Piecewise Mixed-effects Models Research Articles

Short-term responses of meat ewes facing an acute nutritional challenge in early-mid lactation.

Simulating a consequence of a climate change event on feed availability, responses of Mediterranean meat ewes facing an acute undernutritional challenge (CHA; i.e., fed only low nutritional value cereal straw) were evaluated at a sensitive physiological stage (i.e., early suckling). Forty Romane ewes were chosen at early-mid pregnancy (around 2 mo) according to parity (20 primiparous, PRIM; 20 multiparous, MULT); feed efficiency genetic line of their sires (residual feed intake [RFI]; efficient, RFI-, n = 10 per parity; inefficient, RFI+, n = 10 per parity); litter size (i.e., bearing twins, diagnosed by ultrasonography); body weight (BW, kg) and body condition score (BCS) (initial BW and BCS [mean ± SD]: 51.6 ± 7.41kg; 2.5 ± 0.20, respectively; representing flock' averages per parity). Effects on dry matter intake (DMI), ewes' BW and BCS, subcutaneous dorsal fat thickness (DFT), energy metabolism (plasma non-esterified fatty acids [NEFA], β-hydroxybutyrate (β-OHB), glucose, urea, triiodothyronine [T3]), and lambs' growth (BW and average daily gain [ADG]; g/d) were examined before, during and after CHA. Individuals' profiles of the response-recovery to CHA were described using a piecewise mixed-effects model. The fixed effect of parity and genetic line and the random effect of individual (ewe) were considered. A linear mixed-effects model was fitted to explore the effects on lambs' growth. The 2-d straw-only CHA had significant effects on most of the recorded parameters. Meaningful drops and recoveries were observed on ewes' DMI, BW, and DFT with effect on postchallenge levels. BW, BCS, DFT, or DMI were also affected by parity (MULT > PRIM) but not by genetic line. Plasma NEFA, β-OHB, glucose, urea, and T3 responded well to CHA with drops in T3, urea, and glucose levels, whereas NEFA and β-OHB significantly increased after CHA. MULT ewes presented sharper β-OHB recovery from CHA than PRIM (P ≤ 0.05). With this study, we provide tangible and necessary data for an emerging field of research. Our results give new insights into how such a short and abrupt CHA affects some key zootechnical and physiological parameters, and to what extent the impacts of CHA and the ewes' response-recovery are influenced. It also revealed potential between-individual differences in the adaptive capacities of ewes, which require further exploration.

Specifying the Efficacy of Digital Therapeutic Tools for Depression and Anxiety: Retrospective, 2-Cohort, Real-World Analysis.

Depression and anxiety are the main sources of work and social disabilities as well as health-related problems around the world. Digital therapeutic solutions using cognitive behavioral therapy have demonstrated efficacy in depression and anxiety. A common goal of digital health apps is to increase user digital engagement to improve outcomes. However, there is a limited understanding of the association between digital platform components and clinical outcomes. The aim of the study is to investigate the contribution of specific digital engagement tools to mental health conditions. We hypothesized that participation in coaching sessions and breathing exercises would be associated with a reduction in depression and anxiety. Depression and general anxiety symptoms were evaluated in real-world data cohorts using the digital health platform for digital intervention and monitoring change. This retrospective real-world analysis of users on a mobile platform-based treatment followed two cohorts of people: (1) users who started with moderate levels of depression and completed at least 2 depression assessments (n=519) and (2) users who started with moderate levels of anxiety and completed at least 2 anxiety assessments (n=474). Levels of depression (Patient Health Questionnaire-9) and anxiety (Generalized Anxiety Disorder-7) were tracked throughout the first 16 weeks. A piecewise mixed-effects model was applied to model the trajectories of the Patient Health Questionnaire-9 and the Generalized Anxiety Disorder-7 mean scores in 2 segments (1-6 weeks and 7-16 weeks). Finally, simple slope analysis was used for the interpretation of the interactions probing the moderators: coaching sessions and breathing exercises in both depression and anxiety cohorts. Analysis revealed a significant decrease in depression symptoms (β=-.37, 95% CI -0.46 to 0.28; P≤.001) during the period of weeks 1-6 of app use, which was maintained during the period of 7-16 weeks. Coach interaction significantly moderated the reduction in depression symptoms during the period of weeks 1-6 (β=-.03, 95% CI -0.05 to -0.001; P=.02). A significant decrease in anxiety symptoms (β=-.41, 95% CI -0.50 to -0.33; P≤.001) was revealed during the period of 1-6 weeks, which was maintained during the period of 7-16 weeks. Breathing exercises significantly moderated the reduction in anxiety symptoms during the period of 1-6 weeks (β=-.07, 95% CI -0.14 to -0.01; P=.04). This study demonstrated general improvement followed by a period of stability of depression and anxiety symptoms associated with cognitive behavioral therapy-based digital intervention. Interestingly, engagement with a coaching session but not a breathing exercise was associated with a reduction in depression symptoms. Moreover, breathing exercise but not engagement with a coaching session was associated with a reduction of anxiety symptoms. These findings emphasize the importance of using a personalized approach to behavioral health during digital health interventions.

