A joint normal-ordinal (probit) model for ordinal and continuous longitudinal data.

In biomedical studies, continuous and ordinal longitudinal variables are frequently encountered. In many of these studies it is of interest to estimate the effect of one of these longitudinal variables on the other. Time-dependent covariates have, however, several limitations; they can, for example, not be included when the data is not collected at fixed intervals. The issues can be circumvented by implementing joint models, where two or more longitudinal variables are treated as a response and modeled with a correlated random effect. Next, by conditioning on these response(s), we can study the effect of one or more longitudinal variables on another. We propose a normal-ordinal(probit) joint model. First, we derive closed-form formulas to estimate the model-based correlations between the responses on their original scale. In addition, we derive the marginal model, where the interpretation is no longer conditional on the random effects. As a consequence, we can make predictions for a subvector of one response conditional on the other response and potentially a subvector of the history of the response. Next, we extend the approach to a high-dimensional case with more than two ordinal and/or continuous longitudinal variables. The methodology is applied to a case study where, among others, a longitudinal ordinal response is predicted with a longitudinal continuous variable.

Joint modeling in presence of informative censoring on the retrospective time scale with application to palliative care research.

Joint modeling of longitudinal data such as quality of life data and survival data is important for palliative care researchers to draw efficient inferences because it can account for the associations between those two types of data. Modeling quality of life on a retrospective from death time scale is useful for investigators to interpret the analysis results of palliative care studies which have relatively short life expectancies. However, informative censoring remains a complex challenge for modeling quality of life on the retrospective time scale although it has been addressed for joint models on the prospective time scale. To fill this gap, we develop a novel joint modeling approach that can address the challenge by allowing informative censoring events to be dependent on patients' quality of life and survival through a random effect. There are two sub-models in our approach: a linear mixed effect model for the longitudinal quality of life and a competing-risk model for the death time and dropout time that share the same random effect as the longitudinal model. Our approach can provide unbiased estimates for parameters of interest by appropriately modeling the informative censoring time. Model performance is assessed with a simulation study and compared with existing approaches. A real-world study is presented to illustrate the application of the new approach.

Life course predictors of child emotional distress during the COVID-19 pandemic: Findings from a prospective intergenerational cohort study.

BACKGROUND: We examine precursors of child emotional distress during the COVID-19 pandemic in a prospective intergenerational Australian cohort study. METHODS: Parents (N = 549, 60% mothers) of 934 1-9-year-old children completed a COVID-19 specific module in 2020 and/or 2021. Decades prior, a broad range of individual, relational and contextual factors were assessed during parents' own childhood, adolescence and young adulthood (7-8 to 27-28 years old; 1990-2010) and again when their children were 1 year old (2012-2019). RESULTS: After controlling for pre-pandemic socio-emotional behaviour problems, COVID-19 child emotional distress was associated with a range of pre-pandemic parental life course factors including internalising difficulties, lower conscientiousness, social skills problems, poorer relational health and lower trust and tolerance. Additionally, in the postpartum period, pre-pandemic parental internalising difficulties, lower parental warmth, lower cooperation and fewer behavioural competencies predicted child COVID-19 emotional distress. CONCLUSIONS: Findings highlight the importance of taking a larger, intergenerational perspective to better equip young populations for future adversities. This involves not only investing in child, adolescent, and young adult emotional and relational health, but also in parents raising young families.

Nonparametric predictive model for sparse and irregular longitudinal data.

We propose a kernel-based estimator to predict the mean response trajectory for sparse and irregularly measured longitudinal data. The kernel estimator is constructed by imposing weights based on the subject-wise similarity on L2 metric space between predictor trajectories, where we assume that an analogous fashion in predictor trajectories over time would result in a similar trend in the response trajectory among subjects. In order to deal with the curse of dimensionality caused by the multiple predictors, we propose an appealing multiplicative model with multivariate Gaussian kernels. This model is capable of achieving dimension reduction as well as selecting functional covariates with predictive significance. The asymptotic properties of the proposed nonparametric estimator are investigated under mild regularity conditions. We illustrate the robustness and flexibility of our proposed method via extensive simulation studies and an application to the Framingham Heart Study.

