Effectiveness of Covid-19 Vaccines over a 9-Month Period in North Carolina.

BACKGROUND: The duration of protection afforded by coronavirus disease 2019 (Covid-19) vaccines in the United States is unclear. Whether the increase in postvaccination infections during the summer of 2021 was caused by declining immunity over time, the emergence of the B.1.617.2 (delta) variant, or both is unknown. METHODS: We extracted data regarding Covid-19-related vaccination and outcomes during a 9-month period (December 11, 2020, to September 8, 2021) for approximately 10.6 million North Carolina residents by linking data from the North Carolina Covid-19 Surveillance System and the Covid-19 Vaccine Management System. We used a Cox regression model to estimate the effectiveness of the BNT162b2 (Pfizer-BioNTech), mRNA-1273 (Moderna), and Ad26.COV2.S (Johnson & Johnson-Janssen) vaccines in reducing the current risks of Covid-19, hospitalization, and death, as a function of time elapsed since vaccination. RESULTS: For the two-dose regimens of messenger RNA (mRNA) vaccines BNT162b2 (30 µg per dose) and mRNA-1273 (100 µg per dose), vaccine effectiveness against Covid-19 was 94.5% (95% confidence interval [CI], 94.1 to 94.9) and 95.9% (95% CI, 95.5 to 96.2), respectively, at 2 months after the first dose and decreased to 66.6% (95% CI, 65.2 to 67.8) and 80.3% (95% CI, 79.3 to 81.2), respectively, at 7 months. Among early recipients of BNT162b2 and mRNA-1273, effectiveness decreased by approximately 15 and 10 percentage points, respectively, from mid-June to mid-July, when the delta variant became dominant. For the one-dose regimen of Ad26.COV2.S (5 × 1010 viral particles), effectiveness against Covid-19 was 74.8% (95% CI, 72.5 to 76.9) at 1 month and decreased to 59.4% (95% CI, 57.2 to 61.5) at 5 months. All three vaccines maintained better effectiveness in preventing hospitalization and death than in preventing infection over time, although the two mRNA vaccines provided higher levels of protection than Ad26.COV2.S. CONCLUSIONS: All three Covid-19 vaccines had durable effectiveness in reducing the risks of hospitalization and death. Waning protection against infection over time was due to both declining immunity and the emergence of the delta variant. (Funded by a Dennis Gillings Distinguished Professorship and the National Institutes of Health.).

HMM for discovering decision-making dynamics using reinforcement learning experiments.

Major depressive disorder (MDD), a leading cause of years of life lived with disability, presents challenges in diagnosis and treatment due to its complex and heterogeneous nature. Emerging evidence indicates that reward processing abnormalities may serve as a behavioral marker for MDD. To measure reward processing, patients perform computer-based behavioral tasks that involve making choices or responding to stimulants that are associated with different outcomes, such as gains or losses in the laboratory. Reinforcement learning (RL) models are fitted to extract parameters that measure various aspects of reward processing (e.g. reward sensitivity) to characterize how patients make decisions in behavioral tasks. Recent findings suggest the inadequacy of characterizing reward learning solely based on a single RL model; instead, there may be a switching of decision-making processes between multiple strategies. An important scientific question is how the dynamics of strategies in decision-making affect the reward learning ability of individuals with MDD. Motivated by the probabilistic reward task within the Establishing Moderators and Biosignatures of Antidepressant Response in Clinical Care (EMBARC) study, we propose a novel RL-HMM (hidden Markov model) framework for analyzing reward-based decision-making. Our model accommodates decision-making strategy switching between two distinct approaches under an HMM: subjects making decisions based on the RL model or opting for random choices. We account for continuous RL state space and allow time-varying transition probabilities in the HMM. We introduce a computationally efficient Expectation-maximization (EM) algorithm for parameter estimation and use a nonparametric bootstrap for inference. Extensive simulation studies validate the finite-sample performance of our method. We apply our approach to the EMBARC study to show that MDD patients are less engaged in RL compared to the healthy controls, and engagement is associated with brain activities in the negative affect circuitry during an emotional conflict task.

Associations of alcohol and cannabis use with change in posttraumatic stress disorder and depression symptoms over time in recently trauma-exposed individuals.