Association of Digital Engagement With Relaxation Tools and Stress Level Reduction: Retrospective Cohort Study.

Stress is an emotional response caused by external triggers and is a high-prevalence global problem affecting mental and physical health. Several different digital therapeutic solutions are effective for stress management. However, there is limited understanding of the association between relaxation components and stress levels when using a digital app. This study investigated the contribution of relaxation tools to stress levels over time. We hypothesized that participation in breathing exercises and cognitive behavioral therapy-based video sessions would be associated with a reduction in stress levels. We also hypothesized a significant reduction specifically in participants' perceived sense of burden and lack of productivity when engaged with breathing exercises and video sessions. Stress levels were evaluated in a real-world data cohort using a behavioral health app for digital intervention and monitoring change. This retrospective real-world analysis of users on a mobile platform-based treatment followed users (N=490) who started with moderate and above levels of stress and completed at least 2 stress assessments. The levels of stress were tracked throughout the first 10 weeks. A piecewise mixed effects model was applied to model the trajectories of weekly stress mean scores in 2 time segments (1-6 weeks and 6-10 weeks). Next, a simple slope analysis was used for interpreting interactions probing the moderators: breathing exercises and video sessions. Piecewise mixed-effects models were also used to model the trajectories of specific perceived stress item rates in the stress questionnaire in the 2 segments (1-6 weeks and 6-10 weeks) and whether they are moderated by the relaxation engagements. Simple slope analysis was also used here for the interpretation of the interactions. Analysis revealed a significant decrease in stress symptoms (β=-.25; 95% CI -0.32 to -0.17; P<.001) during the period of 1-6 weeks of app use that was maintained during the period of 6-10 weeks. Breathing exercises significantly moderated the reduction in stress symptoms during the period of 1-6 weeks (β=-.07; 95% CI -0.13 to -0.01; P=.03), while engagement in digital video sessions did not moderate stress scores. Engagement in digital video sessions, as well as breathing exercises, significantly moderated the reduction in perceived sense of burden and lack of productivity during weeks 1-6 and remained stable during weeks 6-10 on both items. This study sheds light on the association between stress level reduction and specific components of engagement in a digital health app, breathing exercises, and cognitive behavioral therapy-based video sessions. Our findings provide a basis for further investigation of current and moderating factors that contribute to the personalization of digital intervention. In addition, results may aid in developing a more comprehensive understanding of how digital intervention tools work for mental health and for whom they are most effective.

Personalizing digital pain management with adapted machine learning approach.

