajectory depend on both time and survival, which is flexibly modeled by a bivariate varying coefficient function. The model is estimated by generalized estimating equations with an extended marginal mean structure to accommodate censored survival time as a covariate. We established the pointwise confidence interval of the varying coefficient and a test for the covariate effect. The numerical performance was extensively studied in simulations. We applied the proposed methodology to medical cost data of prostate cancer patients from the Surveillance, Epidemiology, and End Results-Medicare-Linked Database.

Leveraging baseline covariates to analyze small cluster-randomized trials with a rare binary outcome

Cluster-randomized trials (CRTs) involve randomizing entire groups of participants-called clusters-to treatment arms but are often comprised of a limited or fixed number of available clusters. While covariate adjustment can account for chance imbalances between treatment arms and increase statistical efficiency in individually randomized trials, analytical methods for individual-level covariate adjustment in small CRTs have received little attention to date. In this paper, we systematically investigate, through extensive simulations, the operating characteristics of propensity score weighting and multivariable regression as two individual-level covariate adjustment strategies for estimating the participant-average causal effect in small CRTs with a rare binary outcome and identify scenarios where each adjustment strategy has a relative efficiency advantage over the other to make practical recommendations. We also examine the finite-sample performance of the bias-corrected sandwich variance estimators associated with propensity score weighting and multivariable regression for quantifying the uncertainty in estimating the participant-average treatment effect. To illustrate the methods for individual-level covariate adjustment, we reanalyze a recent CRT testing a sedation protocol in 31 pediatric intensive care units.

Trajectories of fear of cancer recurrence and its influence factors: A longitudinal study on Chinese newly diagnosed cancer patients

OBJECTIVE

The fear of cancer recurrence (FCR) is an ongoing and common psychological problem faced by cancer patients. The objective of this study was to explore the variation trend of FCR and its influencing factors in Chinese newly diagnosed cancer patients from admission to 2 months after discharge. Demographic and tumor characteristics, as well as experiential avoidance (EA), were used as predictors.

METHOD

A longitudinal design and a consecutive sampling method were used to select 266 newly diagnosed cancer patients admitted to a tertiary cancer hospital in China from July to December 2022. Measurements of FCR and EA were obtained at admission (T1), 1 month after discharge (T2), and 2 months post-discharge (T3). Generalized estimating equations were used to identify factors associated with FCR for longitudinal data analysis.

RESULTS

A total of 266 participants completed the follow-up. Both FCR and EA scores of patients with newly diagnosed cancer showed a significant trend of first increasing and then decreasing at baseline and follow-up (p < 0.001). The junior secondary and less education level, rural residence, advanced tumor and high EA level were risk factors for higher FCR.

CONCLUSIONS

Our findings suggest that the FCR levels of most newly diagnosed cancer patients in China are different at the three time points and affected by different factors, with the highest level at 1 month after discharge. These results have significant implications for future identifying populations in need of targeted intervention based on their FCR trajectories.

Analysis of Adverse Drug Reactions in Pediatric Patients with Epilepsy: An Intensive Pharmacovigilance Study

Epilepsy is a chronic neurological disease characterized by the presence of spontaneous seizures, with a higher incidence in the pediatric population. Anti-seizure medication (ASM) may produce adverse drug reactions (ADRs) with an elevated frequency and a high severity. Thus, the objective of the present study was to analyze, through intensive pharmacovigilance over 112 months, the ADRs produced by valproic acid (VPA), oxcarbazepine (OXC), phenytoin (PHT), and levetiracetam (LEV), among others, administered to monotherapy or polytherapy for Mexican hospitalized pediatric epilepsy patients. A total of 1034 patients were interviewed; 315 met the inclusion criteria, 211 patients presented ADRs, and 104 did not. A total of 548 ASM-ADRs were identified, and VPA, LEV, and PHT were the main culprit drugs. The most frequent ADRs were drowsiness, irritability, and thrombocytopenia, and the main systems affected were hematologic, nervous, and dermatologic. LEV and OXC caused more nonsevere ADRs, and PHT caused more severe ADRs. The risk analysis showed an association between belonging to the younger groups and polytherapy with ADR presence and between polytherapy and malnutrition with severe ADRs. In addition, most of the severe ADRs were preventable, and most of the nonsevere ADRs were nonpreventable.

Patterns of site-level periodontal disease and within-mouth correlation among older adults in the Hispanic Community Health Study/Study of Latinos

OBJECTIVES

Clinical measures of periodontal disease such as attachment loss (CAL) and probing depth (PD) vary considerably between and within individuals with periodontitis and are known to be influenced by person-level factors (e.g. age and race/ethnicity) as well as intraoral characteristics (e.g. tooth type and location). This study sought to characterize site-level disease patterns and correlations using both person-level and intraoral factors through a model-based approach.

METHODS

This study used full-mouth, six sites per tooth, periodontal examination data collected from 2301 Hispanic/Latino adults aged 60-74 years in the Hispanic Community Health Study/Study of Latinos (HCHS/SOL). The presence of site-level CAL ≥3 mm and PD ≥4 mm was estimated using generalized estimating equations (GEE), explicitly modelling pairwise periodontal site correlations, while adjusting for number of teeth, sex and Hispanic/Latino background. Subsequently tooth- and tooth-site patterns of intraoral CAL ≥3 mm and PD ≥4 mm were estimated and visualized in the HCHS/SOL population.

RESULTS

The findings showed that posterior sites had the highest odds of CAL ≥3 mm and PD ≥4 mm. Sites located in the interproximal space had higher odds of PD ≥4 mm but lower odds of CAL ≥3 mm than non-interproximal sites. Mexicans had the lowest odds of CAL ≥3 mm among all Hispanic/Latino backgrounds. While Mexicans had lower odds of PD ≥4 mm than Central Americans and Cubans, they had higher odds than Dominicans and Puerto Ricans. Site-level proportions and pairwise correlations of PD ≥4 mm were generally smaller than those of CAL ≥3 mm.

CONCLUSIONS

The patterns of site-level probabilities of clinical measures of periodontal disease can be defined based on tooth, site and individual-level characteristics. Intraoral correlation patterns, while complex, are quantifiable. The risk factors for site-level CAL ≥3 mm may differ from those of PD ≥4 mm. Likewise, participant risk factors for site-level clinical measures of periodontal disease are distinct from those that affect individual-level periodontitis prevalence. Future epidemiological investigations should consider model-based approaches when examining site-level disease probabilities to identify intra-oral patterns of periodontal disease and make inferences about the larger population.

The Dosing of Mobile-Based Just-in-Time Adaptive Self-Management Prompts for Caregivers: Preliminary Findings From a Pilot Microrandomized Study

BACKGROUND

Caregivers of people with chronic illnesses often face negative stress-related health outcomes and are unavailable for traditional face-to-face interventions due to the intensity and constraints of their caregiver role. Just-in-time adaptive interventions (JITAIs) have emerged as a design framework that is particularly suited for interventional mobile health studies that deliver in-the-moment prompts that aim to promote healthy behavioral and psychological changes while minimizing user burden and expense. While JITAIs have the potential to improve caregivers' health-related quality of life (HRQOL), their effectiveness for caregivers remains poorly understood.

OBJECTIVE

The primary objective of this study is to evaluate the dose-response relationship of a fully automated JITAI-based self-management intervention involving personalized mobile app notifications targeted at decreasing the level of caregiver strain, anxiety, and depression. The secondary objective is to investigate whether the effectiveness of this mobile health intervention was moderated by the caregiver group. We also explored whether the effectiveness of this intervention was moderated by (1) previous HRQOL measures, (2) the number of weeks in the study, (3) step count, and (4) minutes of sleep.