BACKGROUND: Several hypotheses may explain the association between substance use, posttraumatic stress disorder (PTSD), and depression. However, few studies have utilized a large multisite dataset to understand this complex relationship. Our study assessed the relationship between alcohol and cannabis use trajectories and PTSD and depression symptoms across 3 months in recently trauma-exposed civilians. METHODS: In total, 1618 (1037 female) participants provided self-report data on past 30-day alcohol and cannabis use and PTSD and depression symptoms during their emergency department (baseline) visit. We reassessed participant's substance use and clinical symptoms 2, 8, and 12 weeks posttrauma. Latent class mixture modeling determined alcohol and cannabis use trajectories in the sample. Changes in PTSD and depression symptoms were assessed across alcohol and cannabis use trajectories via a mixed-model repeated-measures analysis of variance. RESULTS: Three trajectory classes (low, high, increasing use) provided the best model fit for alcohol and cannabis use. The low alcohol use class exhibited lower PTSD symptoms at baseline than the high use class; the low cannabis use class exhibited lower PTSD and depression symptoms at baseline than the high and increasing use classes; these symptoms greatly increased at week 8 and declined at week 12. Participants who already use alcohol and cannabis exhibited greater PTSD and depression symptoms at baseline that increased at week 8 with a decrease in symptoms at week 12. CONCLUSIONS: Our findings suggest that alcohol and cannabis use trajectories are associated with the intensity of posttrauma psychopathology. These findings could potentially inform the timing of therapeutic strategies.

Structural inequities contribute to racial/ethnic differences in neurophysiological tone, but not threat reactivity, after trauma exposure.

Considerable racial/ethnic disparities persist in exposure to life stressors and socioeconomic resources that can directly affect threat neurocircuitry, particularly the amygdala, that partially mediates susceptibility to adverse posttraumatic outcomes. Limited work to date, however, has investigated potential racial/ethnic variability in amygdala reactivity or connectivity that may in turn be related to outcomes such as post-traumatic stress disorder (PTSD). Participants from the AURORA study (n = 283), a multisite longitudinal study of trauma outcomes, completed functional magnetic resonance imaging and psychophysiology within approximately two-weeks of trauma exposure. Seed-based amygdala connectivity and amygdala reactivity during passive viewing of fearful and neutral faces were assessed during fMRI. Physiological activity was assessed during Pavlovian threat conditioning. Participants also reported the severity of posttraumatic symptoms 3 and 6 months after trauma. Black individuals showed lower baseline skin conductance levels and startle compared to White individuals, but no differences were observed in physiological reactions to threat. Further, Hispanic and Black participants showed greater amygdala connectivity to regions including the dorsolateral prefrontal cortex (PFC), dorsal anterior cingulate cortex, insula, and cerebellum compared to White participants. No differences were observed in amygdala reactivity to threat. Amygdala connectivity was associated with 3-month PTSD symptoms, but the associations differed by racial/ethnic group and were partly driven by group differences in structural inequities. The present findings suggest variability in tonic neurophysiological arousal in the early aftermath of trauma between racial/ethnic groups, driven by structural inequality, impacts neural processes that mediate susceptibility to later PTSD symptoms.

Internal capsule microstructure mediates the relationship between childhood maltreatment and PTSD following adulthood trauma exposure.

Childhood trauma is a known risk factor for trauma and stress-related disorders in adulthood. However, limited research has investigated the impact of childhood trauma on brain structure linked to later posttraumatic dysfunction. We investigated the effect of childhood trauma on white matter microstructure after recent trauma and its relationship with future posttraumatic dysfunction among trauma-exposed adult participants (n = 202) recruited from emergency departments as part of the AURORA Study. Participants completed self-report scales assessing prior childhood maltreatment within 2-weeks in addition to assessments of PTSD, depression, anxiety, and dissociation symptoms within 6-months of their traumatic event. Fractional anisotropy (FA) obtained from diffusion tensor imaging (DTI) collected at 2-weeks and 6-months was used to index white matter microstructure. Childhood maltreatment load predicted 6-month PTSD symptoms (b = 1.75, SE = 0.78, 95% CI = [0.20, 3.29]) and inversely varied with FA in the bilateral internal capsule (IC) at 2-weeks (p = 0.0294, FDR corrected) and 6-months (p = 0.0238, FDR corrected). We observed a significant indirect effect of childhood maltreatment load on 6-month PTSD symptoms through 2-week IC microstructure (b = 0.37, Boot SE = 0.18, 95% CI = [0.05, 0.76]) that fully mediated the effect of childhood maltreatment load on PCL-5 scores (b = 1.37, SE = 0.79, 95% CI = [-0.18, 2.93]). IC microstructure did not mediate relationships between childhood maltreatment and depressive, anxiety, or dissociative symptomatology. Our findings suggest a unique role for IC microstructure as a stable neural pathway between childhood trauma and future PTSD symptoms following recent trauma. Notably, our work did not support roles of white matter tracts previously found to vary with PTSD symptoms and childhood trauma exposure, including the cingulum bundle, uncinate fasciculus, and corpus callosum. Given the IC contains sensory fibers linked to perception and motor control, childhood maltreatment might impact the neural circuits that relay and process threat-related inputs and responses to trauma.