Bayesian two-stage modeling of longitudinal and time-to-event data with an integrated fractional Brownian motion covariance structure.

It is difficult to characterize complex variations of biological processes, often longitudinally measured using biomarkers that yield noisy data. While joint modeling with a longitudinal submodel for the biomarker measurements and a survival submodel for assessing the hazard of events can alleviate measurement error issues, the continuous longitudinal submodel often uses random intercepts and slopes to estimate both between- and within-patient heterogeneity in biomarker trajectories. To overcome longitudinal submodel challenges, we replace random slopes with scaled integrated fractional Brownian motion (IFBM). As a more generalized version of integrated Brownian motion, IFBM reasonably depicts noisily measured biological processes. From this longitudinal IFBM model, we derive novel target functions to monitor the risk of rapid disease progression as real-time predictive probabilities. Predicted biomarker values from the IFBM submodel are used as inputs in a Cox submodel to estimate event hazard. This two-stage approach to fit the submodels is performed via Bayesian posterior computation and inference. We use the proposed approach to predict dynamic lung disease progression and mortality in women with a rare disease called lymphangioleiomyomatosis who were followed in a national patient registry. We compare our approach to those using integrated Ornstein-Uhlenbeck or conventional random intercepts-and-slopes terms for the longitudinal submodel. In the comparative analysis, the IFBM model consistently demonstrated superior predictive performance.

A Bayesian zero-inflated beta-binomial model for longitudinal data with group-specific changepoints.

Timeline followback (TLFB) is often used in addiction research to monitor recent substance use, such as the number of abstinent days in the past week. TLFB data usually take the form of binomial counts that exhibit overdispersion and zero inflation. Motivated by a 12-week randomized trial evaluating the efficacy of varenicline tartrate for smoking cessation among adolescents, we propose a Bayesian zero-inflated beta-binomial model for the analysis of longitudinal, bounded TLFB data. The model comprises a mixture of a point mass that accounts for zero inflation and a beta-binomial distribution for the number of days abstinent in the past week. Because treatment effects appear to level off during the study, we introduce random changepoints for each study group to reflect group-specific changes in treatment efficacy over time. The model also includes fixed and random effects that capture group- and subject-level slopes before and after the changepoints. Using the model, we can accurately estimate the mean trend for each study group, test whether the groups experience changepoints simultaneously, and identify critical windows of treatment efficacy. For posterior computation, we propose an efficient Markov chain Monte Carlo algorithm that relies on easily sampled Gibbs and Metropolis-Hastings steps. Our application shows that the varenicline group has a short-term positive effect on abstinence that tapers off after week 9.

Longitudinal joint modeling for assessing parallel interactive development of latent ability and processing speed using responses and response times.

To measure the parallel interactive development of latent ability and processing speed using longitudinal item response accuracy (RA) and longitudinal response time (RT) data, we proposed three longitudinal joint modeling approaches from the structural equation modeling perspective, namely unstructured-covariance-matrix-based longitudinal joint modeling, latent growth curve-based longitudinal joint modeling, and autoregressive cross-lagged longitudinal joint modeling. The proposed modeling approaches can not only provide the developmental trajectories of latent ability and processing speed individually, but also exploit the relationship between the change in latent ability and processing speed through the across-time relationships of these two constructs. The results of two empirical studies indicate that (1) all three models are practically applicable and have highly consistent conclusions in terms of the changes in ability and speed in the analysis of the same data set, and (2) additional analysis of the RT data and acquisition of individual processing speed measurements can reveal the parallel interactive development phenomena that are difficult to detect using RA data alone. Furthermore, the results of our simulation study demonstrate that the proposed Bayesian Markov chain Monte Carlo estimation algorithm can ensure accurate model parameter recovery for all three proposed longitudinal joint models. Finally, the implications of our findings are discussed from the research and practice perspectives.

Continuities in maternal substance use from early adolescence to parenthood: findings from the intergenerational cohort consortium.

