Factors Affecting the Adequacy and Preferability of Semiparametric Groups-Based Approximations of Continuous Growth Trajectories

Maternal weight latent trajectories and associations with adverse pregnancy outcomes using a smoothing mixture model

Class membership is a critical issue in health data sciences. Different types of statistical models have been widely applied to identify participants within a population with heterogeneous longitudinal trajectories. This study aims to identify latent longitudinal trajectories of maternal weight associated with adverse pregnancy outcomes using smoothing mixture model (SMM). Data were collected from the Khuzestan Vitamin D Deficiency Screening Program in Pregnancy. We applied the data of 877 pregnant women living in Shooshtar city, whose weights during the nine months of pregnancy were available. In the first step, maternal weight was classified and participants were assigned to only one group for which the estimated trajectory is the most similar to the observed one using SMM; then, we examined the associations of identified trajectories with risk of adverse pregnancy endpoints by applying logistic regression. Three latent trajectories for maternal weight during pregnancy were identified and named as low, medium and high weight trajectories. Crude estimated odds ratio (OR) for icterus, preterm delivery, NICU admission and composite neonatal events shows significantly higher risks in trajectory 1 (low weight) compared to trajectory 2 (medium weight) by 69% (OR = 1.69, 95%CI 1.20, 2.39), 82% (OR = 1.82, 95%CI 1.14, 2.87), 77% (OR = 1.77, 95%CI 1.17, 2.43), and 85% (OR = 1.85, 95%CI 1.38, 2.76), respectively. Latent class trajectories of maternal weights can be accurately estimated using SMM. It is a powerful means for researchers to appropriately assign individuals to their class. The U-shaped curve of association between maternal weight gain and risk of maternal complications reveals that the optimum place for pregnant women could be in the middle of the growth curve to minimize the risks. Low maternal weight trajectory compared to high had even a significantly higher hazard for some neonatal adverse events. Therefore, appropriate weight gain is critical for pregnant women.Trial registration International Standard Randomized Controlled Trial Number (ISRCTN): 2014102519660N1; http://www.irct.ir/searchresult.php?keyword=&id=19660&number=1&prt=7805&total=10&m=1 (Archived by WebCite at http://www.webcitation.org/6p3lkqFdV ).

Identifying typical trajectories in longitudinal data: modelling strategies and interpretations

Individual-level longitudinal data on biological, behavioural, and social dimensions are becoming increasingly available. Typically, these data are analysed using mixed effects models, with the result summarised in terms of an average trajectory plus measures of the individual variations around this average. However, public health investigations would benefit from finer modelling of these individual variations which identify not just one average trajectory, but several typical trajectories. If evidence of heterogeneity in the development of these variables is found, the role played by temporally preceding (explanatory) variables as well as the potential impact of differential trajectories may have on later outcomes is often of interest. A wide choice of methods for uncovering typical trajectories and relating them to precursors and later outcomes exists. However, despite their increasing use, no practical overview of these methods targeted at epidemiological applications exists. Hence we provide: (a) a review of the three most commonly used methods for the identification of latent trajectories (growth mixture models, latent class growth analysis, and longitudinal latent class analysis); and (b) recommendations for the identification and interpretation of these trajectories and of their relationship with other variables. For illustration, we use longitudinal data on childhood body mass index and parental reports of fussy eating, collected in the Avon Longitudinal Study of Parents and Children.

