Linear Model For Longitudinal Data Research Articles

Large-Scale Generalized Linear Models for Longitudinal Data with Grouped Patterns of Unobserved Heterogeneity

ABSTRACT This article provides methods for flexibly capturing unobservable heterogeneity from longitudinal data in the context of an exponential family of distributions. The group memberships of individual units are left unspecified, and their heterogeneity is influenced by group-specific unobservable factor structures. The model includes, as special cases, probit, logit, and Poisson regressions with interactive fixed effects along with unknown group membership. We discuss a computationally efficient estimation method and derive the corresponding asymptotic theory. Uniform consistency of the estimated group membership is established. To test heterogeneous regression coefficients within groups, we propose a Swamy-type test that allows for unobserved heterogeneity. We apply the proposed method to the study of market structure of the taxi industry in New York City. Our method unveils interesting and important insights from large-scale longitudinal data that consist of over 450 million data points.

Behavioural and psychological patterns of patients with idiopathic pulmonary fibrosis: a prospective study

BackgroundIdiopathic pulmonary fibrosis (IPF) is a chronic and progressive lung condition. Currently, care models predominantly focus on acute medical and pharmacological needs. As a step towards holistic care, the aim of this prospective study was to investigate the psychological and behavioural needs of IPF patients treated with pirfenidone from diagnosis until two years of follow-up.MethodsThe following variables were selected from the literature on patients’ needs and the COM-B model, a theoretical model explaining behaviour: medication adherence, barriers to adherence, importance and intentions of medication adherence, anxiety, depression, health literacy, knowledge, reported side effects, adherence to sun protection recommendations, alcohol use, physical activity, quality of life and health status. Linear and generalised linear models for longitudinal data were used to evaluate the evolution since treatment initiation.ResultsWe included 66 outpatients: 72.7% men, mean age of 70.3 years (range 50–87), predicted mean forced vital capacity of 85.8% (SD 17.4) and predicted mean diffusing capacity for monoxide of 56.9% (SD 15.7). The participants placed considerable importance on following the treatment recommendations. We noticed difficulties regarding health literacy, alcohol use, pirfenidone adherence (decline over time) and adherence to sun protection recommendations (early in follow-up care). There were low levels of physical activity (no effect of time), high body mass indices (decline over time) and moderate levels of depression and anxiety.ConclusionWhen providing care to IPF patients, behavioural issues, health literacy and psychological well-being should be taken into consideration. There is a need to further explore interventions and care models to tackle these difficulties.Trial registration This study was registered in the ClinicalTrials.gov database (identifier NCT03567785) on May 9th, 2018

A two-step estimator for generalized linear models for longitudinal data with time-varying measurement error

A two-step estimator for generalized linear models for longitudinal data with time-varying measurement error

Clinical Outcomes of Radical Surgery and Antimicrobial Agents in Vascular Pythiosis: A Multicenter Prospective Study.

Vascular pythiosis is a rare, neglected, life-threatening disease with mortality of 100% in patients with incomplete surgical resection or patients with persistently elevated serum β-d-glucan (BDG). The study was conducted to understand the clinical outcomes of new treatment protocols and potential use of erythrocyte sedimentation rate (ESR) and c-reactive protein (CRP) as alternative monitoring tools, given recent favorable minimum inhibitory concentrations (MICs) of antibacterial agents and prohibitive cost of serum BDG in Thailand. A prospective cohort study of patients with vascular pythiosis was conducted between February 2019 and August 2020. After diagnosis, patients were followed at 0.5, 1, 1.5, 3, and 6 months. Descriptive statistics, Spearman’s correlation coefficient, and general linear model for longitudinal data were used. Amongst the cohort of ten vascular pythiosis patients, four had residual disease after surgery. Among four with residual disease, one developed disseminated disease and died, one developed relapse disease requiring surgery, and two were successfully managed with antimicrobial agents. The spearman’s correlation coefficients between BDG and ESR, and between BDG and CRP in patients without relapse or disseminated disease were 0.65 and 0.60, respectively. Tetracyclines and macrolides had most favorable minimum inhibitory concentrations and synergistic effects were observed in combinations of these two antibiotic classes. Adjunctive use of azithromycin and doxycycline preliminarily improved survival in vascular pythiosis patients with residual disease. Further studies are needed to understand the trends of ESR and CRP in this population.