METHODS

We examined 36 caregivers from 3 disease groups (10 from spinal cord injury, 11 from Huntington disease, and 25 from allogeneic hematopoietic cell transplantation) in the intervention arm of a larger randomized controlled trial (subjects in the other arm received no prompts from the mobile app) designed to examine the acceptability and feasibility of this intensive type of trial design. A series of multivariate linear models implementing a weighted and centered least squares estimator were used to assess the JITAI efficacy and effect.

RESULTS

We found preliminary support for a positive dose-response relationship between the number of administered JITAI messages and JITAI efficacy in improving caregiver strain, anxiety, and depression; while most of these associations did not meet conventional levels of significance, there was a significant association between high-frequency JITAI and caregiver strain. Specifically, administering 5-6 messages per week as opposed to no messages resulted in a significant decrease in the HRQOL score of caregiver strain with an estimate of -6.31 (95% CI -11.76 to -0.12; P=.046). In addition, we found that the caregiver groups and the participants' levels of depression in the previous week moderated JITAI efficacy.

CONCLUSIONS

This study provides preliminary evidence to support the effectiveness of the self-management JITAI and offers practical guidance for designing future personalized JITAI strategies for diverse caregiver groups.

TRIAL REGISTRATION

ClinicalTrials.gov NCT04556591; https://clinicaltrials.gov/ct2/show/NCT04556591.

Generalizing the information content for stepped wedge designs: A marginal modeling approach

Stepped wedge trials are increasingly adopted because practical constraints necessitate staggered roll-out. While a complete design requires clusters to collect data in all periods, resource and patient-centered considerations may call for an incomplete stepped wedge design to minimize data collection burden. To study incomplete designs, we expand the metric of information content to discrete outcomes. We operate under a marginal model with general link and variance functions, and derive information content expressions when data elements (cells, sequences, periods) are omitted. We show that the centrosymmetric patterns of information content can hold for discrete outcomes with the variance-stabilizing link function. We perform numerical studies under the canonical link function, and find that while the patterns of information content for cells are approximately centrosymmetric for all examined underlying secular trends, the patterns of information content for sequences or periods are more sensitive to the secular trend, and may be far from centrosymmetric.

Combined MIGS: Comparing Additive Effects of Phacoemulsification, Endocyclophotocoagulation, and Kahook Dual Blade

Purpose

Combining two or more MIGS (cMIGS) promises to be more efficacious than single MIGS (sMIGS). This study compared the efficacy of PEcK, which combines Phacoemulsification (Phaco), Endocyclophotocoagulation (ECP), and Kahook dual blade (KDB), relative to both of its constituent sMIGS, Phaco/ECP (Endo Optiks, NJ) and Phaco/KDB (New World Medical, CA) for the first time.

Patients and methods

Data was collected retrospectively from 1833 visits of 271 patients who underwent PEcK, Phaco/ECP, or Phaco/KDB from 2016-2021 at Massachusetts Eye and Ear. Primary outcomes included Generalized Estimating Equations (GEE) of intraocular pressure (IOP) and medication burden, as well as survival models.

Results

Mean preoperative IOP was 17.6 ± 5.0 (SD) mmHg on 3.0 ± 1.4 medications in the PEcK group (n = 128), 17.9 ± 5.1 mmHg on 2.2 ± 1.5 medications in the Phaco/ECP group (n = 78), and 16.1 ± 4.3 mmHg on 0.4 ± 1.0 medications in the Phaco/KDB group (n = 65). For more than 36 months, all procedures resulted in significant patterns of IOP and medication reduction (all p < 0.001), before and after statistical adjustment. The reduction pattern in IOP was significantly different when comparing all groups over time and favored PEcK (p = 0.04), but the reduction pattern in medications was not significantly different (p = 0.11). Procedures did not differ in procedural time (p = 0.18) or in survival to maintain ≥20% IOP reduction (p = 0.43) without additional medication or procedure. There was a trend toward significant difference in maintaining IOP ≤ goal IOP that favored PEcK over Phaco/ECP after adjustment (p = 0.09).

Conclusion

PEcK may confer greater IOP reduction without added procedural time compared to Phaco/ECP and Phaco/KDB in predominantly mild or moderate glaucoma. Further research on cMIGS may benefit from adopting this comparative analysis to constituent MIGS.

The impact of correlated exposures and missing data on multiple informant models used to identify critical exposure windows

There has been heightened interest in identifying critical windows of exposure for adverse health outcomes; that is, time points during which exposures have the greatest impact on a person's health. Multiple informant models implemented using generalized estimating equations (MIM GEEs) have been applied to address this research question because they enable statistical comparisons of differences in associations across exposure windows. As interest rises in using MIMs, the feasibility and appropriateness of their application under settings of correlated exposures and partially missing exposure measurements requires further examination. We evaluated the impact of correlation between exposure measurements and missing exposure data on the power and differences in association estimated by the MIM GEE and an inverse probability weighted extension to account for informatively missing exposures. We assessed these operating characteristics under a variety of correlation structures, sample sizes, and missing data mechanisms considering various exposure-outcome scenarios. We showed that applying MIM GEEs maintains higher power when there is a single critical window of exposure and exposure measures are not highly correlated, but may result in low power and bias under other settings. We applied these methods to a study of pregnant women living with HIV to explore differences in association between trimester-specific viral load and infant neurodevelopment.

Practical strategies for operationalizing optimal allocation in stratified cluster-based outcome-dependent sampling designs

Cluster-based outcome-dependent sampling (ODS) has the potential to yield efficiency gains when the outcome of interest is relatively rare, and resource constraints allow only a certain number of clusters to be visited for data collection. Previous research has shown that when the intended analysis is inverse-probability weighted generalized estimating equations, and the number of clusters that can be sampled is fixed, optimal allocation of the (cluster-level) sample size across strata defined by auxiliary variables readily available at the design stage has the potential to increase efficiency in the estimation of the parameter(s) of interest. In such a setting, the optimal allocation formulae depend on quantities that are unknown in practice, currently making such designs difficult to implement. In this paper, we consider a two-wave adaptive sampling approach, in which data is collected from a first wave sample, and subsequently used to compute the optimal second wave stratum-specific sample sizes. We consider two strategies for estimating the necessary components using the first wave data: an inverse-probability weighting (IPW) approach and a multiple imputation (MI) approach. In a comprehensive simulation study, we show that the adaptive sampling approach performs well, and that the MI approach yields designs that are very near-optimal, regardless of the covariate type. The IPW approach, on the other hand, has mixed results. Finally, we illustrate the proposed adaptive sampling procedures with data on maternal characteristics and birth outcomes among women enrolled in the Safer Deliveries program in Zanzibar, Tanzania.

Improving sandwich variance estimation for marginal Cox analysis of cluster randomized trials

Cluster randomized trials (CRTs) frequently recruit a small number of clusters, therefore necessitating the application of small-sample corrections for valid inference. A recent systematic review indicated that CRTs reporting right-censored, time-to-event outcomes are not uncommon and that the marginal Cox proportional hazards model is one of the common approaches used for primary analysis. While small-sample corrections have been studied under marginal models with continuous, binary, and count outcomes, no prior research has been devoted to the development and evaluation of bias-corrected sandwich variance estimators when clustered time-to-event outcomes are analyzed by the marginal Cox model. To improve current practice, we propose nine bias-corrected sandwich variance estimators for the analysis of CRTs using the marginal Cox model and report on a simulation study to evaluate their small-sample properties. Our results indicate that the optimal choice of bias-corrected sandwich variance estimator for CRTs with survival outcomes can depend on the variability of cluster sizes and can also slightly differ whether it is evaluated according to relative bias or type I error rate. Finally, we illustrate the new variance estimators in a real-world CRT where the conclusion about intervention effectiveness differs depending on the use of small-sample bias corrections. The proposed sandwich variance estimators are implemented in an R package CoxBcv.

