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.