Identifying temporal pathways using biomarkers in the presence of latent non-Gaussian components.

Time-series data collected from a network of random variables are useful for identifying temporal pathways among the network nodes. Observed measurements may contain multiple sources of signals and noises, including Gaussian signals of interest and non-Gaussian noises, including artifacts, structured noise, and other unobserved factors (eg, genetic risk factors, disease susceptibility). Existing methods, including vector autoregression (VAR) and dynamic causal modeling do not account for unobserved non-Gaussian components. Furthermore, existing methods cannot effectively distinguish contemporaneous relationships from temporal relations. In this work, we propose a novel method to identify latent temporal pathways using time-series biomarker data collected from multiple subjects. The model adjusts for the non-Gaussian components and separates the temporal network from the contemporaneous network. Specifically, an independent component analysis (ICA) is used to extract the unobserved non-Gaussian components, and residuals are used to estimate the contemporaneous and temporal networks among the node variables based on method of moments. The algorithm is fast and can easily scale up. We derive the identifiability and the asymptotic properties of the temporal and contemporaneous networks. We demonstrate superior performance of our method by extensive simulations and an application to a study of attention-deficit/hyperactivity disorder (ADHD), where we analyze the temporal relationships between brain regional biomarkers. We find that temporal network edges were across different brain regions, while most contemporaneous network edges were bilateral between the same regions and belong to a subset of the functional connectivity network.

Proportional rates models for multivariate panel count data.

Multivariate panel count data arise when there are multiple types of recurrent events, and the observation for each study subject consists of the number of recurrent events of each type between two successive examinations. We formulate the effects of potentially time-dependent covariates on multiple types of recurrent events through proportional rates models, while leaving the dependence structures of the related recurrent events completely unspecified. We employ nonparametric maximum pseudo-likelihood estimation under the working assumptions that all types of events are independent and each type of event is a nonhomogeneous Poisson process, and we develop a simple and stable EM-type algorithm. We show that the resulting estimators of the regression parameters are consistent and asymptotically normal, with a covariance matrix that can be estimated consistently by a sandwich estimator. In addition, we develop a class of graphical and numerical methods for checking the adequacy of the fitted model. Finally, we evaluate the performance of the proposed methods through simulation studies and analysis of a skin cancer clinical trial.

Fitting the Cox proportional hazards model to big data.

The semiparametric Cox proportional hazards model, together with the partial likelihood principle, has been widely used to study the effects of potentially time-dependent covariates on a possibly censored event time. We propose a computationally efficient method for fitting the Cox model to big data involving millions of study subjects. Specifically, we perform maximum partial likelihood estimation on a small subset of the whole data and improve the initial estimator by incorporating the remaining data through one-step estimation with estimated efficient score functions. We show that the final estimator has the same asymptotic distribution as the conventional maximum partial likelihood estimator using the whole dataset but requires only a small fraction of computation time. We demonstrate the usefulness of the proposed method through extensive simulation studies and an application to the UK Biobank data.

Integrating randomized and observational studies to estimate optimal dynamic treatment regimes.

Sequential multiple assignment randomized trials (SMARTs) are the gold standard for estimating optimal dynamic treatment regimes (DTRs), but are costly and require a large sample size. We introduce the multi-stage augmented Q-learning estimator (MAQE) to improve efficiency of estimation of optimal DTRs by augmenting SMART data with observational data. Our motivating example comes from the Back Pain Consortium, where one of the overarching aims is to learn how to tailor treatments for chronic low back pain to individual patient phenotypes, knowledge which is lacking clinically. The Consortium-wide collaborative SMART and observational studies within the Consortium collect data on the same participant phenotypes, treatments, and outcomes at multiple time points, which can easily be integrated. Previously published single-stage augmentation methods for integration of trial and observational study (OS) data were adapted to estimate optimal DTRs from SMARTs using Q-learning. Simulation studies show the MAQE, which integrates phenotype, treatment, and outcome information from multiple studies over multiple time points, more accurately estimates the optimal DTR, and has a higher average value than a comparable Q-learning estimator without augmentation. We demonstrate this improvement is robust to a wide range of trial and OS sample sizes, addition of noise variables, and effect sizes.