Analysis of the efficacy and safety of inpatient and outpatient initiation of KD for the treatment of pediatric refractory epilepsy using generalized estimating equations

Objective

To compare the efficacy and safety of inpatient and outpatient initiation ketogenic diet (KD) protocol of pediatric refractory epilepsy.

Methods

Eligible children with refractory epilepsy were randomly assigned to receive KD with inpatient and outpatient initiation. The generalized estimation equation (GEE) model was used to analyze the longitudinal variables of seizure reduction, ketone body, weight, height, body mass index (BMI), and BMI Z-score at different follow-up times between the two groups.

Results

Between January 2013 and December 2021, 78 and 112 patients were assigned to outpatient and inpatient KD initiation groups, respectively. There were no statistical differences between the two groups based on baseline demographics and clinical characteristics (all Ps > 0.05). The GEE model indicated that the rate of reduction of seizures≥50% in the outpatient initiation group was higher than that of the inpatient initiation group (p = 0.049). A negative correlation was observed between the seizure reduction and blood ketone body at 1, 6, and 12 months (all Ps < 0.05). There were no significant differences in height, weight, BMI, and BMI Z-score between the two groups over the 12-month period by the GEE models (all Ps > 0.05). Adverse events were reported by 31 patients (43.05%) in the outpatient KD initiation group and 46 patients (42.20%) in the inpatient KD initiation group, but these differences were not statistically significant (p = 0.909).

Conclusion

Our study shows that outpatient KD initiation is a safe and effective treatment for children with refractory epilepsy.

Beyond fear: A longitudinal investigation of emotions and risk of a vasovagal reaction in first-time whole-blood donors

BACKGROUND

Fear is a recognized predictor of vasovagal reactions (VVRs) in blood donors. However, less is known about the role of other emotions, including positive emotions, that donors might experience. The aim of this study was to identify the emotions experienced in center that predict onsite VVRs, and to determine at what point during the donation appointment, the experience of these emotions is most influential.

STUDY DESIGN AND METHODS

A sample of 442 first-time whole-blood donors (57.7% female; mean ± SD age 30.7 ± 11.7 years) completed a survey in the waiting area and before venepuncture in the donation chair to assess their current emotional experience. The survey data were matched with routinely-collected demographic, donation, and donor adverse event information. A generalized estimating equations model was used to identify emotions associated with the occurrence of a VVR.

RESULTS

A total of 56 (12.7%) participants experienced a VVR. The occurrence of a VVR was significantly associated with lower love/closeness/trust (OR: 0.53, 95%CI: 0.34-0.82) and higher scared/fearful/afraid (OR: 1.96, 95%CI: 1.18-3.25) states. Significant interaction effects suggested that the effect of scared/fearful/afraid decreased while stressed/nervous/overwhelmed increased from the waiting area to before venepuncture on the likelihood of a VVR.

DISCUSSION

To effectively reduce donor VVR risk, blood collection agencies need to address a broader range of emotions at different points during the donation process.

On modelling relative risks for longitudinal binomial responses: implications from two dueling paradigms

Although logistic regression is the most popular for modelling regression relationships with binary responses, many find relative risk (RR), or risk ratio, easier to interpret and prefer to use this measure of risk in regression analysis. Indeed, since Zou published his modified Poisson regression approach for modelling RR for cross-sectional data, his paper has been cited over 7 000 times, demonstrating the popularity of this alternative measure of risk in regression analysis involving binary responses. As longitudinal studies have become increasingly popular in clinical trials and observational studies, it is imperative to extend Zou's approach for longitudinal data. The two most popular approaches for longitudinal data analysis are the generalised linear mixed-effects model (GLMM) and generalised estimating equations (GEE). However, the parametric GLMM cannot be used for the extension within the current context, because Zou's approach treats the binary response as a Poisson variable, which is at odds with the Bernoulli distribution for the binary response. On the other hand, as it imposes no mathematical model on data distributions, the semiparametric GEE is coherent with Zou's modified Poisson regression. In this paper, we develop a GEE-based longitudinal model for binary responses to provide inference about RR.

Inverse Probability of Treatment Weighting in 5-Year Quality-of-Life Comparison among Three Surgical Procedures for Hepatocellular Carcinoma

This prospective longitudinal cohort study analyzed long-term changes in individual subscales of quality-of-life (QOL) measures and explored whether these changes were related to effective QOL predictors after hepatocellular carcinoma (HCC) surgery. All 520 HCC patients in this study had completed QOL surveys before surgery and at 6 months, 2 years, and 5 years after surgery. Generalized estimating equation models were used to compare the 5-year QOL among the three HCC surgical procedures. The QOL was significantly (p < 0.05) improved at 6 months after HCC surgery but plateaued at 2−5 years after surgery. In postoperative surveys, the effect size was largest in the nausea and vomiting subscales in patients who had received robotic surgery, and the effect size was smallest in the dyspnea subscale in patients who had received open surgery. It revealed the following explanatory variables for postoperative QOL: surgical procedure type, gender, age, hepatitis C, smoking, tumor stage, postoperative recurrence, and preoperative QOL. The comparisons revealed that, when evaluating QOL after HCC surgery, several factors other than the surgery itself should be considered. The analysis results also implied that postoperative quality of life might depend not only on the success of the surgical procedure, but also on preoperative quality of life.

Beyond ANOVA and MANOVA for repeated measures: Advantages of generalized estimated equations and generalized linear mixed models and its use in neuroscience research

In neuroscience research, longitudinal data are often analysed using analysis of variance (ANOVA) and multivariate analysis of variance (MANOVA) for repeated measures (rmANOVA/rmMANOVA). However, these analyses have special requirements: The variances of the differences between all possible pairs of within-subject conditions (i.e., levels of the independent variable) must be equal. They are also limited to fixed repeated time intervals and are sensitive to missing data. In contrast, other models, such as the generalized estimating equations (GEE) and the generalized linear mixed models (GLMM), suggest another way to think about the data and the studied phenomenon. Instead of forcing the data into the ANOVAs assumptions, it is possible to design a flexible/personalized model according to the nature of the dependent variable. We discuss some advantages of GEE and GLMM as alternatives to rmANOVA and rmMANOVA in neuroscience research, including the possibility of using different distributions for the parameters of the dependent variable, a better approach for different time length points, and better adjustment to missing data. We illustrate these advantages by showing a comparison between rmANOVA and GEE in a real example and providing the data and a tutorial code to reproduce these analyses in R. We conclude that GEE and GLMM may provide more reliable results when compared to rmANOVA and rmMANOVA in neuroscience research, especially in small sample sizes with unbalanced longitudinal designs with or without missing data.

power swgee: GEE-based power calculations in stepped wedge cluster randomized trials

Stepped wedge cluster randomized trials are increasingly being used to evaluate interventions in medical, public health, educational, and social science contexts. With the longitudinal and crossover nature of a SW-CRT, complex analysis techniques are often needed which makes appropriately powering SW-CRTs challenging. In this paper, we introduce a newly-developed SW-CRT power calculator, embedded within the power command in Stata. The power calculator assumes a marginal model (i.e., generalized estimating equations [GEE]) for the primary analysis of SW-CRTs, for which other currently available SW-CRT power calculators may not be suitable. The program accommodates complete cross-sectional and closed-cohort designs, and includes multilevel correlation structures appropriate for such designs. We discuss the methods and formulae underlying our SW-CRT calculator, and provide illustrative examples of the use of power swgee. We provide suggestions about the choice of parameters in power swgee, and conclude by discussing areas of future research which may improve the program.

