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Single case designs (SCDs) are short time series that assess intervention effects by measuring units repeatedly over time both in the presence and absence of treatment. For a variety of reasons, interest in the statistical analysis and meta-analysis of these designs has been growing in recent years. This paper proposes modeling SCD data with Generalized Additive Models (GAMs), a semi-parametric method from which it is possible to estimate the functional form of trend directly from the data, arguably capturing the true functional form better than ordinary least squares regression methods in which the researcher must decide which functional form to impose on the data. Generalized Additive Models provide a flexible way to model SCD data, allowing the data to inform the researcher both as to whether significant trend or trend treatment interaction exists, as well as which of those terms need nonlinear representations and which can remain linear. Tables and figures are appended.

The modeling of longitudinal and multilevel data using a latent variable framework is reviewed. Particular emphasis is placed on growth modeling. Examples are discussed where repeated observations are made on students sampled within classrooms and schools. The concept of a latent variable is a convenient way to represent statistical variation not only in conventional psychometric terms with respect to constructs measured with error, but also in the context of models with random coefficients and variance components. These features are explored. The random coefficient feature is shown to be a useful way to study change and growth over time, while the variance component feature is shown to correctly reflect common cluster sampling procedures. Four tables and four figures are included. (Contains 19 references.) (Author/SLD)

Accountability seems forever engrained into the K-12 environment, as has been the expectation of delivering quality education to school aged children and adolescents. Yet, repeated failure of this expectation has focused the public's and policy maker's attention on the limitations of major accountability systems. This paper explores applications of machine learning, predictive analytics, and data visualization to student information available to educational decision makers. In particular, we demonstrate how to use individual academic performance histories to identify "at-risk" students in real time for advising, academic coaching, and other support services and how to aggregate longitudinal data at the school or district level for system modeling, profiling, comparison, and intervention evaluation.

A typical problem in causal modeling is the instability of model structure learning, i.e., small changes in finite data can result in completely different optimal models. The present work introduces a novel causal modeling algorithm for longitudinal data, that is robust for finite samples based on recent advances in stability selection using subsampling and selection algorithms. Our approach uses exploratory search but allows incorporation of prior knowledge, e.g., the absence of a particular causal relationship between two specific variables. We represent causal relationships using structural equation models. Models are scored along two objectives: the model fit and the model complexity. Since both objectives are often conflicting we apply a multi-objective evolutionary algorithm to search for Pareto optimal models. To handle the instability of small finite data samples, we repeatedly subsample the data and select those substructures (from the optimal models) that are both stable and parsimonious. These substructures can be visualized through a causal graph. Our more exploratory approach achieves at least comparable performance as, but often a significant improvement over state-of-the-art alternative approaches on a simulated data set with a known ground truth. We also present the results of our method on three real-world longitudinal data sets on chronic fatigue syndrome, Alzheimer disease, and chronic kidney disease. The findings obtained with our approach are generally in line with results from more hypothesis-driven analyses in earlier studies and suggest some novel relationships that deserve further research.

A typical problem in causal modeling is the instability of model structure learning, i.e., small changes in finite data can result in completely different optimal models. The present work introduces a novel causal modeling algorithm for longitudinal data, that is robust for finite samples based on recent advances in stability selection using subsampling and selection algorithms. Our approach uses exploratory search but allows incorporation of prior knowledge, e.g., the absence of a particular causal relationship between two specific variables. We represent causal relationships using structural equation models. Models are scored along two objectives: the model fit and the model complexity. Since both objectives are often conflicting we apply a multi-objective evolutionary algorithm to search for Pareto optimal models. To handle the instability of small finite data samples, we repeatedly subsample the data and select those substructures (from the optimal models) that are both stable and parsimonious. These substructures can be visualized through a causal graph. Our more exploratory approach achieves at least comparable performance as, but often a significant improvement over state-of-the-art alternative approaches on a simulated data set with a known ground truth. We also present the results of our method on three real-world longitudinal data sets on chronic fatigue syndrome, Alzheimer disease, and chronic kidney disease. The findings obtained with our approach are generally in line with results from more hypothesis-driven analyses in earlier studies and suggest some novel relationships that deserve further research.