Digital therapeutics (DT) emerged and has been expanding rapidly for pain management. However, the efficacy of such approaches demonstrates substantial heterogeneity. Machine learning (ML) approaches provide a great opportunity for personalizing the efficacy of DT. However, the ML model accuracy is mainly associated with reduced clinical interpretability. Moreover, classical ML models are not adapted for the longitudinal nature of the DT follow-up data, which may also include nonlinear fluctuations. This study presents an analytical framework for personalized pain management using piecewise mixed-effects model trees, considering the data dependencies, nonlinear trajectories, and boosting model interpretability. We demonstrated the implementation of the model with posture biofeedback training data of 3610 users collected during 8 weeks. The users reported their pain levels and posture quality. We developed personalized models for nonlinear time-related fluctuations of pain levels, posture quality, and weekly training duration using age, gender, and body mass index as potential moderating factors. Pain levels and posture quality demonstrated strong improvement during the first 3 weeks of the training, followed by a sustained pattern. The age of the users moderated the time fluctuations in pain levels, whereas age and gender interactively moderated the trajectories in the posture quality. Train duration increased during the first 3 weeks only for older users, whereas all the users decreased the training duration during the next 5 weeks. This analytical framework offers an opportunity for investigating the personalized efficacy of digital therapeutics for pain management, taking into account users' characteristics and boosting interpretability and can benefit from including more users' characteristics.

Bayesian modeling of associations in bivariate piecewise linear mixed-effects models.

Longitudinal processes rarely occur in isolation; often the growth curves of 2 or more variables are interdependent. Moreover, growth curves rarely exhibit a constant pattern of change. Many educational and psychological phenomena are comprised of different developmental phases (segments). Bivariate piecewise linear mixed-effects models (BPLMEM) are a useful and flexible statistical framework that allow simultaneous modeling of 2 processes that portray segmented change and investigates their associations over time. The purpose of the present study was to develop a BPLMEM using a Bayesian inference approach allowing the estimation of the association between the error variances and providing a more robust modeling choice for the joint random-effects of the 2 processes. This study aims to improve upon the limitations of the prior literature on bivariate piecewise mixed-effects models, such as only allowing the modeling of uncorrelated residual errors across the 2 longitudinal processes and restricting modeling choices for the random effects. The performance of the BPLMEM was investigated via a Monte Carlo simulation study. Furthermore, the utility of BPLMEM was illustrated by using a national educational dataset, Early Childhood Longitudinal Study-Kindergarten Cohort (ECLS-K), where we examined the joint development of mathematics and reading achievement scores and the association between their trajectories over 7 measurement occasions. The findings obtained shed new light on the relationship between these 2 prominent educational domains over time. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Growth patterns of uninfected children born to women living with perinatally versus nonperinatally acquired HIV.

The aim of this study was to compare long-term growth between HIV-exposed uninfected children (CHEU) born to women with perinatally acquired HIV (CHEU-PHIV) and CHEU born to women with nonperinatally acquired HIV (CHEU-NPHIV). A longitudinal analysis of anthropometric measurements from a U.S.-based multisite prospective cohort study enrolling CHEU and their mothers since April 2007. CHEU were evaluated for growth annually from birth through age 5 and again at age 7 years. Z-scores were calculated using U.S. growth references for weight (WTZ), height (HTZ), and weight-for-length or BMI-for-age (WLZ/BMIZ). Mid-upper arm circumference (MUACZ) and triceps skinfold thickness (TSFZ) Z-scores were obtained from ages 1 and 2, respectively, through age 7 years. Piecewise mixed-effects models, overall and stratified by race and sex, were fit to assess differential growth patterns across age by maternal PHIV status. One thousand four hundred fifty-four singleton infants (286 CHEU-PHIV and 1168 CHEU-NPHIV) were included. CHEU-PHIV had slower growth rates than CHEU-NPHIV for WTZ and WLZ/BMIZ at earlier ages and continued to have lower mean WTZ [-0.27, 95% confidence interval (95% CI): -0.50, -0.04] and WLZ/BMIZ (-0.39, 95% CI: -0.67, -0.11) through age 7. Among non-Black boys, CHEU-PHIV had slightly lower WTZ and WLZ/BMIZ at birth than CHEU-NPHIV and these growth deficits persisted through age 7 years. Compared with CHEU-NPHIV, CHEU-PHIV had diminished growth in early childhood with differences most pronounced among non-Black male children. Further longitudinal follow-up of CHEU-PHIV into young adulthood is needed to understand whether these early effects of maternal PHIV status on growth persist and have other health consequences.