Optimal sampling allocation for outcome-dependent designs in cluster-correlated data settings

In clinical and public health studies, it is often the case that some variables relevant to the analysis are too difficult or costly to measure for all individuals in the population of interest. Rather, a subsample of these individuals must be identified for additional data collection. A sampling scheme that incorporates readily-available information for the entire target population at the design stage can increase the statistical efficiency of the intended analysis. While there is no universally optimal sampling design, under certain principles and restrictions, a well-designed and efficient sampling strategy can be implemented. In two-phase designs, efficiency can be gained by stratifying on the outcome and/or auxiliary information that is known at phase I. Additional gains in efficiency can be obtained by determining the optimal allocation of the sample sizes across the strata, which depends on the quantity that is being estimated. In this paper, the inference is concerned with one or multiple regression parameter(s) where the study units are naturally clustered and, thus, exhibit correlation in outcomes. We propose several allocation strategies within the framework of two-phase designs for the estimation of the regression parameter(s) obtained from weighted generalized estimating equations. The proposed methods extend existing theory to address the objective of the estimating regression parameters in cluster-correlated data settings by minimizing the asymptotic variance of the estimator subject to a fixed sample size. Through a comprehensive simulation study, we show that the proposed allocation schemes have the potential to yield substantial efficiency gains over alternative strategies.

The Association between Changes in Built Environment and Changes in Walking among Older Women in Portland, Oregon

Some cross-sectional evidence suggests that the objectively measured built environment can encourage walking among older adults. We examined the associations between objectively measured built environment with change in self-reported walking among older women by using data from the Study of Osteoporotic Fractures (SOF). We evaluated the longitudinal associations between built environment characteristics and walking among 1253 older women (median age = 71 years) in Portland, Oregon using generalized estimating equation models. Built environment characteristics included baseline values and longitudinal changes in distance to the closest bus stop, light rail station, commercial area, and park. A difference of 1 km in the baseline distance to the closest bus stop was associated with a 12% decrease in the total number of blocks walked per week during follow-up (e^β = 0.88, 95% CI: 0.78, 0.99). Our study provided limited support for an association between neighborhood transportation and changes in walking among older women. Future studies should consider examining both objective measures and perceptions of the built environment.

Assessing the Impacts of Meteorological Factors on COVID-19 Pandemic Using Generalized Estimating Equations

Background

Meteorological factors have been proven to affect pathogens; both the transmission routes and other intermediate. Many studies have worked on assessing how those meteorological factors would influence the transmissibility of COVID-19. In this study, we used generalized estimating equations to evaluate the impact of meteorological factors on Coronavirus disease 2019 (COVID-19) by using three outcome variables, which are transmissibility, incidence rate, and the number of reported cases.

Methods

In this study, the data on the daily number of new cases and deaths of COVID-19 in 30 provinces and cities nationwide were obtained from the provincial and municipal health committees, while the data from 682 conventional weather stations in the selected provinces and cities were obtained from the website of the China Meteorological Administration. We built a Susceptible-Exposed-Symptomatic-Asymptomatic-Recovered/Removed (SEIAR) model to fit the data, then we calculated the transmissibility of COVID-19 using an indicator of the effective reproduction number (Reff ). To quantify the different impacts of meteorological factors on several outcome variables including transmissibility, incidence rate, and the number of reported cases of COVID-19, we collected panel data and used generalized estimating equations. We also explored whether there is a lag effect and the different times of meteorological factors on the three outcome variables.

Results

Precipitation and wind speed had a negative effect on transmissibility, incidence rate, and the number of reported cases, while humidity had a positive effect on them. The higher the temperature, the lower the transmissibility. The temperature had a lag effect on the incidence rate, while the remaining five meteorological factors had immediate and lag effects on the incidence rate and the number of reported cases.

Conclusion

Meteorological factors had similar effects on incidence rate and number of reported cases, but different effects on transmissibility. Temperature, relative humidity, precipitation, sunshine hours, and wind speed had immediate and lag effects on transmissibility, but with different lag times. An increase in temperature may first cause a decrease in virus transmissibility and then lead to a decrease in incidence rate. Also, the mechanism of the role of meteorological factors in the process of transmissibility to incidence rate needs to be further explored.

Kinetics in HBsAg after Stopping Entecavir or Tenofovir in Patients with Virological Relapse but Not Clinical Relapse

This study investigated the kinetics in HBsAg and the HBsAg loss rate after entecavir or tenofovir disoproxil fumarate (TDF) cessation in patients with chronic hepatitis B (CHB) who achieved virological suppression after virological relapse without clinical relapse. A total 504 HBeAg-negative, non-cirrhotic patients who previously received entecavir or TDF with post-treatment and who were followed up for at least 30 months were included. Of the 504 patients, 128 achieved sustained virological suppression (Group I), and 81 experienced virological relapse without clinical relapse. Of the 81 patients, 52 had intermittent or persistent HBV DNA > 2000 IU/mL (Group II), and 29 achieved persistent virological suppression (HBV DNA < 2000 IU/mL) for at least 1.5 years (Group III) after virological relapse. A generalized estimating equations analysis showed that Groups I and III experienced larger off-treatment HBsAg declines than Group II (both, p < 0.001). The post-treatment HBsAg declines of Group I and Group III were similar (p = 0.414). A multivariate analysis showed that there were no differences in the HBsAg change and HBsAg decline (p = 0.920 and 0.886, respectively) or HBsAg loss rate (p = 0.192) between Group I and Group III. The patients who achieved persistent viral suppression after HBV relapse without clinical relapse have a similar decline in HBsAg and the HBsAg loss rate as the sustained responders.

Clustered restricted mean survival time regression

For multicenter randomized trials or multilevel observational studies, the Cox regression model has long been the primary approach to study the effects of covariates on time-to-event outcomes. A critical assumption of the Cox model is the proportionality of the hazard functions for modeled covariates, violations of which can result in ambiguous interpretations of the hazard ratio estimates. To address this issue, the restricted mean survival time (RMST), defined as the mean survival time up to a fixed time in a target population, has been recommended as a model-free target parameter. In this article, we generalize the RMST regression model to clustered data by directly modeling the RMST as a continuous function of restriction times with covariates while properly accounting for within-cluster correlations to achieve valid inference. The proposed method estimates regression coefficients via weighted generalized estimating equations, coupled with a cluster-robust sandwich variance estimator to achieve asymptotically valid inference with a sufficient number of clusters. In small-sample scenarios where a limited number of clusters are available, however, the proposed sandwich variance estimator can exhibit negative bias in capturing the variability of regression coefficient estimates. To overcome this limitation, we further propose and examine bias-corrected sandwich variance estimators to reduce the negative bias of the cluster-robust sandwich variance estimator. We study the finite-sample operating characteristics of proposed methods through simulations and reanalyze two multicenter randomized trials.

Detecting sparse microbial association signals adaptively from longitudinal microbiome data based on generalized estimating equations

The association between the compositions of microbial communities and various host phenotypes is an important research topic. Microbiome association research addresses multiple domains, such as human disease and diet. Statistical methods for testing microbiome-phenotype associations have been studied recently to determine their ability to assess longitudinal microbiome data. However, existing methods fail to detect sparse association signals in longitudinal microbiome data. In this paper, we developed a novel method, namely aGEEMIHC, which is a data-driven adaptive microbiome higher criticism analysis based on generalized estimating equations to detect sparse microbial association signals from longitudinal microbiome data. aGEEMiHC adopts generalized estimating equations framework that fully considers the correlation among different observations from the same subject in longitudinal data. To be robust to diverse correlation structures for longitudinal data, aGEEMiHC integrates multiple microbiome higher criticism analyses based on generalized estimating equations with different working correlation structures. Extensive simulation experiments demonstrate that aGEEMiHC can control the type I error correctly and achieve superior performance according to a statistical power comparison. We also applied it to longitudinal microbiome data with various types of host phenotypes to demonstrate the stability of our method. aGEEMiHC is also utilized for real longitudinal microbiome data, and we found a significant association between the gut microbiome and Crohn's disease. In addition, our method ranks the significant factors associated with the host phenotype to provide potential biomarkers.