A typical problem in causal modeling is the instability of model structure learning, i.e., small changes in finite data can result in completely different optimal models. The present work introduces a novel causal modeling algorithm for longitudinal data, that is robust for finite samples based on recent advances in stability selection using subsampling and selection algorithms. Our approach uses exploratory search but allows incorporation of prior knowledge, e.g., the absence of a particular causal relationship between two specific variables. We represent causal relationships using structural equation models. Models are scored along two objectives: the model fit and the model complexity. Since both objectives are often conflicting we apply a multi-objective evolutionary algorithm to search for Pareto optimal models. To handle the instability of small finite data samples, we repeatedly subsample the data and select those substructures (from the optimal models) that are both stable and parsimonious. These substructures can be visualized through a causal graph. Our more exploratory approach achieves at least comparable performance as, but often a significant improvement over state-of-the-art alternative approaches on a simulated data set with a known ground truth. We also present the results of our method on three real-world longitudinal data sets on chronic fatigue syndrome, Alzheimer disease, and chronic kidney disease. The findings obtained with our approach are generally in line with results from more hypothesis-driven analyses in earlier studies and suggest some novel relationships that deserve further research.

Simulation study comparing different mixed-effects models and (R)DSEMs for repeated-measures experiments

Prediction of the future trajectory of a disease is an important challenge for personalized medicine and population health management. However, many complex chronic diseases exhibit large degrees of heterogeneity, and furthermore there is not always a single readily available biomarker to quantify disease severity. Even when such a clinical variable exists, there are often additional related biomarkers routinely measured for patients that may better inform the predictions of their future disease state. To this end, we propose a novel probabilistic generative model for multivariate longitudinal data that captures dependencies between multivariate trajectories. We use a Gaussian process based regression model for each individual trajectory, and build off ideas from latent class models to induce dependence between their mean functions. We fit our method using a scalable variational inference algorithm to a large dataset of longitudinal electronic patient health records, and find that it improves dynamic predictions compared to a recent state of the art method. Our local accountable care organization then uses the model predictions during chart reviews of high risk patients with chronic kidney disease.

