Regression Models For Longitudinal Data Research Articles

Order‐restricted hypothesis tests for nonlinear mixed‐effects models with measurement errors in covariates

AbstractOrder‐restricted hypothesis testing problems frequently arise in practice, including studies involving regression models for longitudinal data. These tests are known to be more powerful than tests that ignore such restrictions. In this article, we consider order‐restricted tests for nonlinear mixed‐effects models with measurement errors in time‐dependent covariates. We propose to use a multiple imputation method to address measurement errors, since this approach allows us to use existing complete‐data methods for order‐restricted tests. Some theoretical results are presented. We evaluate our proposed methods via simulation studies that demonstrate they are more powerful than either a competing naive method or a two‐step approach to testing hypotheses. We illustrate the use of our proposed approach by analyzing data from an HIV/AIDS study.

Modeling of Economic Growth Rate in West Nusa Tenggara Province with Longitudinal Kernel Nonparametric Regression

Economic growth can indicate the success of economic development in people's lives, so it is essential to study the relationship between economic growth and factors that affect economic growth. Regression analysis is one of the most widely used statistical data analysis methods to determine the relationship pattern between the independent and dependent variables. Three methods can be used to estimate the regression curve, one of which is nonparametric regression. Economic growth data is one form of longitudinal data, with observations of independent subjects, with each subject being observed repeatedly over different periods. Kernel nonparametric regression model applications can be used for longitudinal data. This research aims to estimate the curve and get the best regression model. In this research, the smoothing technique chosen to estimate the nonparametric regression model for longitudinal data is the kernel triangle estimator, which can be obtained by minimizing the square of error using Weighted Least Squares (WLS) and selecting the optimum bandwidth using the Generalized Cross Validation (GCV) method. This study uses the economic growth rate in West Nusa Tenggara as the dependent variable and the human development index, population density, general allocation funds, local revenue, and labor force participation as independent variables. The result showed that the model is less accurate because of the low value of the coefficient for determination and the high value of the mean absolute percentage error (MAPE). This can be caused by the selection of bandwidth intervals that are too small.

Women’s Work Characteristics and Fertility Expectations

Previous research has shown that employment is an important social context affecting fertility, yet relatively little is known about the extent to which work characteristics affect fertility expectations. Using over 25 years of data from the 1979 National Longitudinal Survey of Youth, we analyzed the associations between part-time work and characteristics associated with autonomy over working time, specifically self-employment and managerial/professional occupation, and childbearing expectations among women ages 18–45 (N = 4,415). Logistic regression models for longitudinal data reveal that work characteristics are significantly associated with fertility expectations, but that the specific nature of the relationship varies by parity. Among women with one child, those working part-time had predicted probabilities of expecting to have additional children that were 2% higher than those working full-time. In contrast, among women without any children, those working part-time had predicted probabilities that were 2% lower than those working full-time. Similar contrasting relationships by parity were found when comparing self-employed women to employees and managers/professionals to those in other occupations. Findings were consistent across racial and ethnic groups. These results suggest that different mechanisms link work characteristics to fertility plans for mothers and non-mothers, specifically that role incompatibility and work-family conflict are more salient for mothers but that financial strain is so for non-mothers.

A mixed effects changepoint quantile regression model for longitudinal data with application on COVID-19 data