Latent trajectories of infant breast milk consumption in the United States

Patterns of breastfeeding over time are not currently well understood. Limited qualitative and quantitative evidence suggests that there may be latent subgroups of mothers in the United States following very different trajectories of breast milk provision for their infants. This study used a quantitative modelling method (group-based trajectory modelling) to identify and describe these subgroups. Using data from the Infant Feeding Practices Study II (n = 3,023), the authors identified four distinct trajectories of breastfeeding intensity, each of which included a substantial subset of the total sample. A model with four groups fit the data well by objective and conceptual standards. Bivariate associations were analysed, and significant difference between trajectory group membership was found on an array of maternal and family determinants, including maternal demographics, hospital experience, and psychosocial resources, as well as on postweaning perceptions. These associations were used to create group profiles for each subgroup. Controlling for sociodemographic covariates, we also found that trajectory membership was significantly associated with several health outcomes for the target child 6 years later, including certain infections, picky eating, and health care utilization; trajectory group membership was also associated with maternal breastfeeding of subsequent children and maternal body mass index (BMI) at Year 6. Child BMI z-score and maternal breast cancer diagnosis were not significantly different across trajectory groups after accounting for confounding covariates, nor was time missed from school for the target child. Though exploratory, the initial identification and description of these four subgroups suggest future directions using breastfeeding trajectory methods, with potential implications for measurement, intervention development, and targeting.

The relationship between multilevel models and non-parametric multilevel mixture models: Discrete approximation of intraclass correlation, random coefficient distributions, and residual heteroscedasticity

Multilevel data structures are common in the social sciences. Often, such nested data are analysed with multilevel models (MLMs) in which heterogeneity between clusters is modelled by continuously distributed random intercepts and/or slopes. Alternatively, the non-parametric multilevel regression mixture model (NPMM) can accommodate the same nested data structures through discrete latent class variation. The purpose of this article is to delineate analytic relationships between NPMM and MLM parameters that are useful for understanding the indirect interpretation of the NPMM as a non-parametric approximation of the MLM, with relaxed distributional assumptions. We define how seven standard and non-standard MLM specifications can be indirectly approximated by particular NPMM specifications. We provide formulas showing how the NPMM can serve as an approximation of the MLM in terms of intraclass correlation, random coefficient means and (co)variances, heteroscedasticity of residuals at level 1, and heteroscedasticity of residuals at level 2. Further, we discuss how these relationships can be useful in practice. The specific relationships are illustrated with simulated graphical demonstrations, and direct and indirect interpretations of NPMM classes are contrasted. We provide an R function to aid in implementing and visualizing an indirect interpretation of NPMM classes. An empirical example is presented and future directions are discussed.

Introducing the fit-criteria assessment plot - A visualisation tool to assist class enumeration in group-based trajectory modelling

Background and objective Group-based trajectory modelling is a model-based clustering technique applied for the identification of latent patterns of temporal changes. Despite its manifold applications in clinical and health sciences, potential problems of the model selection procedure are often overlooked. The choice of the number of latent trajectories (class-enumeration), for instance, is to a large degree based on statistical criteria that are not fail-safe. Moreover, the process as a whole is not transparent. To facilitate class enumeration, we introduce a graphical summary display of several fit and model adequacy criteria, the fit-criteria assessment plot. Methods An R-code that accepts universal data input is presented. The programme condenses relevant group-based trajectory modelling output information of model fit indices in automated graphical displays. Examples based on real and simulated data are provided to illustrate, assess and validate fit-criteria assessment plot's utility. Results Fit-criteria assessment plot provides an overview of fit criteria on a single page, placing users in an informed position to make a decision. Fit-criteria assessment plot does not automatically select the most appropriate model but eases the model assessment procedure. Conclusions Fit-criteria assessment plot is an exploratory, visualisation tool that can be employed to assist decisions in the initial and decisive phase of group-based trajectory modelling analysis. Considering group-based trajectory modelling's widespread resonance in medical and epidemiological sciences, a more comprehensive, easily interpretable and transparent display of the iterative process of class enumeration may foster group-based trajectory modelling's adequate use.