Major Depressive Disorder (MDD) affects more than 300 million people in the world and shows an increasing trend in prevalence (World Health Organization, 2017). Following the first episode, about 15-35% of patients with MDD develop recurrent episodes within the first years (Bukh et al., 2016). Less than half of all patients with MDD remain symptom-free for two years after recovery (Kanai et al., 2003). Moreover, the number of lifetime episodes, severity of preceding episode and presence of subclinical residual symptoms have been identified as risk factors to experience further recurrent episodes (Keller & Boland, 1998; Kennedy et al., 2003; Pettit et al., 2006). Taken together, these factors contribute to the accumulation of disease burden and the development of long-term chronicity of MDD (Hardeveld et al., 2013). Structural neuroimaging techniques may contribute to our understanding of the underlying neural mechanisms of reoccurrence in MDD (Kang & Cho, 2020). Subsequently, this could facilitate relapse prognosis and potentially advance maintenance treatment. Cross-sectional neuroimaging studies, including meta-analyses from international consortia (e.g., ENIGMA), suggest brain structural differences between MDD patients and healthy controls (HC; Gray et al., 2020; Schmaal et al., 2016, 2017), whereas effect sizes are small (Winter et al., 2022). Reductions in gray matter volume (GMV) and cortical thickness in brain areas such as the hippocampus (Campbell et al., 2004; Schmaal et al., 2016; McKinnon et al., 2009), insula (Lai & Wu, 2014; Stratmann et al., 2014; H. Zhang et al., 2016) and the prefrontal cortex (Bora et al., 2012; Schmaal et al., 2017; Zhang et al., 2018) are reported most frequently in association with MDD. These morphometric changes seem to be associated with the course of disease, specifically the number of recurrent episodes and duration of illness (Lemke, Romankiewicz, et al., 2022; McKinnon et al., 2009; Stratmann et al., 2014; Treadway et al., 2015). However, cross-sectional studies are restricted to correlative statements and fail to explain the direct interplay between recurrence of MDD and neural changes. Longitudinal studies in larger, well-characterized samples are needed to classify these changes into risk factors, correlates of the acute depressive state and consequences of prior depressive episodes. In previous longitudinal studies, brain structural alterations in regions, such as the dorsolateral prefrontal cortex (DLPFC), insula, hippocampus, and anterior cingulate cortex were observed (Dohm et al., 2017). Studies have reported a greater decline in GMV in these regions in non-remitters compared to patients whose MDD was in remission at follow-up assessment (Frodl et al., 2008; Phillips et al., 2015; Taylor et al., 2014). Vice versa, some studies reported an increase of GMV and cortical thickness in these regions with achieved remission (Hou et al., 2012; Phillips et al., 2015; Zaremba et al., 2018). Nonetheless, longitudinal research focusing exclusively on remission status at follow-up neglect the course of illness between scans, which is essential for accessing the link between brain alterations and relapse. A few studies investigated morphological changes as a function of relapse during follow-up interval (Frodl et al., 2008; Soriano-Mas et al., 2011), while some additionally controlled for confounding variables such as psychopharmacological treatment (Lemke, Klute, et al., 2022; Zaremba et al., 2018). These studies found that depressive relapse, as a distinct marker of disease progression during the interscan interval, is specifically linked to decline of GMV and cortical thickness and surface area in the insula and DLPFC. A loss of GMV in the insula and hippocampus has further been demonstrated in patients with severe courses of affective disorders, characterized by a hospitalization during a nine-year follow-up (Förster et al., 2023). Taken together, the findings provide first evidence of the negative impact of disease progression on the morphology of these brain regions. However, the studies share two key limitations. Firstly, grouping in dependence of experiencing at least one relapse does not account for variations in length of depressive episodes and thus disregards the duration the depressive state might affect the brain. Secondly, the majority of longitudinal imaging studies are restricted to two time points which frame a follow-up interval and used statistical models that evaluated the effect of relapse by comparing group means (Dohm et al., 2017; Lemke, Klute, et al., 2022; Zaremba et al., 2018). Given the broad heterogeneity of MDD disease course (Steinert et al., 2014), a statistical model that accounts for underlying individual trajectories over multiple time points may be more suitable. Rather than focusing on overall differences between related means of a given outcome variable across all participants, multilevel models estimate an underlying trajectory across all time points within each participant (Bollen & Curran, 2006). Moreover, multilevel models can provide a more nuanced approach to exploring potential cause-and-effect relationships by accounting for individual differences and time-related effects more effectively (Raudenbush, 2001). The lack of longitudinal imaging data in adult patients with MDD comprising multiple scans per individual over several years represents a crucial gap in the literature. This data in combination with differentiated assessment of the clinical course within follow-up intervals is indispensable to model and understand individual trajectories of brain structure in the long-term course of MDD. So far, little research analyzed gray matter trajectories associated with self-reported symptoms of depression over multiple scan waves in community samples of children and adolescents (Bos et al., 2018; Luby et al., 2016; Luking et al., 2022). One study indicated accelerated cortical thinning in the frontal lobe related to depressive symptoms (Bos et al., 2018) while others report a decline for global GMV and thickness (Luby et al., 2016). Nonetheless, generalization to adult MDD is questionable and the studies vary in their selection of ROIs and assessment of depressive symptoms. To fill this gap, we present the first longitudinal study that investigates individual trajectories of brain structure (GMV and cortical thickness) in the DLPFC, insula and hippocampus in association with duration in MDD including 3 to 7 scans per person covering up to 12 years. Our current investigation uses data from an ongoing multimodal longitudinal study of neurobiology in affective disorders. Participants with and without a diagnosis of MDD are re-assessed every two years undergoing MRI and clinical measurements. Patients with MDD were hospitalized at baseline assessment and recurrence of depressive episodes was determined by trained personnel at all assessments in a clinical interview. Due to common challenges of longitudinal studies, e.g. the correlation between repeated measures on the same person, irregularly timed data and most importantly missing data (Garcia & Marder, 2017), a multilevel modeling approach will be applied. To this end, we will first analyze associations of baseline GMV and cortical thickness of the DLPFC, insula and hippocampus with lifetime duration in MDD (analysis 1a and 1b). Then, duration in MDD per interval will be tested as a time varying predictor for GMV and cortical thickness of the three ROIs in multilevel models (MLM) including minimum three scans per person (analysis 2a and 2b). Finally, we rerun these models and account for psychopharmacological treatment effects by adding medication as an additional predictor (analysis 3a and 3b).

