Variance Estimation Research Articles

Impact of Refeeding Syndrome on the Short-Term Clinical Outcomes of Very-Premature Infants.

Refeeding syndrome (RFS) is a potentially life-threatening condition that can occur in preterm infants if nutritional support is initiated or increased after a period of starvation or malnutrition. The current study aimed to examine the short-term clinical outcomes of RFS in preterm infants born at ≤32 weeks of gestation. Infants with a gestational age of ≤32 weeks and a birth weight of <1500 g who were born and admitted to the level III neonatal intensive care unit and received parenteral nutrition upon admission were retrospectively evaluated. The modified log Poisson regression with generalized linear models and a robust variance estimator was applied to adjust the outcomes of infants. In total, 760 infants met this study's inclusion criteria. Of them, 289 (38%) developed RFS. RFS was significantly associated with a composite outcome of mortality and intraventricular hemorrhage. Based on the multivariate Cox regression analysis adjusted for significant potential confounders, RFS was significantly associated with increased mortality risk, with a hazard ratio for death in infants with RFS being 1.74-fold higher compared to those without RFS. Preterm infants born at ≤32 weeks of gestation who develop RFS within the first week of life are at increased risk for both intraventricular hemorrhage and mortality. This study underscores the need for standardized clinical approaches for managing RFS in the neonatal intensive care unit to improve outcomes. Future research should establish a unified RFS definition and conduct clinical trials to optimize parenteral nutrition strategies for this vulnerable population.

COMPARATIVE STUDY OF RESIDUAL VARIANCE ESTIMATORS CONSTRUCTED WITHOUT OR WITH THE PRESENCE OF ATYPICAL VALUES: CASE OF THE PARTIALLY LINEAR MODEL

Error variance is a measure of the goodness of fit for a regression model. Ahoutou et al. [1] proposed estimators of the error variance under the assumption that the dimension of the nonlinear covariate is one. In this paper, assuming that the dimension of the nonlinear covariate is greater than or equal to 2, we propose estimators of error variance in homogeneous and heterogeneous cases. We propose estimators of the error variance that are constructed without taking atypical values into account and others that are constructed by taking all the data into account. Using simulations, we compare the performance of estimators designed without taking into account atypical values with estimators designed taking into account all the data.

The Effects of Morphological Instruction on Literacy Outcomes for Children in English-Speaking Countries: A Systematic Review and Meta-Analysis

In this pre-registered meta-analysis, we investigated the effectiveness of morphology instruction on literacy outcomes for primary school children in English-speaking countries. We were interested in overall reading and spelling outcomes, but we also looked separately at results for trained and untrained words in order to determine whether there was evidence of transfer to untrained words. Further, we were interested in whether results transferred beyond the word level to reading comprehension outcomes. Our screening process revealed 28 eligible studies, which contributed 177 effect sizes to the analyses. Robust variance estimation methods were used to account for dependence between effect sizes. Overall, effect sizes on reading and spelling outcomes were small to moderate. Effect sizes were larger for trained words than untrained words. There was evidence of transfer to untrained words for spelling outcomes, but not for reading outcomes. There was also no clear evidence of effects on reading comprehension outcomes. In general, the evidence was characterised by large amounts of heterogeneity and imprecision, which was reflective of the wide variety within and between studies in terms of intervention content, outcome measures, intervention dosage and type of control group. We discuss the limitations of the current literature and make recommendations for future research and practice in the field of morphology instruction. (207 words – max 250).

Association of early dysglycemia with intraventricular hemorrhage and mortality in very low birth weight infants.