Effects of Sex, Existing Antibodies, and HIV-1-Related and Other Baseline Factors on Antibody Responses to Quadrivalent HPV Vaccine in Persons With HIV

BACKGROUND

We compared antibody (Ab) responses to a quadrivalent (types 6, 11, 16, and 18) human papillomavirus (HPV) vaccine between men and women with HIV-1.

METHODS

A retrospective analysis of participant-level data from published clinical trials of HPV vaccine administered at study entry and at weeks 8 and 24 was conducted separately for baseline Ab undetectable and baseline Ab detectable using Ab titers and titer changes from baseline, respectively, at week 28 and year 1.5. Generalized estimating equations accounted for multiple HPV types and were adjusted for multiple baseline factors, including existing HPV antibodies before vaccination from natural exposure.

RESULTS

We evaluated 575 participants with CD4+ count >200 cells/mm3, 323 men and 252 women: median ages 46 and 38 years, respectively. Week 28 and year 1.5 Ab titers were similar between men and women regardless of the baseline Ab detection in multivariate models. HIV-1 RNA ≥400 copies/mm3 was associated with a lower week 28 Ab response; in baseline Ab detectable, the baseline HPV Ab titer level, HPV DNA detection, and lower CD4+/CD8+ ratio were also associated with a lower response. CD4+/CD8+ ratio was a stronger predictor in the year 1.5 Ab analysis than in the week 28 analysis. Ab responses among baseline Ab detectable were only somewhat higher than those among baseline Ab undetectable (eg, type 16 week 28 median 3.46 vs 3.20 log10 mMU/mL) despite the existing baseline titer (median 1.74).

CONCLUSIONS

We did not find any sex differences of serologic response to HPV vaccine. Ab titer gain was lower in those with preexisting antibodies due to previous natural infection.

Marginal modeling in community randomized trials with rare events: Utilization of the negative binomial regression model

BACKGROUND/AIMS

This work is motivated by the HEALing Communities Study, which is a post-test only cluster randomized trial in which communities are randomized to two different trial arms. The primary interest is in reducing opioid overdose fatalities, which will be collected as a count outcome at the community level. Communities range in size from thousands to over one million residents, and fatalities are expected to be rare. Traditional marginal modeling approaches in the cluster randomized trial literature include the use of generalized estimating equations with an exchangeable correlation structure when utilizing subject-level data, or analogously quasi-likelihood based on an over-dispersed binomial variance when utilizing community-level data. These approaches account for and estimate the intra-cluster correlation coefficient, which should be provided in the results from a cluster randomized trial. Alternatively, the coefficient of variation or R coefficient could be reported. In this article, we show that negative binomial regression can also be utilized when communities are large and events are rare. The objectives of this article are (1) to show that the negative binomial regression approach targets the same marginal regression parameter(s) as an over-dispersed binomial model and to explain why the estimates may differ; (2) to derive formulas relating the negative binomial overdispersion parameter k with the intra-cluster correlation coefficient, coefficient of variation, and R coefficient; and (3) analyze pre-intervention data from the HEALing Communities Study to demonstrate and contrast models and to show how to report the intra-cluster correlation coefficient, coefficient of variation, and R coefficient when utilizing negative binomial regression.

METHODS

Negative binomial and over-dispersed binomial regression modeling are contrasted in terms of model setup, regression parameter estimation, and formulation of the overdispersion parameter. Three specific models are used to illustrate concepts and address the third objective.

RESULTS

The negative binomial regression approach targets the same marginal regression parameter(s) as an over-dispersed binomial model, although estimates may differ. Practical differences arise in regard to how overdispersion, and hence the intra-cluster correlation coefficient is modeled. The negative binomial overdispersion parameter is approximately equal to the ratio of the intra-cluster correlation coefficient and marginal probability, the square of the coefficient of variation, and the R coefficient minus 1. As a result, estimates corresponding to all four of these different types of overdispersion parameterizations can be reported when utilizing negative binomial regression.

CONCLUSION

Negative binomial regression provides a valid, practical, alternative approach to the analysis of count data, and corresponding reporting of overdispersion parameters, from community randomized trials in which communities are large and events are rare.

Evaluating treatment effects in group sequential multivariate longitudinal studies with covariate adjustment

Jeffries et al. (2018) investigated testing for a treatment difference in the setting of a randomized clinical trial with a single outcome measured longitudinally over a series of common follow-up times while adjusting for covariates. That paper examined the null hypothesis of no difference at any follow-up time versus the alternative of a difference for at least one follow-up time. We extend those results here by considering multivariate outcome measurements, where each individual outcome is examined at common follow-up times. We consider the case where there is interest in first testing for a treatment difference in a global function of the outcomes (e.g., weighted average or sum) with subsequent interest in examining the individual outcomes, should the global function show a treatment difference. Testing is conducted for each follow-up time and may be performed in the setting of a group sequential trial. Testing procedures are developed to determine follow-up times for which a global treatment difference exists and which individual combinations of outcome and follow-up time show evidence of a difference while controlling for multiplicity in outcomes, follow-up, and interim analyses. These approaches are examined in a study evaluating the effects of tissue plasminogen activator on longitudinally obtained stroke severity measurements.

Socioeconomic Status and Vision Care Services in Ontario, Canada: A Population-Based Cohort Study

OBJECTIVE

To test the association of material deprivation and the utilization of vision care services for young children.

STUDY DESIGN

We conducted a population-based, repeated measures cohort study using linked health and administrative datasets. All children born in Ontario in 2010 eligible for provincial health insurance were followed from birth until their seventh birthday. The main exposure was neighborhood-level material deprivation quintile, a proxy for socioeconomic status. The primary outcome was receipt of a comprehensive eye examination (not to include a vision screening) by age 7 years from an eye care professional, or family physician.

RESULTS

Of 128 091 children included, female children represented 48.7% of the cohort, 74.4% lived in major urban areas, and 16.2% lived in families receiving income assistance. Only 65% (n = 82 833) had at least 1 comprehensive eye examination, with the lowest uptake (56.9%; n = 31 911) in the most deprived and the highest uptake (70.5%; n =19 860) in the least deprived quintiles. After adjusting for clinical and demographic variables, children living in the least materially deprived quintile had a higher odds of receiving a comprehensive eye examination (aOR 1.43; 95% CI 1.36, 1.51) compared with children in the most materially deprived areas.

CONCLUSIONS

Uptake of comprehensive eye examinations is poor, especially for children living in the most materially deprived neighborhoods. Strategies to improve uptake and reduce inequities are warranted.

A note on the estimation and inference with quadratic inference functions for correlated outcomes

The quadratic inference function approach is a popular method in the analysis of correlated data. The quadratic inference function is formulated based on multiple sets of score equations (or extended score equations) that over-identify the regression parameters of interest, and improves efficiency over the generalized estimating equations under correlation misspecification. In this note, we provide an alternative solution to the quadratic inference function by separately solving each set of score equations and combining the solutions. We provide an insight that an optimally weighted combination of estimators obtained separately from the distinct sets of score equations is asymptotically equivalent to the estimator obtained via the quadratic inference function. We further establish results on inference for the optimally weighted estimator and extend these insights to the general setting with over-identified estimating equations. A simulation study is carried out to confirm the analytical insights and connections in finite samples.

Measuring Changes in Perceptions of Access to Pet Support Care in Underserved Communities

Understanding social, economic, and structural barriers to accessing pet care services is important for improving the health and welfare of companion animals in underserved communities in the U.S. From May 2018-December 2019, six questions from the validated One Health Community Assessment were used to measure perceptions of access to pet care in two urban and two rural zip codes. One urban and one rural community received services from a pet support outreach program (Pets for Life), while the other served as a comparison community. After propensity score matching was performed to eliminate demographic bias in the sample (Urban = 512 participants, Rural = 234 participants), Generalized Estimating Equations were employed to compare the six measures of access to pet care between the intervention and comparison communities. The urban community with the Pets for Life intervention was associated with a higher overall measure of access to pet care compared to the urban site that did not have the Pets for Life intervention. When assessing each of the six measures of access to care, the urban community with the Pets for Life intervention was associated with higher access to affordable pet care options and higher access to pet care service providers who offer payment options than the community without the Pets for Life intervention. Further analyses with a subset of Pets for Life clients comparing pre-intervention and post-intervention survey responses revealed statistically significant positive trends in perceptions of two of the six measures of access to pet care. This study provides evidence that community-based animal welfare programming has the potential to increase perceptions of access to pet support services.