The mission of the National Aeronautics and Space Administration’s (NASA) human research program is to advance safe human spaceflight. This involves conducting experiments, collecting data, and analyzing data. The data are longitudinal and result from a relatively few number of subjects; typically 10 – 20. A longitudinal study refers to an investigation where participant outcomes and possibly treatments are collected at multiple follow-up times. Standard statistical designs such as mean regression with random effects and mixed–effects regression are inadequate for such data because the population is typically not approximately normally distributed. Hence, more advanced data analysis methods are necessary. This research focuses on four such methods for longitudinal data analysis: the recently proposed linear quantile mixed models (lqmm) by Geraci and Bottai (2013), quantile regression, multilevel mixed–effects linear regression, and robust regression. This research also provides computational algorithms for longitudinal data that scientists can directly use for human spaceflight and other longitudinal data applications, then presents statistical evidence that verifies which method is best for specific situations. This advances the study of longitudinal data in a broad range of applications including applications in the sciences, technology, engineering and mathematics fields.

Hepatitis C virus (HCV) coinfection has become one of the most challenging clinical situations to manage in HIV-infected patients. Recently the effect of HCV coinfection on HIV dynamics following initiation of highly active antiretroviral therapy (HAART) has drawn considerable attention. Post-HAART HIV dynamics are commonly studied in short-term clinical trials with frequent data collection design. For example, the elimination process of plasma virus during treatment is closely monitored with daily assessments in viral dynamics studies of AIDS clinical trials. In this article instead we use infrequent cohort data from long-term natural history studies and develop a model for characterizing post-HAART HIV dynamics and their associations with HCV coinfection. Specifically, we propose a joint model for doubly interval-censored data for the time between HAART initiation and viral suppression, and the longitudinal CD4 count measurements relative to the viral suppression. Inference is accomplished using a fully Bayesian approach. Doubly interval-censored data are modeled semiparametrically by Dirichlet process priors and Bayesian penalized splines are used for modeling population-level and individual-level mean CD4 count profiles. We use the proposed methods and data from the HIV Epidemiology Research Study (HERS) to investigate the effect of HCV coinfection on the response to HAART.

An important endpoint variable in a cocaine rehabilitation study is the time to first relapse of a patient after the treatment. We propose a joint modeling approach based on functional data analysis to study the relationship between the baseline longitudinal cocaine-use pattern and the interval censored time to first relapse. For the baseline cocaine-use pattern, we consider both self-reported cocaine-use amount trajectories and dichotomized use trajectories. Variations within the generalized longitudinal trajectories are modeled through a latent Gaussian process, which is characterized by a few leading functional principal components. The association between the baseline longitudinal trajectories and the time to first relapse is built upon the latent principal component scores. The mean and the eigenfunctions of the latent Gaussian process as well as the hazard function of time to first relapse are modeled nonparametrically using penalized splines, and the parameters in the joint model are estimated by a Monte Carlo EM algorithm based on Metropolis-Hastings steps. An Akaike information criterion (AIC) based on effective degrees of freedom is proposed to choose the tuning parameters, and a modified empirical information is proposed to estimate the variance-covariance matrix of the estimators.

Generalized Estimation Equations (GEE) are a well-known method for the analysis of categorical longitudinal responses. GEE method has computational simplicity and population parameter interpretation. In the presence of missing data it is only valid under the strong assumption of missing completely at random. A doubly robust estimator (DRGEE) for correlated ordinal longitudinal data is a nice approach for handling intermittently missing response and covariate under the MAR mechanism. Independent working correlation is the standard way in DRGEE. However, when covariate is not time stationary, efficiency can be gained using a structured association. The goal of this paper is to extend the DRGEE estimator to allow modeling the association structure by means of either the correlation coefficient or local odds ratio. Simulation results revealed better performance of the local odds ratio parametrization, specially for small samples. The method is applied to a data set related to Rheumatic Mitral Stenosis.