Safety signal detection with control of latent factors.

Postmarket drug safety database like vaccine adverse event reporting system (VAERS) collect thousands of spontaneous reports annually, with each report recording occurrences of any adverse events (AEs) and use of vaccines. We hope to identify signal vaccine-AE pairs, for which certain vaccines are statistically associated with certain adverse events (AE), using such data. Thus, the outcomes of interest are multiple AEs, which are binary outcomes and could be correlated because they might share certain latent factors; and the primary covariates are vaccines. Appropriately accounting for the complex correlation among AEs could improve the sensitivity and specificity of identifying signal vaccine-AE pairs. We propose a two-step approach in which we first estimate the shared latent factors among AEs using a working multivariate logistic regression model, and then use univariate logistic regression model to examine the vaccine-AE associations after controlling for the latent factors. Our simulation studies show that this approach outperforms current approaches in terms of sensitivity and specificity. We apply our approach in analyzing VAERS data and report our findings.

Evaluating treatment efficacy in hospitalized COVID-19 patients, with applications to Adaptive COVID-19 Treatment Trials.

BACKGROUND: The current endpoints for therapeutic trials of hospitalized COVID-19 patients capture only part of the clinical course of a patient and have limited statistical power and robustness. METHODS: We specify proportional odds models for repeated measures of clinical status, with a common odds ratio of lower severity over time. We also specify the proportional hazards model for time to each level of improvement or deterioration of clinical status, with a common hazard ratio for overall treatment benefit. We apply these methods to Adaptive COVID-19 Treatment Trials. RESULTS: For remdesivir versus placebo, the common odds ratio was 1.48 (95% confidence interval (CI) = 1.23-1.79; p < 0.001), and the common hazard ratio was 1.27 (95% CI = 1.09-1.47; p = 0.002). For baricitinib plus remdesivir versus remdesivir alone, the common odds ratio was 1.32 (95% CI = 1.10-1.57; p = 0.002), and the common hazard ratio was 1.30 (95% CI = 1.13-1.49; p < 0.001). For interferon beta-1a plus remdesivir versus remdesivir alone, the common odds ratio was 0.95 (95% CI = 0.79-1.14; p = 0.56), and the common hazard ratio was 0.98 (95% CI = 0.85-1.12; p = 0.74). CONCLUSIONS: The proposed methods comprehensively characterize the treatment effects on the entire clinical course of a hospitalized COVID-19 patient.

Connections between reproductive health and cognitive aging among women enrolled in the HCHS/SOL and SOL-INCA.

INTRODUCTION: Reproductive health history may contribute to cognitive aging and risk for Alzheimer's disease, but this is understudied among Hispanic/Latina women. METHODS: Participants included 2126 Hispanic/Latina postmenopausal women (44 to 75 years) from the Study of Latinos-Investigation of Neurocognitive Aging. Survey linear regressions separately modeled the associations between reproductive health measures (age at menarche, history of oral contraceptive use, number of pregnancies, number of live births, age at menopause, female hormone use at Visit 1, and reproductive span) with cognitive outcomes at Visit 2 (performance, 7-year change, and mild cognitive impairment [MCI] prevalence). RESULTS: Younger age at menarche, oral contraceptive use, lower pregnancies, lower live births, and older age at menopause were associated with better cognitive performance. Older age at menarche was protective against cognitive change. Hormone use was linked to lower MCI prevalence. DISCUSSION: Several aspects of reproductive health appear to impact cognitive aging among Hispanic/Latina women.

Semiparametric regression analysis of bivariate censored events in a family study of Alzheimer's disease.