Progression of cognitive and behavioral disturbances in motor neuron diseases assessed using standard and computer-based batteries

Objective: Detecting and monitoring cognitive and behavioral deficits in motor neuron diseases (MND) is critical due to their considerable clinical impact. In this scenario, computer-based batteries may play an important role. In this study, we investigated the progression of cognitive and behavioral deficits in MND patients using both standard and computer-based neuropsychological batteries. Methods: This is a retrospective study on 74 MND patients (52 amyotrophic lateral sclerosis [ALS], 12 primary lateral sclerosis [PLS], and 10 progressive muscular atrophy [PMA]) who were followed up for 12 months and underwent up to three cognitive/behavioral assessments, 6 months apart, including standard and/or computerized based (the Test of Attentional Performance [TAP]) batteries. Behavioral/cognitive changes were investigated over time using generalized linear model for longitudinal data accounting for time and revised-ALS Functional Rating Scale. Results: Over 12 months, ALS patients showed a global cognitive decline (Mini Mental State Examination) at the standard battery and reduced performance in the alertness, sustained and divided attention, go/nogo, cross-modal and incompatibility TAP tasks. Most of these findings remained significant when ALSFRS-R changes over time were included as covariate in the analyses. ALS patients did not show significant behavioral abnormalities over time. No cognitive and behavioral changes were found in PLS and PMA cases. Conclusions: Computer-based neuropsychological evaluations are able to identify subtle cognitive changes in ALS, unique to this condition. This study highlights the need of specific, accurate and well-tolerated tools for the monitoring of cognitive deficits in MND.

Uterine Cervical Change at Term Examined Using Ultrasound Elastography: A Longitudinal Study.

The aim of the study was to investigate if there are changes in elastographic parameters in the cervix at term around the time of delivery and if there are differences in the parameters between women with spontaneous labor and those without labor (labor induction). Nulliparous women at 36 weeks of gestation eligible for vaginal delivery were enrolled. Cervical elastography was performed and cervical length were measured using the E-CervixTM system (WS80A Ultrasound System, Samsung Medison, Seoul, Korea) at each weekly antenatal visit until admission for spontaneous labor or labor induction. E-Cervix parameters of interest included elasticity contrast index (ECI), internal os strain mean level (IOS), external os strain mean level (EOS), IOS/EOS strain mean ratio, strain mean level, and hardness ratio. Regression analysis was performed using days from elastographic measurement at each visit to admission for delivery and the presence or absence of labor against cervical length, and each E-Cervix parameter fitted to a linear model for longitudinal data measured repeatedly. A total of 96 women were included in the analysis, (spontaneous labor, n = 39; labor induction, n = 57). Baseline characteristics were not different between the two groups except for cesarean delivery rate. Cervical length decreased with advancing gestation and was different between the two groups. Most elastographic parameters including ECI, IOS, EOS, strain mean, and hardness ratio were significantly different between the two groups. In addition, ECI, IOS, and strain mean values significantly increased with advancing gestation. Our longitudinal study using ultrasound elastography indicated that E-cervix parameters tended to change linearly at term near the time of admission for delivery and that there were differences in E-Cervix parameters according to the presence or absence of labor.

Valorization of corn cob for the obtention and purification of endoglucanase produced by SSF

Abstract Agro-food by-products contain valuable nutrients which are wasted. In this work, solid-state fermentation (SSF) was carried out using corn cob as substrate for endoglucanase production. The radial growth of three fungal strains -Trichoderma harzianum T104, Aspergillus niger GH1 and Aspergillus niger NRRL3- was analyzed in order to select the most appropriate. Radial growth data were analyzed with a mixed linear model for longitudinal data and no statistically significant differences were found between both A. niger strains. Endoglucanase was separated from the extract of A. niger GH1 by fast protein liquid chromatography (FPLC).The highest endoglucanase activity was detected in fraction number three collected from FPLC corresponding to 72 h of SSF. Seven bands in a range from 24 to 50 kDa, which correspond to endoglucanase from fungal extract, were detected by zymogram analysis. According to protein quantification performed by the ImageJ software, 85% of the proteins present in the samples collected by FPLC corresponded to endoglucanase proteins. The purified endoglucanase retained about 100% of its catalytic activity at 30 °C and 50 °C and was stable in a pH range between 4.00-6.00. These properties make this isolated enzyme suitable for industrial applications such as the saccharification process for bioethanol production.