Ethnic racial discrimination (EthRaDi) refers to unfair treatment of ethnic minorities by people, belonging to the majority, or institutions in a population (Williams & Mohammed, 2009). Even though experiencing discrimination is linked to less favorable development and children are known to be able to grasp the essence of discrimination at an early age (Brown, 2008), its consequences are still mostly researched in adults (Marcelo & Yates, 2019). Evidence shows that experiencing EthRaDi can be a stressor for minorities (Hicks & Kogan, 2019; Pieterse et al., 2012). A stressful situation can in turn lead to diminished self-regulation (Tice et al., 2001). Self-regulation (SR) is an adaptive skill (Groß, 2021) which is linked to various health related outcomes like cardiovascular disease, addiction, and depression (McClelland et al., 2018). Therefore, it is important to focus on researching factors influencing the development of self-regulation. Evidence shows that self-regulation is indirectly influenced by EthRaDi via emotional distress (EmDis; Hicks & Kogan, 2019). Another study has found ethnic racial identity (ERId) to be a protective factor when examining the influence of EthRaDi on behavioral problems (Marcelo & Yates, 2019). The purpose of this study is therefore to answer the following two research questions: 1. Is there a difference in the developmental changes of SR between adolescents who have vs. have not experienced EthRaDi? 2. How does EthRaDi affect adolescents’ SR capacity?

A pair of compliant trailing edge flaps was flown on a modified GIII airplane. Prior to flight test, multiple analysis tools of various levels of complexity were used to predict the aerodynamic effects of the flaps. Vortex lattice, full potential flow, and full Navier-Stokes aerodynamic analysis software programs were used for prediction, in addition to another program that used empirical data. After the flight-test series, lift and pitching moment coefficient increments due to the flaps were estimated from flight data and compared to the results of the predictive tools. The predicted lift increments matched flight data well for all predictive tools for small flap deflections. All tools over-predicted lift increments for large flap deflections. The potential flow and Navier-Stokes programs predicted pitching moment coefficient increments better than the other tools.

We consider the problem of simultaneous variable selection and estimation in additive, partially linear models for longitudinal/clustered data. We propose an estimation procedure via polynomial splines to estimate the nonparametric components and apply proper penalty functions to achieve sparsity in the linear part. Under reasonable conditions, we obtain the asymptotic normality of the estimators for the linear components and the consistency of the estimators for the nonparametric components. We further demonstrate that, with proper choice of the regularization parameter, the penalized estimators of the non-zero coefficients achieve the asymptotic oracle property. The finite sample behavior of the penalized estimators is evaluated with simulation studies and illustrated by a longitudinal CD4 cell count data set.

This article is from BMC Proceedings , volume 8 . Abstract In this paper, we propose a novel mixed-effects model for longitudinal changes of systolic blood pressure (SBP) over time that can estimate the joint effect of multiple sequence variants on SBP after accounting for familial correlation and the time dependencies within individuals. First we carried out agenome-wide association study (GWAS) using chromosome 3 single-nucleotide polymorphisms(SNPs) to identify regions associated with SBP levels. In a second step, we examined the sequence data to fine-map additional variants in these regions. Four SNPs from two intergenic regions (PLXNA1-TPRA1, BPESC1-PISTR1) and one gene (NLGN1) were detected to be significantly associated with SBP after adjusting for multiple testing. These SNPs were used to capture the multilocus genotype diversity in the regions. The multilocus genotypes derived from these four variants were then treated as random effects in the mixed-effects model, and the corresponding confidence intervals (Cis) were built to assess the significance of the joint effect of the sequence variants on SBP. We found that multilocus genotypes (GG,TT,AG,GG), (GG,TT,GG,GG), and (GG,TT,AA,AG) are associated with higher SBPand (GG,CT,AA,AA), (AA,TT,AA,AA), and (AG,CT,AA,AG) are associated with lower SBP. The linear mixed-effects models provide a powerful tool for GWAS and the analysis of joint modeling of multilocus genotypes.