To investigate the combined effect of hyperglycemia and hypoglycemia on intraventricular hemorrhage (IVH) and mortality recognizing that previous research has predominantly focused on examining these conditions independently. This study included very preterm infants who were born at King Saud Medical City, a tertiary referral center, and admitted to a level 3 neonatal intensive care unit between January 2020 and January 2024. Modified log-Poisson regression with generalized linear models and a robust variance estimator (Huber-White) were used to adjust for potential confounding factors. A total of 554 infants met the inclusion criteria. Hyperglycemia and/or hypoglycemia developed in 75.5% (418) patients within the first postnatal week. During the study period, IVH occurred in 28.5% (N = 158), and severe IVH occurred in 13% (72) infants. In addition, 13.7% (76) of infants died during the study period. The multivariate regression revealed an association between the isolated hyperglycemia, combined exposure of hypo- and hyperglycemia, and development of IVH (relative risk [RR], 2.10; 95% confidence interval [CI], 1.36, 3.25; RR, 2.33; 95% CI, 1.34, 4.06, respectively). Severe IVH was significantly associated with isolated hyperglycemia (adjusted relative risk [aRR], 2.46; 95% CI, 1.16, 5.23). Death was associated with combined hypo- and hyperglycemia (adjusted hazardous ratio [aHR], 3.19; 95% CI, 1.23, 8.26).Conclusion: Combined hyper- and hypoglycemia in the first week of life of premature babies increases the risk and severity of IVH and neonatal mortality.

On approximate equality of Z-values of the statistical tests for win statistics (win ratio, win odds, and net benefit)

ABSTRACT Dong et al. (2023) showed that the win statistics (win ratio, win odds, and net benefit) can complement each another to demonstrate the strength of treatment effects in randomized trials with prioritized multiple outcomes. This result was built on the connections among the point and variance estimates of the three statistics, and the approximate equality of Z-values in their statistical tests. However, the impact of this approximation was not clear. This Discussion refines this approach and shows that the approximate equality of Z-values for the win statistics holds more generally. Thus, the three win statistics consistently yield closely similar p-values. In addition, our simulations show an example that the naive approach without adjustment for censoring bias may produce a completely opposite conclusion from the true results, whereas the IPCW (inverse-probability-of-censoring weighting) approach can effectively adjust the win statistics to the corresponding true values (i.e. IPCW-adjusted win statistics are unbiased estimators of treatment effect).

Children's Selective Teaching and Informing: A Meta-Analysis.

Empirical studies on selective teaching and informing indicate that children may vary what they teach depending on whom they are teaching, taking into account how helpful the information is for a given audience. The current meta-analysis quantifies the effect of selective informing and teaching in 2-7-year-olds by examining the relationship between the helpfulness of the information and the frequency of information transmission. Through a systematic search that yielded 1483 results, 28 studies (104 effect sizes, N=2716) met the inclusion criteria. Using robust variance estimation, we found a medium average effect, Hedges' g=0.578, 95% CI (0.331, 0.825), suggesting that children selectively share information based on its perceived helpfulness to the listener. Moderator analyses revealed that age and communicative context were significant factors. Children were more informative in their communication when asked to teach compared to other nonpedagogical prompts. This finding supports and extends natural pedagogy theory-young children not only interpret pedagogical information differently than information acquired through other means, but they are more selective in their informing when teaching. Additionally, we observed a key developmental progression at age 4. Four- to 7-year-olds, but not 2-3-year-olds, selectively shared information that was most helpful for a given learner. This coincides with the development of false-belief understanding, which undergoes significant development at around age 4. Taken together, the present synthesis suggests that young children actively engage in selective social learning from both sides, that of beneficiaries and benefactors of valuable information.

Genetic parameters for direct and maternal genetic components of calving ease in Korean Holstein Cattle using animal models.