BACKGROUND: This study assessed the extent to which women's preconception binge drinking, tobacco use and cannabis use, reported prospectively in adolescence and young adulthood, predicted use of these substances during pregnancy and at 1 year postpartum. METHODS: Data were pooled from two intergenerational cohort studies: the Australian Temperament Project Generation 3 Study (395 mothers, 691 pregnancies) and the Victorian Intergenerational Health Cohort Study (398 mothers, 609 pregnancies). Alcohol, tobacco and cannabis use were assessed in adolescence (13-18 years), young adulthood (19-29 years) and at ages 29-35 years for those transitioning to parenthood. Exposures were weekly or more frequent preconception binge drinking (5 + drinks in one session), tobacco use and cannabis use. Outcomes were any alcohol, tobacco and cannabis use prior to awareness of the pregnancy, after awareness of pregnancy (up to and including the third trimester pregnancy) and at 1 year postpartum. RESULTS: Frequent preconception binge drinking, tobacco use and cannabis use across both adolescence and young adulthood were strong predictors of continued use post-conception, before and after awareness of the pregnancy and at 1 year postpartum. Substance use limited to young adulthood also predicted continued use post-conception. CONCLUSIONS: Persistent alcohol, tobacco use and cannabis use that starts in adolescence has a strong continuity into parenthood. Reducing substance use in the perinatal period requires action well before pregnancy, commencing in adolescence and continuing into the years before conception and throughout the perinatal period.

Multikink quantile regression for longitudinal data with application to progesterone data analysis.

Motivated by investigating the relationship between progesterone and the days in a menstrual cycle in a longitudinal study, we propose a multikink quantile regression model for longitudinal data analysis. It relaxes the linearity condition and assumes different regression forms in different regions of the domain of the threshold covariate. In this paper, we first propose a multikink quantile regression for longitudinal data. Two estimation procedures are proposed to estimate the regression coefficients and the kink points locations: one is a computationally efficient profile estimator under the working independence framework while the other one considers the within-subject correlations by using the unbiased generalized estimation equation approach. The selection consistency of the number of kink points and the asymptotic normality of two proposed estimators are established. Second, we construct a rank score test based on partial subgradients for the existence of the kink effect in longitudinal studies. Both the null distribution and the local alternative distribution of the test statistic have been derived. Simulation studies show that the proposed methods have excellent finite sample performance. In the application to the longitudinal progesterone data, we identify two kink points in the progesterone curves over different quantiles and observe that the progesterone level remains stable before the day of ovulation, then increases quickly in 5 to 6 days after ovulation and then changes to stable again or drops slightly.

Latent group detection in functional partially linear regression models.

In this paper, we propose a functional partially linear regression model with latent group structures to accommodate the heterogeneous relationship between a scalar response and functional covariates. The proposed model is motivated by a salinity tolerance study of barley families, whose main objective is to detect salinity tolerant barley plants. Our model is flexible, allowing for heterogeneous functional coefficients while being efficient by pooling information within a group for estimation. We develop an algorithm in the spirit of the K-means clustering to identify latent groups of the subjects under study. We establish the consistency of the proposed estimator, derive the convergence rate and the asymptotic distribution, and develop inference procedures. We show by simulation studies that the proposed method has higher accuracy for recovering latent groups and for estimating the functional coefficients than existing methods. The analysis of the barley data shows that the proposed method can help identify groups of barley families with different salinity tolerant abilities.

Sample size considerations for micro-randomized trials with binary proximal outcomes.

Micro-randomized trials (MRTs) are a novel experimental design for developing mobile health interventions. Participants are repeatedly randomized in an MRT, resulting in longitudinal data with time-varying treatments. Causal excursion effects are the main quantities of interest in MRT primary and secondary analyses. We consider MRTs where the proximal outcome is binary and the randomization probability is constant or time-varying but not data-dependent. We develop a sample size formula for detecting a nonzero marginal excursion effect. We prove that the formula guarantees power under a set of working assumptions. We demonstrate via simulation that violations of certain working assumptions do not affect the power, and for those that do, we point out the direction in which the power changes. We then propose practical guidelines for using the sample size formula. As an illustration, the formula is used to size an MRT on interventions for excessive drinking. The sample size calculator is implemented in R package MRTSampleSizeBinary and an interactive R Shiny app. This work can be used in trial planning for a wide range of MRTs with binary proximal outcomes.