Power calculation for analyses of cross-sectional stepped-wedge cluster randomized trials with binary outcomes via generalized estimating equations

Power calculation for stepped-wedge cluster randomized trials (SW-CRTs) presents unique challenges, beyond those of standard parallel cluster randomized trials, due to the need to consider temporal within cluster correlations and background period effects. To date, power calculation methods specific to SW-CRTs have primarily been developed under a linear model. When the outcome is binary, the use of a linear model corresponds to assessing a prevalence difference; yet trial analysis often employs a nonlinear link function. We propose power calculation methods for cross-sectional SW-CRTs under a logistic model fitted by generalized estimating equations. Firstly, under an exchangeable correlation structure, we show the power based on a logistic model is lower than that from assuming a linear model in the absence of period effects. We then evaluate the impact of background prevalence changes over time on power. To allow the correlation among outcomes in the same cluster to change over time and with treatment status, we generalize the methods to more complex correlation structures. Our simulation studies demonstrate that the proposed power calculation methods perform well with the model-based variance under the true correlation structure and reveal that a working independence structure can result in substantial efficiency loss, while a working exchangeable structure performs well even when the underlying correlation structure deviates from exchangeable. An extension to our methods accounts for variable cluster sizes and reveals that unequal cluster sizes have a modest impact on power. We illustrate the approaches by application to a quality of care improvement trial for acute coronary syndrome.

Predictive generalized varying-coefficient longitudinal model

We propose a nonparametric bivariate varying coefficient generalized linear model to predict a mean response trajectory in the future given an individual's characteristics at present or an earlier time point in a longitudinal study. Given the measurement time of the predictors, the coefficients vary as functions of the future time over which the prediction of the mean response is concerned and illustrate the dynamic association between the future response and the earlier measured predictors. We use a nonparametric approach that takes advantage of features of both the kernel and the spline methods for estimation. The resulting coefficient estimator is asymptotically consistent under mild regularity conditions. We also develop a new bootstrap approach to construct simultaneous confidence bands for statistical inference about the coefficients and the predicted response trajectory based on the coverage rate of bootstrap estimates. We use the Framingham Heart Study to illustrate the methodology. The proposed procedure is applied to predict the probability trajectory of hypertension risk given individuals' health condition in early adulthood and to examine the impact of risk factors in early adulthood on a long-term risk of hypertension over several decades.

Power and sample size calculations for cluster randomized trials with binary outcomes when intracluster correlation coefficients vary by treatment arm

BACKGROUND/AIMS

Generalized estimating equations are commonly used to fit logistic regression models to clustered binary data from cluster randomized trials. A commonly used correlation structure assumes that the intracluster correlation coefficient does not vary by treatment arm or other covariates, but the consequences of this assumption are understudied. We aim to evaluate the effect of allowing variation of the intracluster correlation coefficient by treatment or other covariates on the efficiency of analysis and show how to account for such variation in sample size calculations.

METHODS

We develop formulae for the asymptotic variance of the estimated difference in outcome between treatment arms obtained when the true exchangeable correlation structure depends on the treatment arm and the working correlation structure used in the generalized estimating equations analysis is: (i) correctly specified, (ii) independent, or (iii) exchangeable with no dependence on treatment arm. These formulae require a known distribution of cluster sizes; we also develop simplifications for the case when cluster sizes do not vary and approximations that can be used when the first two moments of the cluster size distribution are known. We then extend the results to settings with adjustment for a second binary cluster-level covariate. We provide formulae to calculate the required sample size for cluster randomized trials using these variances.

RESULTS

We show that the asymptotic variance of the estimated difference in outcome between treatment arms using these three working correlation structures is the same if all clusters have the same size, and this asymptotic variance is approximately the same when intracluster correlation coefficient values are small. We illustrate these results using data from a recent cluster randomized trial for infectious disease prevention in which the clusters are groups of households and modest in size (mean 9.6 individuals), with intracluster correlation coefficient values of 0.078 in the control arm and 0.057 in an intervention arm. In this application, we found a negligible difference between the variances calculated using structures (i) and (iii) and only a small increase (typically <5%) for the independent correlation structure (ii), and hence minimal effect on power or sample size requirements. The impact may be larger in other applications if there is greater variation in the ICC between treatment arms or with an additional covariate.

CONCLUSION

The common approach of fitting generalized estimating equations with an exchangeable working correlation structure with a common intracluster correlation coefficient across arms likely does not substantially reduce the power or efficiency of the analysis in the setting of a large number of small or modest-sized clusters, even if the intracluster correlation coefficient varies by treatment arm. Our formulae, however, allow formal evaluation of this and may identify situations in which variation in intracluster correlation coefficient by treatment arm or another binary covariate may have a more substantial impact on power and hence sample size requirements.

Impact of unequal cluster sizes for GEE analyses of stepped wedge cluster randomized trials with binary outcomes

The stepped wedge (SW) design is a type of unidirectional crossover design where cluster units switch from control to intervention condition at different prespecified time points. While a convention in study planning is to assume the cluster‐period sizes are identical, SW cluster randomized trials (SW‐CRTs) involving repeated cross‐sectional designs frequently have unequal cluster‐period sizes, which can impact the efficiency of the treatment effect estimator. In this paper, we provide a comprehensive investigation of the efficiency impact of unequal cluster sizes for generalized estimating equation analyses of SW‐CRTs, with a focus on binary outcomes as in the Washington State Expedited Partner Therapy trial. Several major distinctions between our work and existing work include the following: (i) we consider multilevel correlation structures in marginal models with binary outcomes; (ii) we study the implications of both the between‐cluster and within‐cluster imbalances in sizes; and (iii) we provide a comparison between the independence working correlation versus the true working correlation and detail the consequences of ignoring correlation estimation in SW‐CRTs with unequal cluster sizes. We conclude that the working independence assumption can lead to substantial efficiency loss and a large sample size regardless of cluster‐period size variability in SW‐CRTs, and recommend accounting for correlations in the analysis. To improve study planning, we additionally provide a computationally efficient search algorithm to estimate the sample size in SW‐CRTs accounting for unequal cluster‐period sizes, and conclude by illustrating the proposed approach in the context of the Washington State study.

Parents' right strategy on preventing youngsters' recent suicidal ideation: a 13-year prospective cohort study

BACKGROUND

Suicide remains the second leading cause of death among youths. Family-related factors are considered important determinants of children's suicidal ideation, whereas their short-/long-term influence is seldom quantified.

AIMS

We aim to confirm the simultaneous/lagged effects of family-related factors on the occurrence of recent suicidal ideation from childhood to young adulthood (aged from 10 to 22 years old).

METHOD

Data were derived from a longitudinal prospective cohort study. Participants included 2065 students who were followed up for 13 years. Generalized estimating equations were used to clarify the influential effects of family-related factors on suicidal ideation during the past month.

RESULTS

The peak of the rate of recent suicidal ideation arrived during junior high school years. Family interaction, family support, family involvement, and parental punishment had simultaneous effects on recent suicidal ideation. Family involvement, parental conflict, and psychological control had lagged and lasting effects on suicidal ideation. Notably, the lasting protective effects of family involvement were more obvious than simultaneous effects.

CONCLUSIONS

Providing parents with sustained support and education to improve their "positive parenting literacy" can help with their children's mental health development. This is especially the case during COVID-19 quarantine periods when families spend the most time together at home.