We investigated genetic parameters of calving ease (CE) using several animal models in Korean Holstein and searched for suitable models for routine evaluation of CE. Two phenotypic datasets of CE on first-parity Korean Holstein calves were prepared. DS5 and DS10 included at least 5 and 10 CE records per herd-year level and comprised 117,921 and 80,389 observations, respectively. The CE phenotypes ranged from 1 to 4, from a normal to extreme difficulty calving scale. The CE was defined as a trait of the calf. The BLUPF90+ software was used for (co)variances estimation through four animal models with a maternal effect (M1 to M4), where all models included effects of a fixed calf-sex, a fixed dam calving age (covariate), and one or more fixed contemporary group (CG) terms. The CG effects were different across models- a herd-year-season (M1, HYS), a herd-year and year-season (M2, HY+YS), a herd-year and season (M3, HY+S), and a herd and year-season (M4, H+YS). Direct heritability (h2) estimates of CE ranged from 0.005 to 0.234 across models and datasets. Maternal h2 values were low (0.001 to 0.090). Genetic correlations between direct and maternal effects were strongly negative to lowly positive (-0.814 to 0.078), further emphasizing its importance in CE evaluation models. These genetic parameter estimates also indicate slower future selection progress of CE in Korean Holsteins. The M1 fitted many levels with fewer observations per level deriving unreliable parameters, and the M4 did not account for confounded herd and animal structures. The M2 and M3 were deemed more realistic for implementation, and they were better able to account for data structure issues (incompleteness and confounding) than other models. As the pioneering study to employ animal models in Korean Holstein CE evaluation, our findings hold significant potential for this breed's future and routine evaluation development.

Methods for estimating integrated variance: Jump robustness issues in high frequency time series

Integrated variance is a volatility measure of a process in continuous time, which is applicable in financial mathematics as a means to optimize a portfolio, project dynamics of a price of a financial asset. The consistency of an estimator for integrated variance of a random process is at the core of this article. A fundamental diffusion process is extended by adding a jump component as a means of improving the descriptive function of the process. It is activity of jumps that is a factor subject to which is the consistency of the estimator for integrated variance. Due to this fact, consistency is defined as an extent to which the estimator at hand is jump robust. Two main methods for estimating integrated variance are considered and the capacity of corresponding estimators to withstand the effect of jumps while converging is briefly analyzed. The arguments indicating a necessity for further research of the effect of jumps with reference to works of the authors who have established a ground for analysis of integrated variance and those works containing main asymptotic results for consistency of integrated variance estimators are elaborated. Based on this, avenue for further research and development of asymptotic theory for consistency of an estimator for integrated variance is identified.

Non-negative least-squares variance and covariance component estimation using the positive-valued function for errors-in-variables models

Abstract Although (co)variance component estimation has been widely applied in the errors-in-variables (EIV) model, the occurrence of negative variance components is still a major issue in the estimated variance components. This problem may be due to the following unfavorable factors: 1) unreasonable selection of initial variance values; 2) low redundancy in the EIV functional model; 3) improper design in the EIV stochastic model, and 4) other data quality problems. Many attempts have been made to prevent the appearance of negative variance components. In this contribution, a novel and efficient non-negative least-squares variance component estimation using the PVF (PVF-NLS-VCE) is introduced, which can simultaneously estimate the unknown (co)variance components in the EIV stochastic model and the parameters in the EIV functional model. Its principle is to implicitly impose a non-negative constraint by replacing the variance component with the positive-valued function (PVF) whose range is the set of positive real numbers. Two numerical examples using real and simulated data are presented. The numerical results of linear regression are identical to those obtained based on least-squares variance component estimation (LS-VCE) with positive initial values of variance components. The numerical results of two-dimensional affine transformation are shown to prevent negative variance components and precede those obtained by LS-VCE with a negative initial value of variance component. Both numerical examples verify the effectiveness of the PVF-NLS-VCE method whether the initial values of variance components are positive or negative. The proposed PVF-NLS-VCE is a simple, convenient and flexible method to achieve the non-negative estimates of variance components, which can reduce sensitivity to initial value selection and automatically guarantee a non-negative definite covariance matrix.

Trends and determinants of clustering for non-communicable disease risk factors in women of reproductive age in Nepal.

