Linear quantile regression models for longitudinal experiments: an overview

Household food insecurity levels in Ethiopia: quantile regression approach

Introduction

Numerous natural and man-made factors have afflicted Ethiopia, and millions of people have experienced food insecurity. The current cut-points of the WFP food consumption score (FCS) have limitations in measuring the food insecurity level of different feeding patterns due to the diversified culture of the society. The aim of this study is to adapt the WFP food security score cut-points corrected for the different feeding cultures of the society using effect-driven quantile clustering.

Method

The 2012, 2014, and 2016 Ethiopian socio-economic household-based panel data set with a sample size of 3,835 households and 42 variables were used. Longitudinal quantile regression with fixed individual-specific location-shift intercept of the free distribution covariance structure was adopted to identify major indicators that can cluster and level quantiles of the FCS.

Result

Household food insecurity is reduced through time across the quintiles of food security score distribution, mainly in the upper quantiles. The leveling based on effect-driven quantile clustering brings 35.5 and 49 as the FCS cut-points corrected for cultural diversity. This corrected FCS brings wider interval for food insecure households with the same interval range for vulnerable households, where the WFP FCS cut-points under estimate it by 7 score. Education level, employment, fertilizer usage, farming type, agricultural package, infrastructure-related factors, and environmental factors are found to be the significant contributing factors to food security. On the other hand, the age of the head of the household, dependency ratio, shock, and no irrigation in households make significant contributions to food insecurity. Moreover, households living in rural areas and farming crops on small lands are comparatively vulnerable and food insecure.

Conclusion

Measuring food insecurity in Ethiopia using the WFP FCS cut-off points underestimates households' food insecurity levels. Since the WFP FCS cut-points have universality and comparability limitations, there is a need for a universally accepted local threshold, corrected for local factors those resulted in different consumption patterns in the standardization of food security score. Accordingly, the quantile regression approach adjusts the WFP-FCS cut points by adjusting for local situations. Applying WFP cut-points will wrongly assign households on each level, so the proportion of households will be inflated for the security level and underestimated for the insecure level, and the influence of factors can also be wrongly recommended the food security score for the levels. The quantile clustering approach showed that cropping on a small land size would not bring about food security in Ethiopia. This favors the Ethiopian government initiative called integrated farming "ኩታ ገጠም እርሻ" which Ethiopia needs to develop and implement a system that fits and responds to this technology and infrastructure.

SARS-CoV-2 Infection during the Omicron Surge among Patients Receiving Dialysis: The Role of Circulating Receptor-Binding Domain Antibodies and Vaccine Doses

BACKGROUND

It is unclear whether circulating antibody levels conferred protection against SARS-CoV-2 infection among patients receiving dialysis during the Omicron-dominant period.

METHODS

We followed monthly semiquantitative SARS-CoV-2 RBD IgG index values in a randomly selected nationwide cohort of patients receiving dialysis and ascertained SARS-CoV-2 infection during the Omicron-dominant period of December 25, 2021 to January 31, 2022 using electronic health records. We estimated the relative risk for documented SARS-CoV-2 infection by vaccination status and by circulating RBD IgG using a log-binomial model accounting for age, sex, and prior COVID-19.

RESULTS

Among 3576 patients receiving dialysis, 901 (25%) received a third mRNA vaccine dose as of December 24, 2021. Early antibody responses to third doses were robust (median peak index IgG value at assay limit of 150). During the Omicron-dominant period, SARS-CoV-2 infection was documented in 340 (7%) patients. Risk for infection was higher among patients without vaccination and with one to two doses (RR, 2.1; 95% CI, 1.6 to 2.8, and RR, 1.3; 95% CI, 1.0 to 1.8 versus three doses, respectively). Irrespective of the number of vaccine doses, risk for infection was higher among patients with circulating RBD IgG <23 (506 BAU/ml) (RR range, 2.1 to 3.2, 95% CI, 1.3 to 3.4 and 95% CI, 2.2 to 4.5, respectively) compared with RBD IgG ≥23.

CONCLUSIONS

Among patients receiving dialysis, a third mRNA vaccine dose enhanced protection against SARS-CoV-2 infection during the Omicron-dominant period, but a low circulating RBD antibody response was associated with risk for infection independent of the number of vaccine doses. Measuring circulating antibody levels in this high-risk group could inform optimal timing of vaccination and other measures to reduce risk of SARS-CoV-2 infection.