Predicting the risk of a clinical event using longitudinal data: the generalized landmark analysis.

BACKGROUND: In the development of prediction models for a clinical event, it is common to use the static prediction modeling (SPM), a regression model that relates baseline predictors to the time to event. In many situations, the data used in training and validation are from longitudinal studies, where predictor variables are time-varying and measured at clinical visits. But these data are not used in SPM. The landmark analysis (LA), previously proposed for dynamic prediction with longitudinal data, has interpretational difficulty when the baseline is not a risk-changing clinical milestone, as is often the case in observational studies of chronic disease without intervention. METHODS: This paper studies the generalized landmark analysis (GLA), a statistical framework to develop prediction models for longitudinal data. The GLA includes the LA as a special case, and generalizes it to situations where the baseline is not a risk-changing clinical milestone with a more useful interpretation. Unlike the LA, the landmark variable does not have to be time since baseline in the GLA, but can be any time-varying prognostic variable. The GLA can also be viewed as a longitudinal generalization of localized prediction, which has been studied in the context of low-dimensional cross-sectional data. We studied the GLA using data from the Chronic Renal Insufficiency Cohort (CRIC) Study and the Wisconsin Allograft Replacement Database (WisARD) and compared the prediction performance of SPM and GLA. RESULTS: In various validation populations from longitudinal data, the GLA generally had similarly or better predictive performance than SPM, with notable improvement being seen when the validation population deviated from the baseline population. The GLA also demonstrated similar or better predictive performance than LA, due to its more general model specification. CONCLUSIONS: GLA is a generalization of the LA such that the landmark variable does not have to be the time since baseline. It has better interpretation when the baseline is not a risk-changing clinical milestone. The GLA is more adaptive to the validation population than SPM and is more flexible than LA, which may help produce more accurate prediction.

Functional data analysis to characterize disease patterns in frequent longitudinal data: application to bacterial vaginal microbiota patterns using weekly Nugent scores and identification of pattern-specific risk factors.

BACKGROUND: Technology advancement has allowed more frequent monitoring of biomarkers. The resulting data structure entails more frequent follow-ups compared to traditional longitudinal studies where the number of follow-up is often small. Such data allow explorations of the role of intra-person variability in understanding disease etiology and characterizing disease processes. A specific example was to characterize pathogenesis of bacterial vaginosis (BV) using weekly vaginal microbiota Nugent assay scores collected over 2 years in post-menarcheeal women from Rakai, Uganda, and to identify risk factors for each vaginal microbiota pattern to inform epidemiological and etiological understanding of the pathogenesis of BV. METHODS: We use a fully data-driven approach to characterize the longitudinal patters of vaginal microbiota by considering the densely sampled Nugent scores to be random functions over time and performing dimension reduction by functional principal components. Extending a current functional data clustering method, we use a hierarchical functional clustering framework considering multiple data features to help identify clinically meaningful patterns of vaginal microbiota fluctuations. Additionally, multinomial logistic regression was used to identify risk factors for each vaginal microbiota pattern to inform epidemiological and etiological understanding of the pathogenesis of BV. RESULTS: Using weekly Nugent scores over 2 years of 211 sexually active and post-menarcheal women in Rakai, four patterns of vaginal microbiota variation were identified: persistent with a BV state (high Nugent scores), persistent with normal ranged Nugent scores, large fluctuation of Nugent scores which however are predominantly in the BV state; large fluctuation of Nugent scores but predominantly the scores are in the normal state. Higher Nugent score at the start of an interval, younger age group of less than 20 years, unprotected source for bathing water, a woman's partner's being not circumcised, use of injectable/Norplant hormonal contraceptives for family planning were associated with higher odds of persistent BV in women. CONCLUSION: The hierarchical functional data clustering method can be used for fully data driven unsupervised clustering of densely sampled longitudinal data to identify clinically informative clusters and risk-factors associated with each cluster.