IntroductionLongitudinal individual response profiles could exhibit a mixture of two or more phases of increase or decrease in trend throughout the follow-up period, with one or more unknown transition points (changepoints). The detection and estimation of these changepoints is crucial. Most of the proposed statistical methods for detecting and estimating changepoints in literature rely on distributional assumptions that may not hold. In this case, a good alternative is to use a robust approach; the quantile regression model. There are methods in the literature to deal with quantile regression models with a changepoint. These methods ignore the within-subject dependence of longitudinal data.MethodsWe propose a mixed effects quantile regression model with changepoints to account for dependence structure in the longitudinal data. Fixed effects parameters, in addition to the location of the changepoint, are estimated using the profile estimation method. The stochastic approximation EM algorithm is proposed to estimate the fixed effects parameters exploiting the link between an asymmetric Laplace distribution and the quantile regression. In addition, the location of the changepoint is estimated using the usual optimization methods.Results and discussionA simulation study shows that the proposed estimation and inferential procedures perform reasonably well in finite samples. The practical use of the proposed model is illustrated using COVID-19 data. The data focus on the effect of global economic and health factors on the monthly death rate due to COVID-19 from 1 April 2020 to 30th April 2021. the results show a positive effect on the monthly number of patients with COVID-19 in intensive care units (ICUs) for both 0.5th and 0.8th quantiles of new monthly deaths per million. The stringency index, hospital beds, and diabetes prevalence have no significant effect on both 0.5th and 0.8th quantiles of new monthly deaths per million.

Semiparametric function-on-function quantile regression model with dynamic single-index interactions

In this paper we propose a new semiparametric function-on-function quantile regression model with time-dynamic single-index interactions. Our model is very flexible in taking into account of the nonlinear time-dynamic interaction effects of the multivariate longitudinal/functional covariates on the longitudinal response, that most existing quantile regression models for longitudinal data are special cases of our proposed model. We propose to approximate the bivariate nonparametric coefficient functions by tensor product B-splines, and employ a check loss minimization approach to estimate the bivariate coefficient functions and the index parameter vector. Under some mild conditions, we establish the asymptotic normality of the estimated single-index coefficients using projection orthogonalization technique, and obtain the convergence rates of the estimated bivariate coefficient functions. Furthermore, we propose a score test to examine whether there exist interaction effects between the covariates. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and an empirical data analysis.

The Strong Consistency for the Estimators of Longitudinal Data in Semiparametric Regression Model with ρ ̃-Mixing Errors

Consider the following semiparametric regression model for longitudinal data with - mixing errors: , where, the response variable and the covariate vector taken from the -th subject at time , is the - mixing random variables, We establish a strong consistency for the least squares estimator of the parametric and the estimator of the non-parametric function under some mild conditions.

Wine Closure Performance of Three Common Closure Types: Chemical and Sensory Impact on a Sauvignon Blanc Wine

A Napa Valley Sauvignon blanc wine was bottled with 200 each of a natural cork, a screw cap, and a synthetic cork. As browning is an index for wine oxidation, we assessed the brown color of each bottle with a spectrophotometer over 30 months. A random-effects regression model for longitudinal data on all bottles and closure groups found a browning growth trajectory for each closure group. Changes in the wine’s browning behavior at 18 months and 30 months showed that the browning of the wine bottles appeared to slow down later in the storage period, especially for natural corks. The between-bottle variation was the highest for the natural cork. At 30 months, we separated the bottles by the extent of browning and samples were pulled from the high, mid, and low levels of browning levels for each closure. The degree of browning is inversely correlated with free SO2 levels ranging from 5 to 12 mg/L. However, a Quantitative Descriptive Analysis (QDA™) sensory panel could not detect any difference in their aroma and flavor profile between closure types regardless of browning level. Even low levels of free SO2 retain protection against strong oxidation aromas, and visual browning detected by spectrophotometer seemed to precede oxidative aroma and flavor changes of the aging Sauvignon blanc.

Variable selection in semiparametric regression models for longitudinal data with informative observation times.

A common issue in longitudinal studies is that subjects' visits are irregular and may depend on observed outcome values which is known as longitudinal data with informative observation times (follow-up). Semiparametric regression modeling for this type of data has received much attention as it provides more flexibility in studying the association between regression factors and a longitudinal outcome. An important problem here is how to select relevant variables and estimate their coefficients in semiparametric regression models when the number of covariates at baseline is large. The current penalization procedures in semiparametric regression models for longitudinal data do not account for informative observation times. We propose a variable selection procedure that is suitable for the estimation methods based on pseudo-score functions. We investigate the asymptotic properties of penalized estimators and conduct simulation studies to illustrate the theoretical results. We also use the procedure for variable selection in semiparametric regression models for the STAR*D dataset from a multistage randomized clinical trial for treating major depressive disorder.