Assessing disease comorbidity patterns in families represents the first step in gene mapping for diseases and is central to the practice of precision medicine. One way to evaluate the relative contributions of genetic risk factor and environmental determinants of a complex trait (e.g., Alzheimer's disease [AD]) and its comorbidities (e.g., cardiovascular diseases [CVD]) is through familial studies, where an initial cohort of subjects are recruited, genotyped for specific loci, and interviewed to provide extensive disease history in family members. Because of the retrospective nature of obtaining disease phenotypes in family members, the exact time of disease onset may not be available such that current status data or interval-censored data are observed. All existing methods for analyzing these family study data assume single event subject to right-censoring so are not applicable. In this article, we propose a semiparametric regression model for the family history data that assumes a family-specific random effect and individual random effects to account for the dependence due to shared environmental exposures and unobserved genetic relatedness, respectively. To incorporate multiple events, we jointly model the onset of the primary disease of interest and a secondary disease outcome that is subject to interval-censoring. We propose nonparametric maximum likelihood estimation and develop a stable Expectation-Maximization (EM) algorithm for computation. We establish the asymptotic properties of the resulting estimators and examine the performance of the proposed methods through simulation studies. Our application to a real world study reveals that the main contribution of comorbidity between AD and CVD is due to genetic factors instead of environmental factors.

A general framework of nonparametric feature selection in high-dimensional data.

Nonparametric feature selection for high-dimensional data is an important and challenging problem in the fields of statistics and machine learning. Most of the existing methods for feature selection focus on parametric or additive models which may suffer from model misspecification. In this paper, we propose a new framework to perform nonparametric feature selection for both regression and classification problems. Under this framework, we learn prediction functions through empirical risk minimization over a reproducing kernel Hilbert space. The space is generated by a novel tensor product kernel, which depends on a set of parameters that determines the importance of the features. Computationally, we minimize the empirical risk with a penalty to estimate the prediction and kernel parameters simultaneously. The solution can be obtained by iteratively solving convex optimization problems. We study the theoretical property of the kernel feature space and prove the oracle selection property and Fisher consistency of our proposed method. Finally, we demonstrate the superior performance of our approach compared to existing methods via extensive simulation studies and applications to two real studies.

Analyzing clustered continuous response variables with ordinal regression models.

Continuous response data are regularly transformed to meet regression modeling assumptions. However, approaches taken to identify the appropriate transformation can be ad hoc and can increase model uncertainty. Further, the resulting transformations often vary across studies leading to difficulties with synthesizing and interpreting results. When a continuous response variable is measured repeatedly within individuals or when continuous responses arise from clusters, analyses have the additional challenge caused by within-individual or within-cluster correlations. We extend a widely used ordinal regression model, the cumulative probability model (CPM), to fit clustered, continuous response data using generalized estimating equations for ordinal responses. With the proposed approach, estimates of marginal model parameters, cumulative distribution functions , expectations, and quantiles conditional on covariates can be obtained without pretransformation of the response data. While computational challenges arise with large numbers of distinct values of the continuous response variable, we propose feasible and computationally efficient approaches to fit CPMs under commonly used working correlation structures. We study finite sample operating characteristics of the estimators via simulation and illustrate their implementation with two data examples. One studies predictors of CD4:CD8 ratios in a cohort living with HIV, and the other investigates the association of a single nucleotide polymorphism and lung function decline in a cohort with early chronic obstructive pulmonary disease.

Improving trial generalizability using observational studies.

Complementary features of randomized controlled trials (RCTs) and observational studies (OSs) can be used jointly to estimate the average treatment effect of a target population. We propose a calibration weighting estimator that enforces the covariate balance between the RCT and OS, therefore improving the trial-based estimator's generalizability. Exploiting semiparametric efficiency theory, we propose a doubly robust augmented calibration weighting estimator that achieves the efficiency bound derived under the identification assumptions. A nonparametric sieve method is provided as an alternative to the parametric approach, which enables the robust approximation of the nuisance functions and data-adaptive selection of outcome predictors for calibration. We establish asymptotic results and confirm the finite sample performances of the proposed estimators by simulation experiments and an application on the estimation of the treatment effect of adjuvant chemotherapy for early-stage non-small-cell lung patients after surgery.

Multivariate functional mixed model with MRI data: An application to Alzheimer's disease.