Understanding the clustering of two or more risk factors of non-communicable disease, such as smoking, overweight/obesity, and hypertension, among women of reproductive age could facilitate the design and implementation of strategies for prevention and control measures. This study examined the factors associated with smoking, overweight/obesity, and hypertension among Nepalese women of reproductive age (15-49 years). This study used the Nepal Demographic and Health Surveys (NDHS) 2016 (6,079 women for smoking and overweight/obesity, 6076 for hypertension) and 2022 (6,957 women for overweight/obesity and smoking status and 3,749 women for hypertension) for comparison of trends of NCD risk factors among women aged 15-49 years. Additionally, for each participant, risk factors score (range of 0 to 3) was created by summing individual risk factors. We assessed the determinants of risk factor clustering using multivariable Poisson regression models with robust sandwich variance estimator to calculate adjusted prevalence ratios using NDHS 2022. The national prevalence of overweight/obesity increased from 22.2% in 2016 to 29.2% in 2022 among women of reproductive age. In 2022, the prevalence for smoking, overweight/obesity, and hypertension were 3.8%, 29.2%, and 9.6%, respectively. More than one in four women (28.7%) had one NCD risk factor, while 6.5% had two such risk factors. Higher aged women (40-49 years) were more likely to have multiple NCD risk factors than those aged 15-29 years (APR: 3.19; 95% CI: 2.68-3.80). Those in the richest wealth quintile (APR: 1.52; 95% CI: 1.24-1.85), as well as married (APR: 3.02; 95% CI: 2.43-3.76) and widowed/divorced (APR: 2.85; 95% CI: 2.14-3.80) were more likely to have multiple NCD risk factors. Women from Koshi province (APR: 1.74; 95% CI: 1.41-2.15) had more NCD risk factors than those from the Sudurpaschim province. Working women also had a higher prevalence of NCD risk factors compared to non-working women (APR: 1.23; 95% CI: 1.06-1.43). Additionally, Hill Janajatis (APR: 1.44; 95% CI: 1.21-1.72) and Dalits (APR: 1.42; 95% CI: 1.15-1.75) women were more likely to have NCD risk factors compared to women of Brahmin hill origin. Clustering of two or more NCD risk factors was higher among women aged ≥30 years, those who are currently married or widowed/divorced/separated, working women, and individuals from the wealthiest socioeconomic groups. A higher burden of risk factors underscores the importance of targeted public health interventions, particularly among women from advantaged socio-economic groups, those of affluent regions, and in the workplace.

Modified Calibration Variance Estimators in the Presence of Non- response and Measurement Error

Samples from a population that can be divided into smaller groups are taken using a technique called stratified sampling. When subpopulations within the total population differ, it may be beneficial to sample each stratum (subpopulation) separately in sample surveys. Government organizations, independent consultants, and applied statisticians all frequently use this crucial strategy. There are many problems encountered by survey statisticians in estimating the population variance of the study variable. These problems include the presence of outliers in data collected for analysis, non-response, and measurement errors occurring during the survey. Shahzad et al. [1] developed variance estimators by addressing the problem of outliers using the L-moment and calibration approach. However, they do not consider the situation of non-response and measurement errors. This paper addresses these problems by proposing modified variance estimators in the presence of non-response and measurement errors. The properties (Biases and MSEs) were derived up to the first order of approximation using the Taylor series approach. The efficiency conditions of the modified estimators over the existing estimators considered in the study were established. The result of simulation studies revealed that the estimators are efficient.

Firth-Type Penalized Methods of the Modified Poisson and Least-Squares Regression Analyses for Binary Outcomes.