Lonesome no more? A two-year follow-up of internet-administered cognitive behavioral therapy for loneliness

The current study sought to investigate the long-term effects of an internet-administered programme based on CBT principles for which the initial efficacy has been reported in Käll, Jägholm, et al. (In press). Seventy-three participants who were recruited on the basis of experiencing frequent and prolonged loneliness were contacted to complete questionnaires measuring loneliness, quality of life, and symptoms of psychopathology two years after the conclusion of the initial treatment period. Additional items regarding use of the treatment techniques and strategies contained in the programme during the follow-up period was included. In total, 44 participants provided data for the loneliness measure at follow-up. The outcome data were analyzed with a piecewise mixed effects model to provide estimates of change for the continuous measures. Linear multiple regression analysis was used to investigate the relationship between use of treatment techniques and reliable change on the primary outcome measure. The results showed decreases in loneliness during the follow-up period for the sample as a whole. Additionally, an increase in quality of life and a decrease in social anxiety were noted, but no significant changes of depressive symptoms or generalized anxiety. Effect sizes for the observed changes from baseline to follow-up were in the moderate to large range for all measures. Reported use of the treatment techniques was not significantly related to reliable change in loneliness after the two-year period. In conclusion, the results of the study support the utility of internet-based CBT targeting loneliness and indicate that the benefits from the intervention can be enduring.

Diabetic ketoacidosis at diagnosis of type 1 diabetes and glycemic control over time: The SEARCH for diabetes in youth study.

The diagnosis of type 1 diabetes (T1D) in youth is often associated with diabetic ketoacidosis (DKA). We aimed to evaluate if the presence of DKA at diagnosis of T1D is associated with less favorable hemoglobin A1c (HbA1c) trajectories over time. The SEARCH for Diabetes in Youth study of 1396 youth aged <20 years with newly diagnosed T1D were followed for up to 13 (median 8 [interquartile range or IQR 6-9]) years after diagnosis. Of these, 397 (28%) had DKA (bicarbonate level < 15 mmol/L and/or pH < 7.25 (venous) or < 7.30 (arterial or capillary) or mention of DKA in medical records) at diabetes onset. Longitudinal HbA1c levels were measured at each follow-up visit (average number of HbA1c measures 3.4). A linear piecewise mixed effects model was used to analyze the effect of DKA status at diagnosis of T1D on long-term glycemic control, adjusting for age at diagnosis, diabetes duration at baseline, sex, race/ethnicity, household income, health insurance status, time-varying insulin regimen and glucose self-monitoring, study site, and baseline fasting C-peptide level. At baseline, HbA1c levels were significantly higher in youth with T1D diagnosed in DKA vs those who were not (9.9% ± 1.5% vs 8.5% ± 1.4%, respectively). After the first year with diabetes, there was a significant difference in the rate of change in HbA1c levels by DKA status: HbA1c was 0.16% higher each year in youth with DKA compared to those without (interaction P-value<0.0001), after adjusting for aforementioned covariates. DKA at T1D diagnosis is associated with worsening glycemic control over time, independent of demographic, socioeconomic, and treatment-related factors and baseline fasting C-peptide.

A note on estimating single-class piecewise mixed-effects models with unknown change points

Piecewise mixed-effects models are useful for analyzing longitudinal educational and psychological data sets to model segmented change over time. These models offer an attractive alternative to commonly used quadratic and higher-order polynomial models because the coefficients obtained from fitting the model have meaningful substantive interpretation. The current study thus focuses on the estimation of piecewise mixed-effects model with unknown random change points using maximum likelihood (ML) as described in Du Toit and Cudeck (2009). Previous simulation work (Wang & McArdle, 2008) showed that Bayesian estimation produced reliable parameter estimates for the piecewise model in comparison to frequentist procedures (i.e., first-order Taylor expansion and the adaptive Gaussian quadrature) across all simulation conditions. In the current article a small Monte Carlo simulation study was conducted to assess the performance of the ML approach, a frequentist procedure, and the Bayesian approach for fitting linear–linear piecewise mixed-effects model. The obtained findings show that ML estimation approach produces reliable and accurate estimates under the conditions of small residual variance of the observed variables, and that the size of the residual variance had the most impact on the quality of model parameter estimates. Second, neither ML nor Bayesian estimation procedures performed well under all manipulated conditions with respect to the accuracy and precision of the estimated model parameters.

Longitudinal models of reading achievement of students with learning disabilities and without disabilities.