This report describes the growth curve approach to the modeling of longitudinal data from Project Proteus. Desirable properties of the model are presented along with the basic model. Using Project Proteus and data from the Officer Longitudinal Research Data Base (OLRDB), two variables reflecting career intentions and social support were modeled longitudinally. The models were evaluated using chi-square and restricted chi-square tests in LISREL. The results of the exploratory analyses indicate significant effects for cohort and length of time in the Army.... Proteus, Modeling, Longitudinal research, OLRDB, Growth curves, LISREL.

In many medical studies, patients are followed longitudinally and interest is on assessing the relationship between longitudinal measurements and time to an event. Recently, various authors have proposed joint modeling approaches for longitudinal and time-to-event data for a single longitudinal variable. These joint modeling approaches become intractable with even a few longitudinal variables. In this paper we propose a regression calibration approach for jointly modeling multiple longitudinal measurements and discrete time-to-event data. Ideally, a two-stage modeling approach could be applied in which the multiple longitudinal measurements are modeled in the first stage and the longitudinal model is related to the time-to-event data in the second stage. Biased parameter estimation due to informative dropout makes this direct two-stage modeling approach problematic. We propose a regression calibration approach which appropriately accounts for informative dropout. We approximate the conditional distribution of the multiple longitudinal measurements given the event time by modeling all pairwise combinations of the longitudinal measurements using a bivariate linear mixed model which conditions on the event time. Complete data are then simulated based on estimates from these pairwise conditional models, and regression calibration is used to estimate the relationship between longitudinal data and time-to-event data using the complete data. We show that this approach performs well in estimating the relationship between multivariate longitudinal measurements and the time-to-event data and in estimating the parameters of the multiple longitudinal process subject to informative dropout. We illustrate this methodology with simulations and with an analysis of primary biliary cirrhosis (PBC) data.

Motivated by genetic association studies of pleiotropy, we propose here a Bayesian latent variable approach to jointly study multiple outcomes or phenotypes. The proposed method models both continuous and binary phenotypes, and it accounts for serial and familial correlations when longitudinal and pedigree data have been collected. We present a Bayesian estimation method for the model parameters, and we develop a novel MCMC algorithm that builds upon hierarchical centering and parameter expansion techniques to efficiently sample the posterior distribution. We discuss phenotype and model selection in the Bayesian setting, and we study the performance of two selection strategies based on Bayes factors and spike-and-slab priors. We evaluate the proposed method via extensive simulations and demonstrate its utility with an application to a genome-wide association study of various complication phenotypes related to type 1 diabetes.

This paper introduces latent growth modeling (LGM) as a statistical method for analyzing change over time in latent, or unobserved, variables, with particular emphasis of the application of this method in higher education research. While increasingly popular in other areas of education research and despite a wealth of publicly-available datasets relevant to postsecondary education research, LGM has not been utilized widely by higher education researchers. This paper begins by introducing LGM as a desirable mechanism for analyzing variability in individual growth trajectories over time and then presents an illustration of its application. An example of the application of LGM to data obtained from the Integrated Postsecondary Educational Data System (IPEDS) is presented to introduce specific components of LGM, including model specification and goodness-of-fit indices, and to demonstrate the research potential for higher education researchers. Finally, additional datasets offering longitudinal analysis potential for higher education researchers are presented to facilitate research. (Contains 2 tables, 2 figures, and 8 footnotes.)

This paper introduces latent growth modeling (LGM) as a statistical method for analyzing change over time in latent, or unobserved, variables, with particular emphasis of the application of this method in higher education research. While increasingly popular in other areas of education research and despite a wealth of publicly-available datasets relevant to postsecondary education research, LGM has not been utilized widely by higher education researchers. This paper begins by introducing LGM as a desirable mechanism for analyzing variability in individual growth trajectories over time and then presents an illustration of its application. An example of the application of LGM to data obtained from the Integrated Postsecondary Educational Data System (IPEDS) is presented to introduce specific components of LGM, including model specification and goodness-of-fit indices, and to demonstrate the research potential for higher education researchers. Finally, additional datasets offering longitudinal analysis potential for higher education researchers are presented to facilitate research. (Contains 2 tables, 2 figures, and 8 footnotes.)