Confidence interval of the parameter on multipredictor biresponse longitudinal data analysis using local linear estimator for modeling of case increase and case fatality rates COVID-19 in Indonesia: A theoretical discussion

In this paper, we describe a theoretical discussion about confidence intervals for longitudinal data based on local linear estimator. The confidence interval represents the range of possible values in the estimating process. The confidence intervals for the parameter in nonparametric regression can be used to determine the predictor variables that have a significant effect on the response variable. In this research, we theoretically discuss estimation of the confidence interval of the parameter on multipredictor biresponse nonparametric regression model for longitudinal data based on local linear estimator which is applied to data of the case increase and case fatality rates COVID-19 in Indonesia. The estimation result can be used to determine the predictor variable, e.g. temperature which has a significant effect on the case increase and case fatality rates COVID-19 in Indonesia so that it can be advised to the ministry of health to control the case increase and case fatality rates COVID-19 in Indonesia.

Loneliness Predicts Development of Pain, Fatigue, and Depression in Older Adults

Pain, fatigue, and depression form a well-recognized symptom cluster that is posited to have a shared mechanism. It is possible that chronic psychosocial stressors such as loneliness may impact the central nervous system and immune system, potentially leading to symptom cluster development. Loneliness is an increasingly recognized type of psychosocial stress, especially among older American adults. Thus, we investigated whether loneliness increased risk of developing the symptom cluster of pain, fatigue, and depression over time. Using Health and Retirement Study data from 2006 – 2016, we examined self-respondents ≥50 years-old for the presence of co-occurring pain, fatigue, and depressive symptoms surpassing threshold levels (ie., the symptom cluster). Loneliness (measured by the 3-item UCLA Loneliness Scale) at baseline was used as the predictor of interest. Of the total sample (n=11,766), n=5,956 (50.6%) had up to two complete sets of follow-up symptom cluster measurements. Logistic regression models for longitudinal data were fitted using a generalized estimating equation (GEE). After adjusting for demographic and clinical variables, loneliness strongly predicted the development of the symptom cluster (adjusted OR=3.16 (95% CI 2.77, 3.61)) as well as each component symptom (pain adjusted OR=1.54 (95% CI 1.42, 1.67); fatigue adjusted OR=1.88 (95% CI 1.74, 2.03); depression adjusted OR = 3.87 (95% CI 3.55, 4.21). Further research should investigate whether interventions targeting loneliness or other psychosocial stressors may have a role in prevention of this symptom cluster.

Multivariate hidden semi-Markov models for longitudinal data: a dynamic regression modeling

The collection of multiple responses is common in longitudinal studies. It is of interest to assess the effects of covariates on multiple responses simultaneously using regression models. In some longitudinal studies, response variables are related to hidden states during the time-course study. The trend of responses for each subject can be segmented by hidden states. In the present study, we proposed a multivariate hidden semi-Markov regression model for longitudinal data having a multivariate normal distribution for responses in each hidden state. Based on the model, the effects of covariates on multiple responses have been calculated in the presence of hidden states. Simulation studies were conducted to evaluate the properties of the suggested model under different scenarios. The application of the suggested method was shown in hemodialysis patients’ data.