Accurate estimation of developmental trajectories can inform instruction and intervention. We compared the fit of linear, quadratic, and piecewise mixed-effects models of reading development among students with learning disabilities relative to their typically developing peers. We drew an analytic sample of 1,990 students from the nationally representative Early Childhood Longitudinal Study-Kindergarten Cohort of 1998, using reading achievement scores from kindergarten through eighth grade to estimate three models of students' reading growth. The piecewise mixed-effects models provided the best functional form of the students' reading trajectories as indicated by model fit indices. Results showed slightly different trajectories between students with learning disabilities and without disabilities, with varying but divergent rates of growth throughout elementary grades, as well as an increasing gap over time. These results highlight the need for additional research on appropriate methods for modeling reading trajectories and the implications for students' response to instruction. (PsycINFO Database Record

The impact of the severity of early life stress on diurnal cortisol: The role of puberty

Researchers have documented dysregulation of the hypothalamic-pituitary-adrenal (HPA) axis in children and adolescents who experienced early life stress (ELS). The precise nature of this dysregulation, however, has been difficult to discern. In fact, both elevated and blunted patterns of diurnal cortisol regulation have been reported in children and adolescents exposed to greater ELS, including both reduced and heightened cortisol levels and change in cortisol across the day. These divergent findings may be due to developmental changes in the relation between ELS and HPA-axis functioning. The present study was designed to examine the role of puberty in the impact of the severity of ELS on the regulation of diurnal cortisol. Boys and girls (N=145) ages 9–13 years recruited from lower-risk communities completed an interview about their ELS experiences and at-home collection of diurnal cortisol. ELS experiences were objectively coded for severity, and children’s level of pubertal development was measured using Tanner Staging. Multi-level piecewise mixed-effects models tested the effects of ELS severity and pubertal stage on cortisol levels at waking, the cortisol awakening response (CAR), and the daytime cortisol slope. While we found no significant interactive effects of pubertal stage and ELS severity on cortisol levels at waking or the daytime cortisol slope, findings indicated that pubertal stage interacted with ELS severity to predict the cortisol awakening response (CAR). Specifically, in earlier puberty, higher ELS was associated with a blunted CAR compared to lower ELS; in contrast, in later puberty, higher ELS was associated with a heightened CAR compared to lower ELS. Differences in the relation between ELS severity and the CAR were uniquely determined by puberty, and not by age. By considering and examining the role of puberty, the current study provides a developmental explanation for previous divergent findings of both blunted and heightened patterns of diurnal cortisol following ELS. These results indicate that careful attention should be given to children’s pubertal status before drawing conclusions concerning the nature of diurnal cortisol dysregulation.

Initiation of Long-term Proton Pump Inhibitor Use Is Not Associated with Weight Gain

Introduction: Proton pump inhibitors (PPIs) are among the most commonly used class of medications in the U.S. We and others have previously reported on the association between PPI use and weight gain or suboptimal weight loss. However, these few prior studies were limited by small sample size or the inability to control for important confounders. The aims of this study were to assess body weight changes in patients who initiate and became long-term PPI users.Figure 2Methods: This was a retrospective cohort study of 157 PPI-naïve outpatients age 18-75y who were prescribed a daily PPI through a primary care provider associated with the University of Colorado Health system from 2012-2013 and continued to regularly take a PPI for at least one year. The electronic medical record was used to extract a variety of clinical (including obesityrelated comorbidities) and demographic data, including all weights collected between 6 months prior to and 18 months following the index PPI prescription. A linear piece-wise mixed-effects model was used to compare the pre-PPI slope of weight change over time to the post-PPI slope of weight change. Stratified analyses by PPI indication (GERD vs. non-GERD), age ( 56y), gender, and BMI category (normal-weight, overweight, and obese) were also performed. The covariance structure for each model was set to auto-regressive to account for greater variation over time within each subject. Results: The findings indicated that there was no statistical difference in weight trajectories after initiating PPIs compared with the same patients' weight trajectories prior to initiation (Figure 1). This finding was demonstrated in for all patients (p=0.12) and for the subset of patients with a GERD indication (P=0.91). Similar non-significant differences in weight trajectories before and after PPI prescription were found for those below (p=0.20) and above (p=0.92) the median age, for men (p=0.23) and women (p=0.35), and for normal-weight (p=0.52), overweight (p=0.67), and obese (p=0.08) patients. Conclusion: Initiation of long-term PPI use in patients naïve to acid suppression medications was not associated with a significant change in body weight trajectory within 18 months after PPI initiation. These findings contradict prior studies. The study was limited by its retrospective design, emphasizing the need for a prospective study to determine if PPI use leads to weight gain as this might alter prescribing and counseling practices.