The modified Poisson and least-squares regression analyses for binary outcomes have been widely used as effective multivariable analysis methods to provide risk ratio and risk difference estimates in clinical and epidemiological studies. However, there is no certain evidence that assessed their operating characteristics under small and sparse data settings and no effective methods have been proposed for these regression analyses to address this issue. In this article, we show that the modified Poisson regression provides seriously biased estimates under small and sparse data settings. In addition, the modified least-squares regression provides unbiased estimates under these settings. We further show that the ordinary robust variance estimators for both of the methods have certain biases under situations that involve small or moderate sample sizes. To address these issues, we propose the Firth-type penalized methods for the modified Poisson and least-squares regressions. The adjustment methods lead to a more accurate and stable risk ratio estimator under small and sparse data settings, although the risk difference estimator is not invariant. In addition, to improve the inferences of the effect measures, we provide an improved robust variance estimator for these regression analyses. We conducted extensive simulation studies to assess the performances of the proposed methods under real-world conditions and found that the accuracies of the point and interval estimations were markedly improved by the proposed methods. We illustrate the effectiveness of these methods by applying them to a clinical study of epilepsy.

Inference in cluster randomized trials with matched pairs

This paper studies inference in cluster randomized trials where treatment status is determined according to a “matched pairs” design. Here, by a cluster randomized experiment, we mean one in which treatment is assigned at the level of the cluster; by a “matched pairs” design, we mean that a sample of clusters is paired according to baseline, cluster-level covariates and, within each pair, one cluster is selected at random for treatment. We study the large-sample behavior of a weighted difference-in-means estimator and derive two distinct sets of results depending on if the matching procedure does or does not match on cluster size. We then propose a single variance estimator which is consistent in either regime. Combining these results establishes the asymptotic exactness of tests based on these estimators. Next, we consider the properties of two common testing procedures based on t-tests constructed from linear regressions, and argue that both are generally conservative in our framework. We additionally study the behavior of a randomization test which permutes the treatment status for clusters within pairs, and establish its finite-sample and asymptotic validity for testing specific null hypotheses. Finally, we propose a covariate-adjusted estimator which adjusts for additional baseline covariates not used for treatment assignment, and establish conditions under which such an estimator leads to strict improvements in precision. A simulation study confirms the practical relevance of our theoretical results.

Ochratoxin A Status at Birth Is Associated with Reduced Birth Weight and Ponderal Index in Rural Burkina Faso

Background: Mycotoxin exposure during pregnancy has been associated with adverse birth outcomes and poor infant growth. We assessed multiple biomarkers and metabolites of exposure to mycotoxins at birth and their associations with birth outcomes and infant growth in 274 newborns in rural Burkina Faso. MethodsWhole-blood microsamples were analyzed for mycotoxin concentrations in newborns in the Biospecimen substudy nested in the MIcronutriments pour la SAnté de la Mère et de l’Enfant-III trial using ultra-performance liquid chromatography coupled with tandem mass spectrometry. Unadjusted and adjusted associations between mycotoxin exposure, and birth outcomes and infant growth at 6 mo were estimated using linear regression models for continuous outcomes and linear probability models with robust variance estimation for binary outcomes. Infant growth trajectories from birth to 6 mo were compared by exposure status using mixed-effects models with a random intercept for the individual infant and a random slope for the infant’s age. ResultsOchratoxin A (OTA) exposure was detected in 38.3% of newborns, with other mycotoxins being detected in the range of 0.36% and 4.01%. OTA exposure was significantly associated with adverse birth outcomes, such as lower birth weight [β (95% CI): −0.11 kg (−0.21, 0.00); P = 0.042] and ponderal index [β (95% CI): −0.62 gm/cm3 (−1.19, −0.05); P = 0.034], and a marginally significant lower length growth trajectories during the first 6 mo [β (95% CI): −0.08 cm/mo (−0.15, 0.0); P = 0.057]. ConclusionsOTA exposure was prevalent among newborns and also associated with lower growth at birth and during the first 6 mo. The results emphasize the importance of nutrition-sensitive strategies to mitigate dietary OTA, as well as adopting food safety measures in Burkina Faso during the fetal period of development.

A Mixed-Effect Kernel Machine Regression Model for Integrative Analysis of Alpha Diversity in Microbiome Studies.