Modelling of South African Hypertension: Application of Panel Quantile Regression

Hypertension is one of the crucial risk factors for morbidity and mortality around the world, and South Africa has a significant unmet need for hypertension care. This study aims to establish the potential risk factors of hypertension amongst adults in South Africa attributable to high systolic and diastolic blood pressure over time by fitting panel quantile regression models. Data obtained from the South African National Income Dynamics Study (NIDS) Household Surveys carried out from 2008 to 2018 (Wave 1 to Wave 5) was employed to develop both the fixed effects and random effects panel quantile regression models. Age, BMI, gender (males), race, exercises, cigarette consumption, and employment status were significantly associated with either one of the BP measures across all the upper quantiles or at the 75th quantile only. Suggesting that these risk factors have contributed to the exacerbation of uncontrolled hypertension prevalence over time in South Africa.

SARS-CoV-2 vaccine antibody response and breakthrough infection in dialysis

BACKGROUND

Patients receiving dialysis are a sentinel population for groups at high risk for death and disability from COVID-19. Understanding correlates of protection post-vaccination can inform immunization and mitigation strategies.

METHODS

Monthly since January 2021, we tested plasma from 4791 patients receiving dialysis for antibodies to the receptor-binding domain (RBD) of SARS-CoV-2 using a high-throughput assay. We qualitatively assessed the proportion without a detectable RBD response and among those with a response, semiquantitative median IgG index values. Using a nested case-control design, we matched each breakthrough case to five controls by age, sex, and vaccination-month to determine whether peak and pre-breakthrough RBD IgG index values were associated with risk for infection post-vaccination.

RESULTS

Among 2563 vaccinated patients, the proportion without a detectable RBD response increased from 6.6% [95% CI 5.5-8.1] in 14-30 days post-vaccination to 20.2% [95% CI 17.1-23.8], and median index values declined from 92.7 (95% CI 77.8-107.5) to 3.7 (95% CI 3.1-4.3) after 5 months. Persons with SARS-CoV-2 infection prior-to-vaccination had higher peak index values than persons without prior infection, but values equalized by 5 months (p=0.230). Breakthrough infections occurred in 56 patients, with samples collected a median of 21 days pre-breakthrough. Peak and pre-breakthrough RBD values <23 (equivalent to <506 WHO BAU/mL) were associated with higher odds for breakthrough infection (OR: 3.7 [95% CI 2.0-6.8] and 9.8 [95% CI 2.9-32.8], respectively).

CONCLUSIONS

The antibody response to SARS-CoV-2 vaccination wanes rapidly, and in persons receiving dialysis, the persisting antibody response is associated with risk for breakthrough infection.

A new GEE method to account for heteroscedasticity using asymmetric least-square regressions

Generalized estimating equations ( G E E ) are widely used to analyze longitudinal data; however, they are not appropriate for heteroscedastic data, because they only estimate regressor effects on the mean response - and therefore do not account for data heterogeneity. Here, we combine the G E E with the asymmetric least squares (expectile) regression to derive a new class of estimators, which we call generalized expectile estimating equations ( G E E E ) . The G E E E model estimates regressor effects on the expectiles of the response distribution, which provides a detailed view of regressor effects on the entire response distribution. In addition to capturing data heteroscedasticity, the GEEE extends the various working correlation structures to account for within-subject dependence. We derive the asymptotic properties of the G E E E estimators and propose a robust estimator of its covariance matrix for inference (see our R package, github.com/AmBarry/expectgee). Our simulations show that the GEEE estimator is non-biased and efficient, and our real data analysis shows it captures heteroscedasticity.

Two-part quantile regression models for semi-continuous longitudinal data: A finite mixture approach

This article develops a two-part finite mixture quantile regression model for semi-continuous longitudinal data. The proposed methodology allows heterogeneity sources that influence the model for the binary response variable to also influence the distribution of the positive outcomes. As is common in the quantile regression literature, estimation and inference on the model parameters are based on the asymmetric Laplace distribution. Maximum likelihood estimates are obtained through the EM algorithm without parametric assumptions on the random effects distribution. In addition, a penalized version of the EM algorithm is presented to tackle the problem of variable selection. The proposed statistical method is applied to the well-known RAND Health Insurance Experiment dataset which gives further insights on its empirical behaviour.