Are women who quit smoking at high risk of excess weight gain throughout pregnancy?

BackgroundSmoking cessation has been reported to be associated with high total gestational weight gain (GWG), which itself is a risk factor for adverse maternal-infant outcomes. Recent studies have criticized conventional single measures of GWG, since they may lead to biased results. Therefore, we aimed to compare patterns of GWG based on serial antenatal weight measurements between women who: never smoked, quit during pregnancy, continued to smoke.MethodsParticipants (N = 509) of our longitudinal study were recruited from seven antenatal clinics in Southwestern Ontario. Serial GWG measurements were abstracted from medical charts, while information on smoking status was obtained from a self-administered questionnaire at a median gestational age of 32 (27–37) weeks. GWG patterns were assessed by fitting piecewise mixed-effects models. First trimester weight gains and weekly rates for the last two trimesters were compared by smoking status.ResultsDuring the first trimester, women who never smoked and those who quit during pregnancy gained on average 1.7 kg (95 % CI: 1.4–2.1) and 1.2 kg (0.3–2.1), respectively, whereas women who continued smoking gained more than twice as much (3.5 kg, 2.4–4.6). Weekly rate of gain in the second and third trimesters was highest in women who quit smoking (0.60 kg/week, 0.54–0.65), approximately 20 and 50 % higher than in women who never smoked and those who smoked during pregnancy, respectively.ConclusionsIn this longitudinal study to examine GWG by smoking status based on serial GWG measurements, we found that women who quit smoking experienced a rapid rate of gain during the last two trimesters, suggesting that this high-risk group may benefit from targeted interventions.Electronic supplementary materialThe online version of this article (doi:10.1186/s12884-016-1056-z) contains supplementary material, which is available to authorized users.

Piecewise Mixed Effects Model to Compare the Weight-gain Patter ns Before and After Diagnosis of Asthma in Children Younger than 5 Years.

Asthma and obesity are two significant public health problems that both originate in early childhood and have shared risk factors and manifestations. Studies suggest a strong association between asthma development and subsequent accelerated weight gain. Children are diagnosed with asthma in early childhood and are often exposed to factors associated with rapid weight gain. This article intends to demonstrate an innovative application of the piecewise mixed effects model to characterize the difference in the temporal rate of change in BMIz, the standardized scores of body mass index and weight-for-length that measure weight status, before and after asthma diagnosis in children younger than 5 years. The data consist of unique sequences from 1194 children's clinic visits during the first 5 years of life. We used a knot at the time of diagnosis and detected a differential weight-gain pattern before and after asthma diagnosis. The pre- and post-asthma-diagnosis weight-gain patterns further differ by sex and race-ethnicity. After asthma diagnosis, female children showed a higher increase in the rate of change in BMIz than males. Non-Hispanic African Americans and Hispanics had higher post-diagnosis rates of change in BMIz than Caucasians. The differential weight-gain patterns between male and female children were mainly contributed by Caucasian children. These findings could have important implications in the clinical care of children after asthma diagnosis.