Effect of insecticide treated nets fence in protecting cattle against tsetse and other biting flies in Arba Minch Zuria district, Southern Ethiopia

A field trial was carried out to assess the effect of insecticide treated net in protecting cattle from tsetse and other flies. A total of 35 pens were constructed, out of which 30 of them were fenced with insecticide treated net which served as treatment group and the remaining 5 pens were untreated controls. The fly populations around the pens were monthly monitored for five months using NGU traps deployed 5 m away from the cattle pens. The defensive movements of different body parts manifested by an animal for fly protections were observed for 5 minutes in each of the experimental and control groups. Additionally, other parameters such as packed cell volume, milk yield and body condition scores and buffy coat examination were investigated for both groups. Milk yield, body condition scores, packed cell volume (PCV) and data of defensive movements of animals were analyzed using linear model for longitudinal data or repeated measures by specifying time (monitoring cycles) and cattle as repeated variables. The result of this study showed that the overall proportion of fly catches was significantly lower in treated (38.3%) than control group (61.7%). Similarly, a significantly lower proportion of tsetse flies (28.4% versus 71.6%), biting flies (40.7% versus 59.3) and non-biting nuisance flies (39.7% versus 60.3%) compared to treatment. As a result, animals in treatment group had significantly lower average defensive movements of different body parts (7.84) compared to those in controls (16.37). All animals in both groups were negative for trypanosome infection and and there was no significant difference in their mean PCV values. Significant variation was not observed in daily milk yield between cows in treatment (0.83 liter) and in controls (0.53 liter). Fly densities had showed positive and negative relationships with defensive movements and PCV values over the monitoring time period, respectively. Body condition score of animals in the treatment group was also significantly higher (p<0.05) than those in controls. In conclusion, deltamethrin treated netting was found to reduce the challenges of tsetse and other biting flies, and thus can contribute to improved performances of animals in treatment groups.Keywords: Cattle; Fly protection; Insecticide treated net; Southern Ethiopia; Zero-grazing

Doubly robust estimation of partially linear models for longitudinal data with dropouts and measurement error in covariates

ABSTRACTIn longitudinal studies, missing responses and mismeasured covariates are commonly seen due to the data collection process. Without cautiousness in data analysis, inferences from the standard statistical approaches may lead to wrong conclusions. In order to improve the estimation for longitudinal data analysis, a doubly robust estimation method for partially linear models, which can simultaneously account for the missing responses and mismeasured covariates, is proposed. Imprecisions of covariates are corrected by taking advantage of the independence between replicate measurement errors, and missing responses are handled by the doubly robust estimation under the mechanism of missing at random. The asymptotic properties of the proposed estimators are established under regularity conditions, and simulation studies demonstrate desired properties. Finally, the proposed method is applied to data from the Lifestyle Education for Activity and Nutrition study.

Applying the hierarchical linear model to longitudinal data / La aplicación del modelo lineal jerárquico a datos longitudinales

Educational researchers and school administrators frequently evaluate academic outcomes collected from cross-sectional sampling designs with overt nested structures, such as when students are nested within schools. More recently, interest has focused on the longitudinal collection of academic outcomes to evaluate a student’s growth across time. In a longitudinal context, the repeatedly measured academic outcomes are nested within a student. Proper analysis of longitudinal data requires the hierarchical linear model to quantify the extra correlations within students created by the nested sampling structure. In this article, we introduce the hierarchical linear model used to quantify and predict between-student differences in a repeatedly measured continuous maths achievement outcome. This introduction is presented as a conversation representative of those we have frequently with individuals who lack statistical training in hierarchical linear models for longitudinal data. Specifically, we cover why repeated-measures ANOVA may not always be appropriate, how the hierarchical linear model can be used to quantify between-student differences in change and how student- and occasion-level predictors can be properly modelled and interpreted.

Doubly robust estimation of generalized partial linear models for longitudinal data with dropouts.

We develop a doubly robust estimation of generalized partial linear models for longitudinal data with dropouts. Our method extends the highly efficient aggregate unbiased estimating function approach proposed in Qu et al. (2010) to a doubly robust one in the sense that under missing at random (MAR), our estimator is consistent when either the linear conditional mean condition is satisfied or a model for the dropout process is correctly specified. We begin with a generalized linear model for the marginal mean, and then move forward to a generalized partial linear model, allowing for nonparametric covariate effect by using the regression spline smoothing approximation. We establish the asymptotic theory for the proposed method and use simulation studies to compare its finite sample performance with that of Qu's method, the complete-case generalized estimating equation (GEE) and the inverse-probability weighted GEE. The proposed method is finally illustrated using data from a longitudinal cohort study.