Long-term safety and efficacy of highly purified cannabidiol for treatment refractory epilepsy

ObjectiveTo evaluate the safety, efficacy, and tolerability of highly purified cannabidiol (CBD) for the treatment of seizures in children and adults with treatment-resistant epilepsy (TRE) in an open-label, expanded access program (EAP). MethodsOne hundred sixty-nine participants (89 children and 80 adults) with TRE received plant-derived highly purified CBD (Epidiolex® in the U.S.; 100 mg/mL oral solution) with a starting dose of 5 mg/kg/day divided twice per day and titrated to a maximum dose of 50 mg/kg/day over the study period to seizure control and tolerability and followed for up to 2 years. Seizure frequency (calendars) and severity (Chalfont Seizure Severity Score; CSSS) were collected at every study visit. Adverse Events were reported at/between study visits as required, and participants also completed Adverse Events Profile (AEP) which generates a numerical representation of AEs. Response to CBD was defined as ≥50% reduction in seizure frequency. Given non-normal distribution of seizure frequency, a log transformation was applied after which the generalized least squares regression model for longitudinal data was used. ResultsEvidence from the adjusted model revealed a significant mean reduction in seizure frequency compared to baseline in children and adults at all time points (1 month and 1 and 2 years). Percentage of children achieving ≥50% seizure frequency reduction was 44% at month 1, and 41% at year 1, and 61% reduction at year 2, while adult responder rates were 34% at month 1, 53% at year 1, and 71% at year 2 (all P < 0.0001). CSSS showed a sustained reduction from baseline to all 3 time points. Children displayed 52% seizure reduction at month 1, a 51% reduction at year 1, and 75% reduction at year 2. Seizure reductions in adults were 60%, 81%, and 85%, respectively (all P < 0.0001). While there were no significant differences between seizure frequency reduction between children and adults at all time points, there was a significant difference in seizure severity reduction at year 1, with adults reporting greater improvement in seizure severity (P < 0.001). The most commonly reported adverse events in the study period were diarrhea, sedation, and decreased appetite. AEP revealed significant improvement from baseline at multiple time points in adults and children, and the mean AEP scores were always lower compared to baseline over the duration of the study. SignificanceOur study provides further evidence of sustained seizure frequency and severity reduction over two years of treatment with highly purified CBD in TRE. In addition, CBD was generally well tolerated with minority of participants experiencing adverse events resulting in stopping CBD.

Heterogeneity in food expenditure among US families: evidence from longitudinal quantile regression

Empirical studies on food expenditure are largely based on cross-section data and for a few studies based on longitudinal (or panel) data the focus has been on the conditional mean. While the former, by construction, cannot model the dependencies between observations across time, the latter cannot look at the relationship between food expenditure and covariates (such as income, education, etc.) at lower (or upper) quantiles, which are of interest to policymakers. This paper analyzes expenditures on total food (TF), food at home (FAH), and food away from home (FAFH) using mean regression and quantile regression models for longitudinal data to examine the impact of economic recession and various demographic, socioeconomic, and geographic factors. The data are taken from the Panel Study of Income Dynamics (PSID) and comprise of 2174 families in the United States (US) observed between 2001 and 2015. Results indicate that age and education of the head, family income, female-headed family, marital status, and economic recession are important determinants for all three types of food expenditure. Spouse education, family size, and some regional indicators are important for expenditures on TF and FAH, but not for FAFH. Quantile analysis reveals considerable heterogeneity in the covariate effects for all types of food expenditure, which cannot be captured by models focused on conditional mean. The study ends by showing that modeling conditional dependence between observations across time for the same family unit is crucial to reducing/avoiding heterogeneity bias and better model fitting.

Effect of phthalates exposure during perinatal period on hormonal profile in Mexican males during their first months of life.

Phthalates affect development of male reproductive system acting as an antiandrogenic agents. We sought to explore if perinatal exposure to phthalates could alter male hormone levels in humans during the first months of life. A cohort of 83 pregnant women and their male infants were studied. Five phthalate metabolites were measured in the mother's urine during the first, second, and third trimesters of pregnancy and during the first, third, and sixth months of life in the infants. Luteinizing hormone (LH), follicle-stimulating hormone (FSH), testosterone and inhibin B were analyzed. Association between phthalate exposure and hormone variation was assessed using regression models for longitudinal data. Mono-butyl phthalate reduced FSH concentration (ß = -0.0012 international units [IU]/L, p < 0.01), mono-ethylhexyl phthalate reduced inhibin B (ß = -0.0094 pg/mL, p = 0.02), monoethyl phthalate reduced testosterone (ß = -0.0071 ng/L, p = 0.07), mono-ocytl phthalate reduced LH (ß = -0.0041 IU/L, p = 0.13). No effects were observed for exposure to mono-methyl phthalate. Our results are consistent with the findings in animal and human studies. Special precaution should be taken when measuring phthalate exposure in susceptible populations such as pregnant women and infants.