Estimation of marginal structural models under irregular visits and unmeasured confounder: calibrated inverse probability weights.

Clinical information collected in electronic health records (EHRs) is becoming an essential source to emulate randomized experiments. Since patients do not interact with the healthcare system at random, the longitudinal information in large observational databases must account for irregular visits. Moreover, we need to also account for subject-specific unmeasured confounders which may act as a common cause for treatment assignment mechanism (e.g. glucose-lowering medications) while also influencing the outcome (e.g. Hemoglobin A1c). We used the calibration of longitudinal weights to improve the finite sample properties and to account for subject-specific unmeasured confounders. A Monte Carlo simulation study is conducted to evaluate the performance of calibrated inverse probability estimators using time-dependent treatment assignment and irregular visits with subject-specific unmeasured confounders. The simulation study showed that the longitudinal weights with calibrated restrictions improved the finite sample bias when compared to the stabilized weights. The application of the calibrated weights is demonstrated using the exposure of glucose lowering medications and the longitudinal outcome of Hemoglobin A1c. Our results support the effectiveness of glucose lowering medications in reducing Hemoglobin A1c among type II diabetes patients with elevated glycemic index ([Formula: see text]) using stabilized and calibrated weights.

Time-varying exposure analysis of the relationship between sustained natural dentition and cognitive decline.

AIM: Tooth loss and cognitive decline progress over time and influence each other. This study estimated the impact of sustaining natural dentition on cognitive function in U.S. adults, accounting for the fact that dental and cognitive statuses change over time. MATERIALS AND METHODS: Data from adults aged ≥51 years who participated in five waves of the Health and Retirement Study from 2004 to 2016 (n = 10,953) were analysed. The impact of retaining some natural teeth from 2006 to 2012 on cognitive function score (0-27) and cognitive impairment (defined as having a cognitive function score of <12) in 2016 was evaluated using the doubly robust targeted maximum likelihood estimation method by considering both time-invariant and time-varying confounders, including cognitive function at baseline and during follow-up. RESULTS: Respondents with some natural teeth between 2006 and 2012 had a 0.40 point (95% confidence interval [CI]: 0.10-0.71) higher cognitive function score and 3.27 percentage point (95% CI: 0.11-6.66) lower cognitive impairment prevalence in 2016 than those with complete tooth loss. CONCLUSIONS: Considering past cognitive function assessed at multiple time points, sustained natural dentition was associated with better cognitive function.

Causal inference for longitudinal data based on historical controls.

Use of historical data has become a hot topic recently, considered to provide a way to reduce patient burden, lower drug development cost, and make innovative therapies available to patients earlier. In a single-arm study designed to examine the benefit of an experimental treatment, there is often a desire to compare the outcomes of patients receiving the new intervention with those receiving a control treatment, which can be extracted from sources such as historical trials or electronic medical records. Since the treatment is not randomly assigned, there is a need to adjust for the potential imbalance in key patient characteristics between the current study and historical controls. If the outcome of interest is measured longitudinally and subject to random missing, the required adjustment becomes more complicated. In this paper, we propose a doubly robust adjustment procedure specifically designed for longitudinal data analysis with missing data. The proposed method yields valid analysis results, if either the propensity score model or the mixed effects model for repeated measures (MMRM) regression model is correctly specified. An extensive numerical study is conducted to examine the performance of the proposed method. Data from a real clinical trial comparing with historical data are analyzed as an example applying the proposed procedure.

Purpose and goal pursuit as a self-sustaining system: Evidence of daily within-person reciprocity among adolescents in self-driven learning.