Increasing evidence suggests that human microbiota plays a crucial role in many diseases. Alpha diversity, a commonly used summary statistic that captures the richness and/or evenness of the microbial community, has been associated with many clinical conditions. However, individual studies that assess the association between alpha diversity and clinical conditions often provide inconsistent results due to insufficient sample size, heterogeneous study populations and technical variability. In practice, meta-analysis tools have been applied to integrate data from multiple studies. However, these methods do not consider the heterogeneity caused by sequencing protocols, and the contribution of each study to the final model depends mainly on its sample size (or variance estimate). To combine studies with distinct sequencing protocols, a robust statistical framework for integrative analysis of microbiome datasets is needed. Here, we propose a mixed-effect kernel machine regression model to assess the association of alpha diversity with a phenotype of interest. Our approach readily incorporates the study-specific characteristics (including sequencing protocols) to allow for flexible modeling of microbiome effect via a kernel similarity matrix. Within the proposed framework, we provide three hypothesis testing approaches to answer different questions that are of interest to researchers. We evaluate the model performance through extensive simulations based on two distinct data generation mechanisms. We also apply our framework to data from HIV reanalysis consortium to investigate gut dysbiosis in HIV infection.

Outcomes of pregnancies with varying levels of nuchal translucency measurements: A population-based retrospective study in Ontario, Canada.

Nuchal translucency prenatal ultrasound is widely used to screen for chromosomal abnormalities. An elevated nuchal translucency has been associated with adverse outcomes such as pregnancy loss; however, extant studies investigating these associations have had important limitations, including selection bias. This study aimed to investigate the association between nuchal translucency measurements and pregnancy outcome, specifically, a composite of pregnancy loss, termination, stillbirth, or neonatal death. This was a population-based retrospective cohort study conducted with data from the prescribed perinatal registry in Ontario, Canada, Better Outcomes Registry & Network. All singleton pregnancies with an estimated date of delivery from September 1, 2016, to March 31, 2021, and multiple marker screening including a nuchal translucency were included. Pregnancies with measurements 2.0- < 2.5 mm, 2.5- < 3.0 mm, 3.0- < 3.5 mm, 3.5- < 5.0 mm, 5.0- < 6.5 mm, and ≥6.5 mm were compared to a reference group with measurements <2.0 mm. We used multivariable modified Poisson regression models with robust variance estimation to estimate associations between nuchal translucency measurement and pregnancy outcome, with adjustment for age at estimated date of delivery and gestational age at screening. There were 414 268 singleton pregnancies included in the study. The risk of pregnancy loss, termination, stillbirth, or neonatal death increased with increasing levels of nuchal translucency measurements, with an adjusted risk ratio (aRR) of 11.9 (95% confidence interval (CI) 9.9, 14.3) in the group with measurements 3.5- < 5.0 mm. When pregnancies with diagnosed chromosomal abnormalities were excluded, this association remained strong, with an aRR of 6.4 (95% CI 4.8, 8.5). Among pregnancies with a live birth, those with a higher nuchal translucency measurement (>5.0 mm vs. <2.0 mm) were also at increased risk of adverse perinatal outcomes such as admission to the neonatal intensive care unit and APGAR score <7. In this population-based study using robust methods to reduce the risk of selection bias, we found that pregnancies with increased nuchal translucency measurements are less likely to result in a live birth, even with the exclusion of chromosomal abnormalities. Pregnancies with increased nuchal translucency measurements that resulted in a live birth may also be at increased risk of adverse perinatal outcomes.