Discuss ACTE aerodynamic modeling efforts and provide comparisons of predictions to flight results for lift and pitching moment increments.\n\n

There is a surge in medical follow-up studies that include longitudinal covariates in the modeling of survival data. So far, the focus has been largely on right-censored survival data. We consider survival data that are subject to both left truncation and right censoring. Left truncation is well known to produce biased sample. The sampling bias issue has been resolved in the literature for the case which involves baseline or time-varying covariates that are observable. The problem remains open, however, for the important case where longitudinal covariates are present in survival models. A joint likelihood approach has been shown in the literature to provide an effective way to overcome those difficulties for right-censored data, but this approach faces substantial additional challenges in the presence of left truncation. Here we thus propose an alternative likelihood to overcome these difficulties and show that the regression coefficient in the survival component can be estimated unbiasedly and efficiently. Issues about the bias for the longitudinal component are discussed. The new approach is illustrated numerically through simulations and data from a multi-center AIDS cohort study.

Longitudinal data are often plagued with sparsity of time points where measurements are available. The functional data analysis perspective has been shown to provide an effective and flexible approach to address this problem for the case where measurements are sparse but their times are randomly distributed over an interval. Here we focus on a different scenario where available data can be characterized as snippets, which are very short stretches of longitudinal measurements. For each subject the stretch of available data is much shorter than the time frame of interest, a common occurrence in accelerated longitudinal studies. An added challenge is introduced if a time proxy that is basic for usual longitudinal modeling is not available. This situation arises in the case of Alzheimer's disease and comparable scenarios, where one is interested in time dynamics of declining performance, but the time of disease onset is unknown and the chronological age does not provide a meaningful time reference for longitudinal modeling. Our main methodological contribution is to address this problem with a novel approach. Key quantities for our approach are conditional quantile trajectories for monotonic processes that emerge as solutions of a dynamic system, and for which we obtain uniformly consistent estimates. These trajectories are shown to be useful to describe processes that quantify deterioration over time, such as hippocampal volumes in Alzheimer's patients.

Longitudinal data are often plagued with sparsity of time points where measurements are available. The functional data analysis perspective has been shown to provide an effective and flexible approach to address this problem for the case where measurements are sparse but their times are randomly distributed over an interval. Here we focus on a different scenario where available data can be characterized as snippets, which are very short stretches of longitudinal measurements. For each subject the stretch of available data is much shorter than the time frame of interest, a common occurrence in accelerated longitudinal studies. An added challenge is introduced if a time proxy that is basic for usual longitudinal modeling is not available. This situation arises in the case of Alzheimer's disease and comparable scenarios, where one is interested in time dynamics of declining performance, but the time of disease onset is unknown and the chronological age does not provide a meaningful time reference for longitudinal modeling. Our main methodological contribution is to address this problem with a novel approach. Key quantities for our approach are conditional quantile trajectories for monotonic processes that emerge as solutions of a dynamic system, and for which we obtain uniformly consistent estimates. These trajectories are shown to be useful to describe processes that quantify deterioration over time, such as hippocampal volumes in Alzheimer's patients.

This article is from BMC Proceedings , volume 8 . Abstract Genetic association analysis on complex phenotypes under a longitudinal design involving pedigrees encounters the problem of correlation within pedigrees, which could affect statistical assessment of the genetic effects. Approaches have been proposed to integrate kinship correlation into the mixed-effect models to explicitly model the genetic relationship. These have proved to be an efficient way of dealing with sample clustering in pedigree data. Although current algorithms implemented in popular statistical packages are useful for adjusting relatedness in the mixed modeling of genetic effects on the mean level of a phenotype, they are not sufficiently straightforward to handle the kinship correlation on the time-dependent trajectories of a phenotype. We introduce a 2-level hierarchical linear model to separately assess the genetic associations with the mean level and the rate of change of a phenotype, integrating kinship correlation in the analysis. We apply our method to the Genetic Analysis Workshop 18 genome-wide association studies data on chromosome 3 to estimate the genetic effects on systolic blood pressure measured over time in large pedigrees. Our method identifies genetic variants associated with blood pressure with estimated inflation factors of 0.99, suggesting that our modeling of random effects efficiently handles the genetic relatedness in pedigrees. Application to simulated data captures important variants specified in the simulation. Our results show that the method is useful for genetic association studies in related samples using longitudinal design.