Subject-wise empirical likelihood inference in partial linear models for longitudinal data

In analyzing longitudinal data, within-subject correlations are a major factor that affects statistical efficiency. Working with a partially linear model for longitudinal data, a subject-wise empirical likelihood based method that takes the within-subject correlations into consideration is proposed to estimate the model parameters. A nonparametric version of the Wilks Theorem for the limiting distribution of the empirical likelihood ratio, which relies on a kernel regression smoothing method to properly centered data, is derived. The estimation of the nonparametric baseline function is also considered. A simulation study and an application are reported to investigate the finite sample properties of the proposed method. The numerical results demonstrate the usefulness of the proposed method.

Joint partially linear model for longitudinal data with informative drop-outs: Joint Partially Linear Model for Longitudinal Data with Informative Drop-Outs

Joint partially linear model for longitudinal data with informative drop-outs: Joint Partially Linear Model for Longitudinal Data with Informative Drop-Outs

Generalized empirical likelihood inference in partially linear model for longitudinal data with missing response variables and error-prone covariates

ABSTRACTIn this article, we consider statistical inference for longitudinal partial linear models when the response variable is sometimes missing with missingness probability depending on the covariate that is measured with error. A generalized empirical likelihood (GEL) method is proposed by combining correction attenuation and quadratic inference functions. The method that takes into consideration the correlation within groups is used to estimate the regression coefficients. Furthermore, residual-adjusted empirical likelihood (EL) is employed for estimating the baseline function so that undersmoothing is avoided. The empirical log-likelihood ratios are proven to be asymptotically Chi-squared, and the corresponding confidence regions for the parameters of interest are then constructed. Compared with methods based on NAs, the GEL does not require consistent estimators for the asymptotic variance and bias. The numerical study is conducted to compare the performance of the EL and the normal approximation-based method, and a real example is analysed.

Joint partially linear model for longitudinal data with informative drop-outs.

In biomedical research, a steep rise or decline in longitudinal biomarkers may indicate latent disease progression, which may subsequently cause patients to drop out of the study. Ignoring the informative drop-out can cause bias in estimation of the longitudinal model. In such cases, a full parametric specification may be insufficient to capture the complicated pattern of the longitudinal biomarkers. For these types of longitudinal data with the issue of informative drop-outs, we develop a joint partially linear model, with an aim to find the trajectory of the longitudinal biomarker. Specifically, an arbitrary function of time along with linear fixed and random covariate effects is proposed in the model for the biomarker, while a flexible semiparametric transformation model is used to describe the drop-out mechanism. Advantages of this semiparametric joint modeling approach are the following: 1) it provides an easier interpretation, compared to standard nonparametric regression models, and 2) it is a natural way to control for common (observable and unobservable) prognostic factors that may affect both the longitudinal trajectory and the drop-out process. We describe a sieve maximum likelihood estimation procedure using the EM algorithm, where the Akaike information criterion (AIC) and Bayesian information criterion (BIC) are considered to select the number of knots. We show that the proposed estimators achieve desirable asymptotic properties through empirical process theory. The proposed methods are evaluated by simulation studies and applied to prostate cancer data.

Robust estimation of partially linear models for longitudinal data with dropouts and measurement error

Outliers, measurement error, and missing data are commonly seen in longitudinal data because of its data collection process. However, no method can address all three of these issues simultaneously. This paper focuses on the robust estimation of partially linear models for longitudinal data with dropouts and measurement error. A new robust estimating equation, simultaneously tackling outliers, measurement error, and missingness, is proposed. The asymptotic properties of the proposed estimator are established under some regularity conditions. The proposed method is easy to implement in practice by utilizing the existing standard generalized estimating equations algorithms. The comprehensive simulation studies show the strength of the proposed method in dealing with longitudinal data with all three features. Finally, the proposed method is applied to data from the Lifestyle Education for Activity and Nutrition study and confirms the effectiveness of the intervention in producing weight loss at month 9. Copyright © 2016 John Wiley & Sons, Ltd.

The weighted general linear model for longitudinal medical cost data – an application in colorectal cancer

ABSTRACTIdentifying cost-effective decisions that can take into account of medical cost and health outcome is an important issue under very limited resources. Analyzing medical costs has been challenged owing to skewness of cost distributions, heterogeneity across samples and censoring. When censoring is due to administrative reasons, the total cost might be related to the survival time since longer survivals are likely to be censored and the corresponding total cost will be censored as well. This paper uses the general linear model for the longitudinal data to model the repeated medical cost data and the weighted estimating equation is used to find more accurate estimates for the parameter. Furthermore, the asymptotic properties for the proposed model are discussed. Simulations are used to evaluate the performance of estimators under various scenarios. Finally, the proposed model is implemented on the data extracted from National Health Insurance database for patients with the colorectal cancer.