The influence of external load variables on creatine kinase change during preseason training period

Objective

The aim of the present study was to analyse the relationships between creatine kinase (CK) concentration, an indirect marker of muscle damage, and global positioning system (GPS)-derived metrics of a continuous two-week-long preseason training period in elite football.

Design

Twenty-one elite male professional soccer players were assessed during a 14-day preseason preparatory period. CK concentrations were determined each morning, and a GPS system was used to quantify the external load. A generalized estimating equation (GEE) model was established to determine the extent to which the external load parameter explained post-training CK levels.

Results

The GEE model found that higher numbers of decelerations (χ 2 = 7.83, P = 0.005) were most strongly associated with the post-training CK level. Decelerations and accelerations accounted for 62% and 11% of the post-training CK level, respectively, and considerable interindividual variability existed in the data.

Conclusion

The use of GPS to predict muscle damage could be of use to coaches and practitioners in prescribing recovery practices. Based on GPS data, more individualized strategies could be devised and could potentially result in better subsequent performance.

Critical windows of fluoride neurotoxicity in Canadian children

BACKGROUND

Fluoride has been associated with IQ deficits during early brain development, but the period in which children are most sensitive is unknown.

OBJECTIVE

We assessed effects of fluoride on IQ scores across prenatal and postnatal exposure windows.

METHODS

We used repeated exposures from 596 mother-child pairs in the Maternal-Infant Research on Environmental Chemicals pregnancy and birth cohort. Fluoride was measured in urine (mg/L) collected from women during pregnancy and in their children between 1.9 and 4.4 years; urinary fluoride was adjusted for specific gravity. We estimated infant fluoride exposure (mg/day) using water fluoride concentration and duration of formula-feeding over the first year of life. Intelligence was assessed at 3-4 years using the Wechsler Preschool and Primary Scale of Intelligence-III. We used generalized estimating equations to examine the associations between fluoride exposures and IQ, adjusting for covariates. We report results based on standardized exposures given their varying units of measurement.

RESULTS

The association between fluoride and performance IQ (PIQ) significantly differed across prenatal, infancy, and childhood exposure windows collapsing across child sex (p = .001). The strongest association between fluoride and PIQ was during the prenatal window, B = -2.36, 95% CI: -3.63, -1.08; the association was also significant during infancy, B = -2.11, 95% CI: -3.45, -0.76, but weaker in childhood, B = -1.51, 95% CI: -2.90, -0.12. Within sex, the association between fluoride and PIQ significantly differed across the three exposure windows (boys: p = .01; girls: p = .01); among boys, the strongest association was during the prenatal window, B = -3.01, 95% CI: -4.60, -1.42, whereas among girls, the strongest association was during infancy, B = -2.71, 95% CI: -4.59, -0.83. Full-scale IQ estimates were weaker than PIQ estimates for every window. Fluoride was not significantly associated with Verbal IQ across any exposure window.

CONCLUSION

Associations between fluoride exposure and PIQ differed based on timing of exposure. The prenatal window may be critical for boys, whereas infancy may be a critical window for girls.

Fitting marginal models in small samples: A simulation study of marginalized multilevel models and generalized estimating equations

In correlated data settings, analysts typically choose between fitting conditional and marginal models, whose parameters come with distinct interpretations, and as such the choice between the two should be made on scientific grounds. For settings where interest lies in marginal-or population-averaged-parameters, the question of how best to estimate those parameters is a statistical one, and analysts have at their disposal two distinct modeling frameworks: generalized estimating equations (GEE) and marginalized multilevel models (MMMs). The two have been contrasted theoretically and in large sample settings, but asymptotic theory provides no guarantees in the small sample settings that are commonplace. In a comprehensive series of simulation studies, we shed light on the relative performance of GEE and MMMs in small-sample settings to help guide analysis decisions in practice. We find that both GEE and MMMs exhibit similar small-sample bias when the correct correlation structure is adopted (ie, when the random effects distribution is correctly specified or moderately misspecified)-but MMMs can be sensitive to misspecification of the correlation structure. When there are a small number of clusters, MMMs only slightly underestimate standard errors (SEs) for within-cluster associations but can severely underestimate SEs for between-cluster associations. By contrast, while GEE severely underestimates SEs, the Mancl and DeRouen correction provides approximately valid inference.

Optimal allocation in stratified cluster-based outcome-dependent sampling designs

In public health research, finite resources often require that decisions be made at the study design stage regarding which individuals to sample for detailed data collection. At the same time, when study units are naturally clustered, as patients are in clinics, it may be preferable to sample clusters rather than the study units, especially when the costs associated with travel between clusters are high. In this setting, aggregated data on the outcome and select covariates are sometimes routinely available through, for example, a country's Health Management Information System. If used wisely, this information can be used to guide decisions regarding which clusters to sample, and potentially obtain gains in efficiency over simple random sampling. In this article, we derive a series of formulas for optimal allocation of resources when a single-stage stratified cluster-based outcome-dependent sampling design is to be used and a marginal mean model is specified to answer the question of interest. Specifically, we consider two settings: (i) when a particular parameter in the mean model is of primary interest; and, (ii) when multiple parameters are of interest. We investigate the finite population performance of the optimal allocation framework through a comprehensive simulation study. Our results show that there are trade-offs that must be considered at the design stage: optimizing for one parameter yields efficiency gains over balanced and simple random sampling, while resulting in losses for the other parameters in the model. Optimizing for all parameters simultaneously yields smaller gains in efficiency, but mitigates the losses for the other parameters in the model.

Sample size and power considerations for cluster randomized trials with count outcomes subject to right truncation

Cluster randomized trials (CRTs) are widely used in epidemiological and public health studies assessing population-level effect of group-based interventions. One important application of CRTs is the control of vector-borne disease, such as malaria. However, a particular challenge for designing these trials is that the primary outcome involves counts of episodes that are subject to right truncation. While sample size formulas have been developed for CRTs with clustered counts, they are not directly applicable when the counts are right truncated. To address this limitation, we discuss two marginal modeling approaches for the analysis of CRTs with truncated counts and develop two corresponding closed-form sample size formulas to facilitate the design of such trials. The proposed sample size formulas allow investigators to explore the power under a large number of scenarios without computationally intensive simulations. The proposed formulas are validated in extensive simulations. We further explore the implication of right truncation on power and apply the proposed formulas to illustrate the power calculation for a malaria control CRT where the primary outcome is subject to right truncation.

Differential COVID-19 case positivity in New York City neighborhoods: Socioeconomic factors and mobility

BACKGROUND

New York City (NYC) has been one of the hotspots of the COVID-19 pandemic in the United States. By the end of April 2020, close to 165 000 cases and 13 000 deaths were reported in the city with considerable variability across the city's ZIP codes.

OBJECTIVES

In this study, we examine: (a) the extent to which the variability in ZIP code-level case positivity can be explained by aggregate markers of socioeconomic status (SES) and daily change in mobility; and (b) the extent to which daily change in mobility independently predicts case positivity.

METHODS

COVID-19 case positivity by ZIP code was modeled using multivariable linear regression with generalized estimating equations to account for within-ZIP clustering. Daily case positivity was obtained from NYC Department of Health and Mental Hygiene and measures of SES were based on data from the American Community Survey. Changes in human mobility were estimated using anonymized aggregated mobile phone location systems.

RESULTS

Our analysis indicates that the socioeconomic markers considered together explained 56% of the variability in case positivity through April 1 and their explanatory power decreased to 18% by April 30. Changes in mobility during this time period are not likely to be acting as a mediator of the relationship between ZIP-level SES and case positivity. During the middle of April, increases in mobility were independently associated with decreased case positivity.

CONCLUSIONS

Together, these findings present evidence that heterogeneity in COVID-19 case positivity during NYC's spring outbreak was largely driven by residents' SES.