Nonparametric Regression Model for Longitudinal Data with Mixed Truncated Spline and Fourier Series

Existing literature in nonparametric regression has established a model that only applies one estimator to all predictors. This study is aimed at developing a mixed truncated spline and Fourier series model in nonparametric regression for longitudinal data. The mixed estimator is obtained by solving the two-stage estimation, consisting of a penalized weighted least square (PWLS) and weighted least square (WLS) optimization. To demonstrate the performance of the proposed method, simulation and real data are provided. The results of the simulated data and case study show a consistent finding.

Mindfulness meditation and exercise both improve sleep quality: Secondary analysis of a randomized controlled trial of community dwelling adults

ObjectivesTo assess the benefits of training in mindfulness-based stress reduction (MBSR) or moderate intensity exercise (EX) for improving sleep quality. DesignRandomized controlled trial. SettingOutpatient, community-based. ParticipantsHealthy adults (n = 413) aged 30–69 who did not regularly exercise or practice meditation, and who had no known prior sleep problems. Interventions1) 8-weeks of MBSR training; 2) matched EX training; or 3) wait-list control. MeasurementsThe Pittsburgh Sleep Quality Index (PSQI) was administered at baseline and at 1, 3, 5, and 7-month follow-up visits. AnalysisTotal PSQI scores and three PSQI factors (perceived sleep quality; daily disturbance, sleep efficiency) were assessed using linear mixed effects regression models for longitudinal data. ResultsCompared to controls, PSQI global scores improved significantly for EX (mean change -0.98 points [95% CI -1.56, -0.41] p = 0.001) and marginally for MBSR (-0.53 [-1.10, 0.04] p = 0.07). The perceived sleep quality factor improved for both EX (-0.18 [-0.30, -0.07] p = 0.002) and MBSR (-0.12 [-0.24, -0.01] p = 0.035). The daily disturbance factor improved slightly more for MBSR (-0.13 [-0.22, -0.033] p = 0.008) than EX (-0.09 [-0.19, 0.004] p = 0.06). The sleep efficiency factor did not improve after MBSR (0.08 [-0.045, 0.21] p = 0.2) or EX (-0.07 [-0.20, 0.06] p = 0.3). Improvements in the sleep quality were sustained over 7 months for both groups. ConclusionsTraining in MBSR and EX produced small but statistically significant and sustained improvements in sleep quality. For EX participants, this improvement was due primarily to improvements in perceived sleep quality. For MBSR, the decrease in daily disturbance was more important.

Do caregivers’ perspectives matter? Working alliances and treatment outcomes in trauma-focused cognitive behavioural therapy with children and adolescents

ABSTRACT Background: Caregivers play a key role in the success of trauma-focused cognitive behavioural therapy (TF-CBT). Yet, the effect of their alliance on treatment outcomes besides the other parties in treatment has hardly been studied. Objective: This study examined the working alliance (WA) of therapists, patients and caregivers in TF-CBT and its contribution on treatment outcome over time. Methods: N = 76 children and adolescents (mean age = 12.66 years, range 7–17, M/F ratio: .43) participated in the TF-CBT arm of a randomized controlled trial. The WA was assessed with the Working Alliance Inventory Short Version (WAI-S) at two measurement points, while symptom level of posttraumatic stress symptoms (PTSS) was assessed with the Clinician-Administered PTSD Scale for Children and Adolescents (CAPS-CA). Paired sample t-tests, intraclass correlations (ICC), and mixed-effects regression models for longitudinal data were performed. Results: The alliance rating was high across all informants, with caregivers achieving the highest rating. The average level of cross-informant agreement on the alliance was low between therapists and caregivers (ICC = .26) and moderate between therapists and patients (ICC =.65). A significant contribution of an alliance improvement to the reduction of PTSS over time was found in each of the two tested models: therapists with patients model (b = .682) and therapists with caregivers model (b = .807). However, these effects were not detected with all four perspectives in one comprehensive model. Conclusion: In summary, the potential of caregivers’ views should receive more attention in the therapeutic process of trauma-focused therapy.