Alzheimer's Disease (AD) is the leading cause of dementia and impairment in various domains. Recent AD studies, (ie, Alzheimer's Disease Neuroimaging Initiative (ADNI) study), collect multimodal data, including longitudinal neurological assessments and magnetic resonance imaging (MRI) data, to better study the disease progression. Adopting early interventions is essential to slow AD progression for subjects with mild cognitive impairment (MCI). It is of particular interest to develop an AD predictive model that leverages multimodal data and provides accurate personalized predictions. In this article, we propose a multivariate functional mixed model with MRI data (MFMM-MRI) that simultaneously models longitudinal neurological assessments, baseline MRI data, and the survival outcome (ie, dementia onset) for subjects with MCI at baseline. Two functional forms (the random-effects model and instantaneous model) linking the longitudinal and survival process are investigated. We use Markov Chain Monte Carlo (MCMC) method based on No-U-Turn Sampling (NUTS) algorithm to obtain posterior samples. We develop a dynamic prediction framework that provides accurate personalized predictions of longitudinal trajectories and survival probability. We apply MFMM-MRI to the ADNI study and identify significant associations among longitudinal outcomes, MRI data, and the risk of dementia onset. The instantaneous model with voxels from the whole brain has the best prediction performance among all candidate models. The simulation study supports the validity of the estimation and dynamic prediction method.

Modeling longitudinal change in biomarkers using data from a complex survey sampling design: An application to the Hispanic Community Health Study/Study of Latinos.

In observational cohort studies, there is frequently interest in modeling longitudinal change in a biomarker (ie, physiological measure indicative of metabolic dysregulation or disease; eg, blood pressure) in the absence of treatment (ie, medication), and its association with modifiable risk factors expected to affect health (eg, body mass index). However, individuals may start treatment during the study period, and consequently biomarker values observed while on treatment may be different than those that would have been observed in the absence of treatment. If treated individuals are excluded from analysis, then effect estimates may be biased if treated individuals differ systematically from untreated individuals. We addressed this concern in the setting of the Hispanic Community Health Study/Study of Latinos (HCHS/SOL), an observational cohort study that employed a complex survey sampling design to enable inference to a finite target population. We considered biomarker values measured while on treatment to be missing data, and applied missing data methodology (inverse probability weighting (IPW) and doubly robust estimation) to this problem. The proposed methods leverage information collected between study visits on when individuals started treatment, by adapting IPW and doubly robust approaches to model the treatment mechanism using survival analysis methods. This methodology also incorporates sampling weights and uses a bootstrap approach to estimate standard errors accounting for the complex survey sampling design. We investigated variance estimation for these methods, conducted simulation studies to assess statistical performance in finite samples, and applied the methodology to model temporal change in blood pressure in HCHS/SOL.

Rank intraclass correlation for clustered data.

Clustered data are common in biomedical research. Observations in the same cluster are often more similar to each other than to observations from other clusters. The intraclass correlation coefficient (ICC), first introduced by R. A. Fisher, is frequently used to measure this degree of similarity. However, the ICC is sensitive to extreme values and skewed distributions, and depends on the scale of the data. It is also not applicable to ordered categorical data. We define the rank ICC as a natural extension of Fisher's ICC to the rank scale, and describe its corresponding population parameter. The rank ICC is simply interpreted as the rank correlation between a random pair of observations from the same cluster. We also extend the definition when the underlying distribution has more than two hierarchies. We describe estimation and inference procedures, show the asymptotic properties of our estimator, conduct simulations to evaluate its performance, and illustrate our method in three real data examples with skewed data, count data, and three-level ordered categorical data.

Comparisons of statistical methods for handling attrition in a follow-up visit with complex survey sampling.

Design-based analysis, which accounts for the design features of the study, is commonly used to conduct data analysis in studies with complex survey sampling, such as the Hispanic Community Health Study/Study of Latinos (HCHS/SOL). In this type of longitudinal study, attrition has often been a problem. Although there have been various statistical approaches proposed to handle attrition, such as inverse probability weighting (IPW), non-response cell weighting (NRCW), multiple imputation (MI), and full information maximum likelihood (FIML) approach, there has not been a systematic assessment of these methods to compare their performance in design-based analyses. In this article, we perform extensive simulation studies and compare the performance of different missing data methods in linear and generalized linear population models, and under different missing data mechanism. We find that the design-based analysis is able to produce valid estimation and statistical inference when the missing data are handled appropriately using IPW, NRCW, MI, or FIML approach under missing-completely-at-random or missing-at-random missing mechanism and when the missingness model is correctly specified or over-specified. We also illustrate the use of these methods using data from HCHS/SOL.