The first-order Markov conditional linear expectation approach for analysis of longitudinal data

We consider longitudinal discrete data that may be unequally spaced in time and may exhibit overdispersion, so that the variance of the outcome variable is inflated relative to its assumed distribution. We implement an approach that extends generalized linear models for analysis of longitudinal data and is likelihood based, in contrast to generalized estimating equations (GEE) that are semiparametric. The method assumes independence between subjects; first-order antedependence within subjects; exponential family distributions for the first outcome on each subject and for the subsequent conditional distributions; and linearity of the expectations of the conditional distributions. We demonstrate application of the method in an analysis of seizure counts and in a study to evaluate the performance of transplant centers. Simulations for both studies demonstrate the benefits of the proposed likelihood based approach; however, they also demonstrate better than anticipated performance for GEE.

Small-sample inference for cluster-based outcome-dependent sampling schemes in resource-limited settings: Investigating low birthweight in Rwanda

The neonatal mortality rate in Rwanda remains above the United Nations Sustainable Development Goal 3 target of 12 deaths per 1000 live births. As part of a larger effort to reduce preventable neonatal deaths in the country, we conducted a study to examine risk factors for low birthweight. The data were collected via a cost-efficient cluster-based outcome-dependent sampling (ODS) scheme wherein clusters of individuals (health centers) were selected on the basis of, in part, the outcome rate of the individuals. For a given data set collected via a cluster-based ODS scheme, estimation for a marginal model may proceed via inverse-probability-weighted generalized estimating equations, where the cluster-specific weights are the inverse probability of the health center's inclusion in the sample. In this paper, we provide a detailed treatment of the asymptotic properties of this estimator, together with an explicit expression for the asymptotic variance and a corresponding estimator. Furthermore, motivated by the study we conducted in Rwanda, we propose a number of small-sample bias corrections to both the point estimates and the standard error estimates. Through simulation, we show that applying these corrections when the number of clusters is small generally reduces the bias in the point estimates, and results in closer to nominal coverage. The proposed methods are applied to data from 18 health centers and 1 district hospital in Rwanda.

Using Multiple Imputation with GEE with Non-monotone Missing Longitudinal Binary Outcomes

This paper considers multiple imputation (MI) approaches for handling non-monotone missing longitudinal binary responses when estimating parameters of a marginal model using generalized estimating equations (GEE). GEE has been shown to yield consistent estimates of the regression parameters for a marginal model when data are missing completely at random (MCAR). However, when data are missing at random (MAR), the GEE estimates may not be consistent; the MI approaches proposed in this paper minimize bias under MAR. The first MI approach proposed is based on a multivariate normal distribution, but with the addition of pairwise products among the binary outcomes to the multivariate normal vector. Even though the multivariate normal does not impute 0 or 1 values for the missing binary responses, as discussed by Horton et al. (Am Stat 57:229-232, 2003), we suggest not rounding when filling in the missing binary data because it could increase bias. The second MI approach considered is the fully conditional specification (FCS) approach. In this approach, we specify a logistic regression model for each outcome given the outcomes at other time points and the covariates. Typically, one would only include main effects of the outcome at the other times as predictors in the FCS approach, but we explore if bias can be reduced by also including pairwise interactions of the outcomes at other time point in the FCS. In a study of asymptotic bias with non-monotone missing data, the proposed MI approaches are also compared to GEE without imputation. Finally, the proposed methods are illustrated using data from a longitudinal clinical trial comparing four psychosocial treatments from the National Institute on Drug Abuse Collaborative Cocaine Treatment Study, where patients' cocaine use is collected monthly for 6 months during treatment.

A robust and unified framework for estimating heritability in twin studies using generalized estimating equations

The 'heritability' of a phenotype measures the proportion of trait variance due to genetic factors in a population. In the past 50 years, studies with monozygotic and dizygotic twins have estimated heritability for 17,804 traits;¹ thus twin studies are popular for estimating heritability. Researchers are often interested in estimating heritability for non-normally distributed outcomes such as binary, counts, skewed or heavy-tailed continuous traits. In these settings, the traditional normal ACE model (NACE) and Falconer's method can produce poor coverage of the true heritability. Therefore, we propose a robust generalized estimating equations (GEE2) framework for estimating the heritability of non-normally distributed outcomes. The traditional NACE and Falconer's method are derived within this unified GEE2 framework, which additionally provides robust standard errors. Although the traditional Falconer's method cannot adjust for covariates, the corresponding 'GEE2-Falconer' can incorporate mean and variance-level covariate effects (e.g. let heritability vary by sex or age). Given a non-normally distributed outcome, the GEE2 models are shown to attain better coverage of the true heritability compared to traditional methods. Finally, a scenario is demonstrated where NACE produces biased estimates of heritability while Falconer remains unbiased. Therefore, we recommend GEE2-Falconer for estimating the heritability of non-normally distributed outcomes in twin studies.

Risk factors for hospitalization in youth with type 1 diabetes: Development and validation of a multivariable prediction model

OBJECTIVE

To develop a multivariable prediction model to identify patients with type 1 diabetes at increased risk of hospitalization for diabetic ketoacidosis or hyperglycemia with ketosis in the 12 months following assessment.

METHODS

Retrospective review of clinical data from patients with type 1 diabetes less than 17 years old at a large academic children's hospital (5732 patient years, 652 admissions). Data from the previous 12 months were assessed on October 15, 2015, 2016, 2017, and 2018, and used to predict hospitalization in the following 12 months using generalized estimating equations. Variables that were significant predictors of hospitalization in univariate analyses were entered into a multivariable model. 2014 to 2016 data were used as a training dataset, and 2017 to 2019 data for validation. Discrimination of the model was assessed with receiver operator characteristic curves.

RESULTS

Admission in the preceding year, hemoglobin (Hb)A1c, non-commercial insurance, female sex, and non-White race were all individual predictors of hospitalization, but age, duration of diabetes and number of office visits in the preceding year were not. In multivariable analysis with threshold P < .0033, admissions in the previous 12 months, HbA1c, and non-commercial insurance remained as significant predictors. The model identified a subset of ~8% of the patients with a collective 42% risk of hospitalization, thus increased 5-fold compared with the 8% risk of hospitalization in the remaining 93% of patients. Similar results were obtained with the validation dataset.

CONCLUSION

Our multivariable prediction model identified patients at increased risk of admission in the 12 months following assessment.

A trait-like propensity to experience internalizing symptoms is associated with problem alcohol involvement across adulthood, but not adolescence

There are stable between-person differences in an internalizing "trait," or the propensity to experience symptoms of internalizing disorders, such as social anxiety, generalized anxiety disorder, and depression. Trait internalizing may serve as a marker of heightened risk for problem alcohol outcomes (such as heavier drinking, binge drinking, or alcohol dependence). However, prior research on the association between internalizing symptoms and alcohol outcomes has been largely mixed in adolescence, with more consistent support for an association during adulthood. It may be that trait internalizing is only associated with problem alcohol outcomes in adulthood, after individuals have gained experience with alcohol. Some evidence suggested that these effects may be stronger for women than men. We used data from a community sample (n = 790) interviewed during adolescence (ages 14-16) and again at ages 21, 24, 27, 30, 33, and 39. Using generalized estimating equations, we tested the association between trait internalizing and alcohol outcomes during both adolescence and adulthood, and tested whether adult trait internalizing mediated the association between adolescent trait internalizing and adult alcohol outcomes. Trait internalizing in adulthood (but not adolescence) was associated with more frequent alcohol use, binge drinking and symptoms of alcohol use disorders, and mediated the effects of adolescent trait internalizing on alcohol outcomes. We observed no moderation by gender or change in these associations over time. Understanding the developmental pathways of trait internalizing may provide further insights into preventing the emergence of problem alcohol use behavior during adulthood. (PsycInfo Database Record (c) 2020 APA, all rights reserved).