Semiparametric regression curve estimation for longitudinal data using mixed spline truncated and fourier series estimator

Semiparametric regression is a regression approach that is used when the form of regression curve is assumed to be partly known and partly unknown. In the semiparametric regression model, the same type of estimation method is generally used for some or all of the predictor variables. There are many examples of data cases that have different patterns on each predictor variable, so if the data is forced to use only one form of estimator to estimate the regression curve, it will produce estimation that will not be appropriate to the data pattern. Therefore, a mixed estimator needs to be developed. However, mixed estimator in previous studies was only able to handle cross-sectional data. So this study uses longitudinal data that has advantages, one of which is estimation of each individual characteristic and time (period) characteristic are obtained separately in longitudinal data. Therefore, this study develops a mixed Spline Truncated and Fourier Series estimator in semiparametric regression for longitudinal data using the Weighted Least Square method. Estimation of the semiparametric regression model for longitudinal data using mixed estimator of Spline Truncated and Fourier Series is where D (K,m) = XA (K,m) + TB (K,m) + ZC (K,m). The selection of the best model is based on knot points and optimum oscillation parameters that should be selected optimally using minimum Generalized Cross Validation (GCV) value.

Loss Reserving Estimation With Correlated Run-Off Triangles in a Quantile Longitudinal Model

In this paper, we consider a loss reserving model for a general insurance portfolio consisting of a number of correlated run-off triangles that can be embedded within the quantile regression model for longitudinal data. The model proposes a combination of the between- and within-subportfolios (run-off triangles) estimating functions for regression parameter estimation, which take into account the correlation and variation of the run-off triangles. The proposed method is robust to the error correlation structure, improves the efficiency of parameter estimators, and is useful for the estimation of the reserve risk margin and value at risk (VaR) in actuarial and finance applications.

Indoor air pollution and respiratory health effects in inner city children with moderate to severe asthma

Indoor air pollution is increasingly recognized as a significant risk for respiratory illness, particularly in vulnerable populations. Thirty-six children aged 6–14 years with moderate/severe asthma from inner city areas in New York City were studied for 2-week periods (summer and winter) using diaries and spirometry. Seven-day integrated indoor samples of PM10, PM2.5, trace elements, elemental/organic carbon, black carbon, and criteria gases (NO2, SO2, and O3) were collected in the subjects’ residences. Asthma outcomes included cough and wheeze severity, albuterol use, and pulmonary function. Mixed effects regression models for longitudinal data were used to relate weekly indoor pollutant concentrations to asthma outcomes. Odds ratios (ORs) were calculated for ordinal outcomes. During winter, significant positive associations for average weekly symptom severity scores were seen for NO2 (OR = 2.83; p = 0.02), calcium (OR = 3.29; p = 0.02), and silicon (OR = 3.64; p = 0.04). In summer, chlorine was associated with average weekly symptom scores (OR = 1.85; p = 0.004). Average albuterol puff use per day in winter was associated with NO2 (OR = 5.89; p = 0.009), nickel (OR = 2.27; p = 0.05), and silicon (OR = 5.59; p = 0.05). Albuterol use was not associated with indoor pollutants in summer. Asthma severity was associated with specific indoor pollutants. Seasonal differences were observed by pollutant and by clinical index studied.