The effect of bidding success in construction bidding

PurposeWinning a bid will carry implications for capacity level of a construction firm. This paper aims to examine the impact of a winning bid on contractors' bid pricing strategies.Design/methodology/approachIn identifying the specific types of bidding trends before and after a winning bid, the variations in bids are expressed as a function of time relative to winning bid – the “event” of interest in this study – using a piecewise mixed effects model. The bids analysed comprised series of bids with a winning bid in between, recorded from Hong Kong building contractors.FindingsThe results show that there is a relationship between bid price and bidding success. The bidders in general bid low for time periods before a winning bid and they are less competitive in time periods after a winning bid. However, by considering the individual bidders' characteristics that relate to differences in bidding competitiveness, it is shown that there is remarkable heterogeneity among the bidders in bid pricing decision for pre‐ and post‐winning periods. Nevertheless, the statistically significant bidding trends before and after a winning bid strengthen the notion that systematic changes in bidding behaviour over time do occur in reality in response to changes in firm capacity level.Originality/valueThis empirical investigation provides strong evidence on the systematic changes in bidding behaviour over time in response to changes in firm capacity level, supporting the need to incorporate firm capacity level in the future development of a suitable theoretical framework on construction bidding.

Piecewise mixed-effects models with skew distributions for evaluating viral load changes: A Bayesian approach

Studies of human immunodeficiency virus dynamics in acquired immuno deficiency syndrome (AIDS) research are very important in evaluating the effectiveness of antiretroviral (ARV) therapies. The potency of ARV agents in AIDS clinical trials can be assessed on the basis of a viral response such as viral decay rate or viral load change in plasma. Following ARV treatment, the profile of each subject's viral load tends to follow a 'broken stick'-like dynamic trajectory, indicating multiple phases of decline and increase in viral loads. Such multiple-phases (change-points) can be described by a random change-point model with random subject-specific parameters. One usually assumes a normal distribution for model error. However, this assumption may be unrealistic, obscuring important features of within- and among-subject variations. In this article, we propose piecewise linear mixed-effects models with skew-elliptical distributions to describe the time trend of a response variable under a Bayesian framework. This methodology can be widely applied to real problems for longitudinal studies. A real data analysis, using viral load data from an AIDS study, is carried out to illustrate the proposed method by comparing various candidate models. Biologically important findings are reported, and these findings also suggest that it is very important to assume a model with skew distribution in order to achieve reliable results, in particular, when the data exhibit skewness.

Differential Growth Patterns Among Healthy Infants Fed Protein Hydrolysate or Cow-Milk Formulas

Infant formulas differ considerably in composition and sensory profiles. In this randomized study, we examined whether healthy infants fed an extensively protein hydrolysate formula (PHF) would differ in feeding behavior and growth from those fed cow-milk formula (CMF). Infants were randomly assigned to be fed CMF or PHF between 0.5 and 7.5 months of age. Each month for 7 months, infants were weighed and measured and then videotaped while being fed their assigned formula. Anthropometric z scores were calculated by using World Health Organization growth standards. Multilevel linear growth and piecewise mixed-effects models compared trajectories for growth measures and formula acceptance. When compared with infants fed CMF, infants fed PHF had significantly lower weight-for-length z scores across ages 2.5 to 7.5 months. There were no differences in length-for-age z scores, which indicate that group differences resulted from gains in weight, not length. Infants fed PHF also had significantly slower weight gain velocity compared with infants fed CMF. During the monthly assessments, PHF-fed infants consumed less formula to satiation than did CMF-fed infants across the study period. Maternal ratings of infants' acceptance of the formula did not differ at any age. z-score trajectories indicate that CMF-fed infants' weight gain was accelerated, whereas PHF-fed infants' weight gain was normative. Whether such differences in growth are because of differences in the protein content or amino acid profile of the formulas and, in turn, metabolism is unknown. Research on the long-term consequences of these early growth differences is needed.

Tutorial in Biostatistics: Evaluating the impact of 'critical periods' in longitudinal studies of growth using piecewise mixed effects models.

Recent developments in modern multivariate methods provide applied researchers with the means to address many important research questions that arise in studies with repeated measures data collected on individuals over time. One such area of applied research is focused on studying change associated with some event or critical period in human development. This tutorial deals with the use of the general linear mixed model for regression analysis of correlated data with a two-piece linear function of time corresponding to the pre- and post-event trends. The model assumes a continuous outcome is linearly related to a set of explanatory variables, but allows for the trend after the event to be different from the trend before it. This task can be accomplished using a piecewise linear random effects model for longitudinal data where the response depends upon time of the event. A detailed example that examines the influence of menarche on changes in body fat accretion will be presented using data from a prospective study of 162 girls measured annually from approximately age 10 until 4 years post menarche.