OBJECTIVE: Despite long-standing assumptions that a sense of purpose in life and goal pursuit are mutually supportive, empirical evidence of their reciprocity remains deficient. In the context of a unique out-of-school time program that empowers youth to pursue passions through self-driven learning, we examined whether purpose and one aspect of goal pursuit-perceptions of goal progress-work together to sustain themselves and each other over time. METHOD: Adolescents (N = 321) completed daily surveys throughout program enrollment (Menrollment = 69.09 days). Through dynamic structural equation modeling, we derived within-person patterns of day-to-day prediction as well as individual differences in these patterns. RESULTS: We found purpose and perceived goal progress exhibited significant daily inertia (i.e., autoregressive prediction) and reciprocity (i.e., cross-lagged prediction) at the within-person level. We also found initial evidence suggesting (a) tighter reciprocity was related to greater perceived goal progress overall and (b) people with greater purpose inertia may rely less on making goal progress to sustain momentum. CONCLUSIONS: With evidence of daily purpose-progress reciprocity, the field can look forward to replicating this work in other contexts, diving deeper into interesting patterns of within-person dynamics, and developing interventions to support youth striving.

Adjusting for Measurement Noninvariance with Alignment in Growth Modeling.

Longitudinal measurement invariance-the consistency of measurement in data collected over time-is a prerequisite for any meaningful inferences of growth patterns. When one or more items measuring the construct of interest show noninvariant measurement properties over time, it leads to biased parameter estimates and inferences on the growth parameters. In this paper, I extend the recently developed alignment-within-confirmatory factor analysis (AwC) technique to adjust for measurement biases for growth models. The proposed AwC method does not require a priori knowledge of noninvariant items and the iterative searching of noninvariant items in typical longitudinal measurement invariance research. Results of a Monte Carlo simulation study comparing AwC with the partial invariance modeling method show that AwC largely reduces biases in growth parameter estimates and gives good control of Type I error rates, especially when the sample size is at least 1,000. It also outperforms the partial invariance method in conditions when all items are noninvariant. However, all methods give biased growth parameter estimates when the proportion of noninvariant parameters is over 25%. Based on the simulation results, I conclude that AO is a viable alternative to the partial invariance method in growth modeling when it is not clear whether longitudinal measurement invariance holds. The current paper also demonstrates AwC in an example modeling neuroticism over three time points using a public data set, which shows how researchers can compute effect size indices for noninvariance in AwC to assess to what degree invariance holds and whether AwC results are trustworthy.

Natural cubic splines for the analysis of Alzheimer's clinical trials.

Mixed model repeated measures (MMRM) is the most common analysis approach used in clinical trials for Alzheimer's disease and other progressive diseases measured with continuous outcomes over time. The model treats time as a categorical variable, which allows an unconstrained estimate of the mean for each study visit in each randomized group. Categorizing time in this way can be problematic when assessments occur off-schedule, as including off-schedule visits can induce bias, and excluding them ignores valuable information and violates the intention to treat principle. This problem has been exacerbated by clinical trial visits which have been delayed due to the COVID19 pandemic. As an alternative to MMRM, we propose a constrained longitudinal data analysis with natural cubic splines that treats time as continuous and uses test version effects to model the mean over time. Compared to categorical-time models like MMRM and models that assume a proportional treatment effect, the spline model is shown to be more parsimonious and precise in real clinical trial datasets, and has better power and Type I error in a variety of simulation scenarios.

Temporal dynamics of interoceptive attention and positive and negative affect in adults engaging in disordered eating and nonsuicidal self-injury.

OBJECTIVE: Interoception (the sense of the body's state) is associated with eating disorders and nonsuicidal self-injury, potentially through relationships with affect. We examined the relationship between interoceptive attention and both positive and negative affect. METHODS: Participants (N = 128) who reported recent self-harm (i.e., disordered eating and/or non-suicidal self-injury) completed ecological momentary assessment for 16 days. Participants completed multiple daily assessments of affect and interoceptive attention. We then tested the temporal dynamic relationship between interoceptive attention and affect. RESULTS: There was a relationship between positive affect and interoceptive attention such that people with higher average positive affect, and times when people were above their typical positive affect, were associated with higher interoceptive attention. There was a negative relationship between negative affect and interoceptive attention, such that people with higher average negative affect, and times when people were above their own typical negative affect, were associated with lower interoceptive attention. CONCLUSIONS: Better mood may associate with greater willingness to attend to body sensations. Our findings support active inference models of interoception and highlight the importance of refining our understanding of the dynamic nature of interoception and its relationship with affect.