The relationship between plasma interleukin-6 and cognition based on curve correlation in drug-naïve patients with major depressive disorder

BackgroundThe effect of interleukin-6 (IL-6) on cognition in patients with major depressive disorder (MDD) remains unclear. The aim of the present study was to investigate for the first time the non-linear relationship between plasma IL-6 and cognition and its sex-specific associations in patients with drug-naïve MDD. MethodsA total of 326 participants, including 237 drug-naïve MDD patients and 89 healthy controls (HCs), were included in this study. All participants completed the Repeatable Battery for the Assessment of Neuropsychological Status (RBANS) and fasting venous blood was collected for IL-6 measurement. Patients with MDD completed the Hamilton Depression Scale-17 (HAMD-17) and the Hamilton Anxiety Scale-14 (HAMA-14) assessments. Two-way analysis of variance and curve estimation analyses were used to explore the effects of IL-6 on cognition and its sex differences. ResultsWe found that IL-6 and cognition were associated in different patterns in HCs and MDD patients. The best model for curve estimation between IL-6 and attention (F = 2.736, p = 0.045) and HAMA (F = 6.416, p < 0.001) in females with MDD was the cubic model. In male MDD patients, the best model for curve estimation between IL-6 and immediate memory was the cubic model (F = 3.077, p = 0.034). However, in HCs, the best model for curve estimation analysis between IL-6 and language was the quadratic model (F = 3.803, p = 0.026). LimitationsThe main limitations were cross-sectional design. ConclusionThere was a non-linear and sex-specific relationship between IL-6 levels and cognition in patients with MDD.

The Use of Digital Interventions for Children and Adolescents with Autism Spectrum Disorder-A Meta-Analysis.

This comprehensive meta-analysis aimed to assess the effectiveness of digital interventions in improving developmental skills for children and adolescents with autism spectrum disorder (ASD). We conducted a systematic literature search based on three databases. A pre-test adjusted between-group standardized effect size was computed for effect size synthesis. We utilized a robust variance estimation model to analyze overall treatment effect. Moderator analyses and publication bias were also addressed. Twenty-eight studies (150 effect sizes) using randomized control trials (RCT; n = 22) or quasi-experimental designs (QED; n = 6) were included. Most studies (n = 22) included social-emotional skills as primary outcomes. The meta-analysis revealed a medium to large overall effect size, with Hedges' g = 0.62, 95% CI [0.36, 0.88], p < 0.001. We found that digital interventions have a statistically significantly large effect on enhancing social-emotional skills compared with language and communication skills, cognitive skills, daily living skills, and physical skills. The results of moderator analyses indicated that computer-based interventions have larger effect sizes in comparison to tablet/smartphone-based interventions. No statistically significant differences were observed between studies utilizing RCT and those using QED. We recommended the integration of digital interventions as supplemental resources in behavioral and educational interventions. Further research needs to focus on more females, young children, and adolescents with ASD in digital intervention research.

Multivariate moment least-squares variance estimators for reversible Markov chains

Markov chain Monte Carlo (MCMC) is a commonly used method for approximating expectations with respect to probability distributions. Uncertainty assessment for MCMC estimators is essential in practical applications. Moreover, for multivariate functions of a Markov chain, it is important to estimate not only the auto-correlation for each component but also to estimate cross-correlations, in order to better assess sample quality, improve estimates of effective sample size, and use more effective stopping rules. Berg and Song (2023) introduced the moment least squares (momentLS) estimator, a shape-constrained estimator for the autocovariance sequence from a reversible Markov chain, for univariate functions of the Markov chain. Based on this sequence estimator, they proposed an estimator of the asymptotic variance of the sample mean from MCMC samples. In this study, we propose novel autocovariance sequence and asymptotic variance estimators for Markov chain functions with multiple components, based on the univariate momentLS estimators from Berg and Song (2023). We demonstrate strong consistency of the proposed auto(cross)-covariance sequence and asymptotic variance matrix estimators. We conduct empirical comparisons of our method with other state-of-the-art approaches on simulated and real-data examples, using popular samplers including the random-walk Metropolis sampler and the No-U-Turn sampler from STAN. Supplemental materials for this article are available online.

Mean square error and variance estimation of the sample ratio under Lahiri ’s design

The mean square error of the sample ratio under Lahiri’s design is derived and is compared with that under simple random sampling without replacement. New variance estimators of the sample ratio under the design are proposed. A simulation study is conducted to confirm the main results.