A family of linear mixed-effects models using the generalized Laplace distribution

We propose a new family of linear mixed-effects models based on the generalized Laplace distribution. Special cases include the classical normal mixed-effects model, models with Laplace random effects and errors, and models where Laplace and normal variates interchange their roles as random effects and errors. By using a scale-mixture representation of the generalized Laplace, we develop a maximum likelihood estimation approach based on Gaussian quadrature. For model selection, we propose likelihood ratio testing and we account for the situation in which the null hypothesis is at the boundary of the parameter space. In a simulation study, we investigate the finite sample properties of our proposed estimator and compare its performance to other flexible linear mixed-effects specifications. In two real data examples, we demonstrate the flexibility of our proposed model to solve applied problems commonly encountered in clustered data analysis. The newly proposed methods discussed in this paper are implemented in the R package nlmm.

Modelling and estimation of nonlinear quantile regression with clustered data

In regression applications, the presence of nonlinearity and correlation among observations offer computational challenges not only in traditional settings such as least squares regression, but also (and especially) when the objective function is nonsmooth as in the case of quantile regression. Methods are developed for the modelling and estimation of nonlinear conditional quantile functions when data are clustered within two-level nested designs. The proposed estimation algorithm is a blend of a smoothing algorithm for quantile regression and a second order Laplacian approximation for nonlinear mixed models. This optimization approach has the appealing advantage of reducing the original nonsmooth problem to an approximated L 2 problem. While the estimation algorithm is iterative, the objective function to be optimized has a simple analytic form. The proposed methods are assessed through a simulation study and two applications, one in pharmacokinetics and one related to growth curve modelling in agriculture.

Quantile regression and empirical likelihood for the analysis of longitudinal data with monotone missing responses due to dropout, with applications to quality of life measurements from clinical trials

The analysis of quality of life (QoL) data can be challenging due to the skewness of responses and the presence of missing data. In this paper, we propose a new weighted quantile regression method for estimating the conditional quantiles of QoL data with responses missing at random. The proposed method makes use of the correlation information within the same subject from an auxiliary mean regression model to enhance the estimation efficiency and takes into account of missing data mechanism. The asymptotic properties of the proposed estimator have been studied and simulations are also conducted to evaluate the performance of the proposed estimator. The proposed method has also been applied to the analysis of the QoL data from a clinical trial on early breast cancer, which motivated this study.

Quantile Regression Modeling of Latent Trajectory Features with Longitudinal Data

Quantile regression has demonstrated promising utility in longitudinal data analysis. Existing work is primarily focused on modeling cross-sectional outcomes, while outcome trajectories often carry more substantive information in practice. In this work, we develop a trajectory quantile regression framework that is designed to robustly and flexibly investigate how latent individual trajectory features are related to observed subject characteristics. The proposed models are built under multilevel modeling with usual parametric assumptions lifted or relaxed. We derive our estimation procedure by novelly transforming the problem at hand to quantile regression with perturbed responses and adapting the bias correction technique for handling covariate measurement errors. We establish desirable asymptotic properties of the proposed estimator, including uniform consistency and weak convergence. Extensive simulation studies confirm the validity of the proposed method as well as its robustness. An application to the DURABLE trial uncovers sensible scientific findings and illustrates the practical value of our proposals.

Mixed hidden Markov quantile regression models for longitudinal data with possibly incomplete sequences

Quantile regression provides a detailed and robust picture of the distribution of a response variable, conditional on a set of observed covariates. Recently, it has be been extended to the analysis of longitudinal continuous outcomes using either time-constant or time-varying random parameters. However, in real-life data, we frequently observe both temporal shocks in the overall trend and individual-specific heterogeneity in model parameters. A benchmark dataset on HIV progression gives a clear example. Here, the evolution of the CD4 log counts exhibits both sudden temporal changes in the overall trend and heterogeneity in the effect of the time since seroconversion on the response dynamics. To accommodate such situations, we propose a quantile regression model, where time-varying and time-constant random coefficients are jointly considered. Since observed data may be incomplete due to early drop-out, we also extend the proposed model in a pattern mixture perspective. We assess the performance of the proposals via a large-scale simulation study and the analysis of the CD4 count data.