Simultaneous mean and covariance estimation of partially linear models for longitudinal data with missing responses and covariate measurement error

Missing responses and covariate measurement error are very commonly seen in practice. New estimating equations are developed to simultaneously estimate the mean and covariance under a partially linear model for longitudinal data with missing responses and covariate measurement error. Specifically, a novel approach is proposed to handle measurement error by using independent replicate measurements. Compared with existing methods, the proposed method requires fewer assumptions. For example, it does not require to specify the distribution of the mismeasured covariate or the measurement error, and does not need a parametric model to estimate the probability of being observed or to impute the missing responses. Additionally, the proposed estimating equations are easy to implement in most popular statistical softwares by applying existing algorithms for standard generalized estimating equations. The asymptotic properties of the proposed estimators are established under regularity conditions, and simulation studies demonstrate desired properties. Finally, the proposed method is applied to data from the Lifestyle Education for Activity and Nutrition (LEAN) study. This data analysis confirms the effectiveness of the intervention in producing weight loss at month nine.

Bayesian logistic mixed-effects modelling of transect data: relating red tree coral presence to habitat characteristics

Abstract The collection of continuous data on transects is a common practice in habitat and fishery stock assessments; however, the application of standard regression models that assume independence to serially correlated data is problematic. We show that generalized linear mixed models (GLMMs), i.e. generalized linear models for longitudinal data, that are normally used for studies performed over time can also be applied to other types of clustered or serially correlated data. We apply a specific GLMM for longitudinal data, a hierarchical Bayesian logistic mixed-effects model (BLMM), to a marine ecology dataset obtained from submersible video recordings of the seabed on transects at two sites in the Gulf of Alaska. The BLMM was effective in relating the presence of red tree corals (Primnoa pacifica; i.e. binary data) to habitat characteristics: the presence of red tree corals is highly associated with bedrock as the primary substrate (estimated odds ratio 9–19), high to very high seabed roughness (estimated odds ratio 3–5), and medium to high slope (estimated odds ratio 2–3). The covariate depth was less important at the sites. We also demonstrate and compare two methods of model checking: full and mixed posterior predictive assessments, the latter of which provided a more realistic assessment, and we calculate the variance partition coefficient for reporting the variation explained by multiple levels of the hierarchical model.

Productive and reproductive performances of dairy cattle herds in Treviso province, Italy (2009-2012): an assessment of the potential impact of Schmallenberg virus epidemic.

BackgroundSchmallenberg virus (SBV) has spread across Europe since mid-2011, causing unspecific and transitory symptoms in ruminants and congenital malformations in their offspring. Evidence for the impact of SBV on cattle (re)productive performance is limited. Using a comprehensive data set from a SBV-affected province in North-East Italy, this study aimed at assessing the potential impact of SBV emergence on 11 productive and reproductive performance indicators of dairy cattle herds, accounting for weather conditions and other herd-level factors that could also influence these indicators.ResultsA total of 127 farms with an average of 71 cows per farm (range 29–496) were monitored monthly from January 2009 to June 2012. Mixed-effects linear models for longitudinal data were used to assess the average variation in herds’ performance indicators over semesters (Jan-Jun 2009, Jul-Dec 2009, Jan-Jun 2010, Jul-Dec 2010, Jan-Jun 2011, Jul-Dec 2011, Jan-Jun 2012) and trimesters therein. Taking the second semester of 2011 as reference, significant decreases in the average lactation length (−6 days, on average) and calving-to-conception interval (−4 days, on average) were observed relative to the same semesters of the years 2010 and 2009, respectively. Similarly, during the last trimester of 2011, which is most likely to cover the SBV infection period in the study area, there was an average decrease of −4 days (lactation length) and −7 days (calving-to-conception interval) compared to the same trimesters of the years 2010 and 2009, respectively. However, the observed decreases actually represent a positive outcome that is not as such imputable to SBV emergence, but rather reflects other beneficial changes in farm management. None of the other indicators showed significant variations, confirming the relatively mild expression of SBV infection in cattle.ConclusionsAlthough the emergence of SBV might have significantly affected the (re)productive performance of some individual farms, we concluded that overall at the province level there were no significant variations attributable to SBV, at least not in a way that would lead to negative effects on farm profitability.Electronic supplementary materialThe online version of this article (doi:10.1186/s12917-015-0527-1) contains supplementary material, which is available to authorized users.