Handling Missing Covariates in Conditional Mixture Models Under Missing at Random Assumptions

Mixture modeling is a popular method that accounts for unobserved population heterogeneity using multiple latent classes that differ in response patterns. Psychologists use conditional mixture models to incorporate covariates into between-class and/or within-class regressions. Although psychologists often have missing covariate data, conditional mixtures are currently fit with a conditional likelihood, treating covariates as fixed and fully observed. Under this exogenous-x approach, missing covariates are handled primarily via listwise deletion. This sacrifices efficiency and does not allow missingness to depend on observed outcomes. Here we describe a modified joint likelihood approach that (a) allows inference about parameters of the exogenous-x conditional mixture even with nonnormal covariates, unlike a conventional multivariate mixture; (b) retains all cases under missing at random assumptions; (c) yields lower bias and higher efficiency than the exogenous-x approach under a variety of conditions with missing covariates; and (d) is straightforward to implement in available commercial software. The proposed approach is illustrated with an empirical analysis predicting membership in latent classes of conduct problems. Recommendations for practice are discussed.

Using a shared parameter mixture model to estimate change during treatment when termination is related to recovery speed

OBJECTIVE

This study demonstrates how to use a shared parameter mixture model (SPMM) in longitudinal psychotherapy studies to accommodate missingness that is due to a correlation between rate of improvement and termination of therapy. Traditional growth models assume that such a relationship does not exist (i.e., assume that data are missing at random) and produce biased results if this assumption is incorrect.

METHOD

We used longitudinal data from 4,676 patients enrolled in a naturalistic study of psychotherapy to compare results from a latent growth model and an SPMM.

RESULTS

In this data set, estimates of the rate of improvement during therapy differed by 6.50%-6.66% across the two models, indicating that participants with steeper trajectories left psychotherapy earliest, thereby potentially biasing inference for the slope in the latent growth model.

CONCLUSION

We conclude that reported estimates of change during therapy may be underestimated in naturalistic studies of therapy in which participants and their therapists determine the end of treatment. Because non-randomly missing data can also occur in randomized controlled trials or in observational studies of development, the utility of the SPMM extends beyond naturalistic psychotherapy data.

A discrete-time Multiple Event Process Survival Mixture (MEPSUM) model

Traditional survival analysis was developed to investigate the occurrence and timing of a single event, but researchers have recently begun to ask questions about the order and timing of multiple events. A multiple event process survival mixture model is developed here to analyze nonrepeatable events measured in discrete-time that may occur at the same point in time. Building on both traditional univariate survival analysis and univariate survival mixture analysis, the model approximates the underlying multivariate distribution of hazard functions via a discrete-point finite mixture in which the mixing components represent prototypical patterns of event occurrence. The model is applied in an empirical analysis concerning transitions to adulthood, where the events under study include parenthood, marriage, beginning full-time work, and obtaining a college degree. Promising opportunities, as well as possible limitations of the model and future directions for research, are discussed.

Modeling Change in the Presence of Non-Randomly Missing Data: Evaluating A Shared Parameter Mixture Model

In longitudinal research, interest often centers on individual trajectories of change over time. When there is missing data, a concern is whether data are systematically missing as a function of the individual trajectories. Such a missing data process, termed random coefficient-dependent missingness, is statistically non-ignorable and can bias parameter estimates obtained from conventional growth models that assume missing data are missing at random. This paper describes a shared-parameter mixture model (SPMM) for testing the sensitivity of growth model parameter estimates to a random coefficient-dependent missingness mechanism. Simulations show that the SPMM recovers trajectory estimates as well as or better than a standard growth model across a range of missing data conditions. The paper concludes with practical advice for longitudinal data analysts.

Understanding Linkages Among Mixture Models

The methodological literature on mixture modeling has rapidly expanded in the past 15 years, and mixture models are increasingly applied in practice. Nonetheless, this literature has historically been diffuse, with different notations, motivations, and parameterizations making mixture models appear disconnected. This pedagogical review facilitates an integrative understanding of mixture models. First, 5 prototypic mixture models are presented in a unified format with incremental complexity while highlighting their mutual reliance on familiar probability laws, common assumptions, and shared aspects of interpretation. Second, 2 recent extensions-hybrid mixtures and parallel-process mixtures-are discussed. Both relax a key assumption of classic mixture models but do so in different ways. Similarities in construction and interpretation among hybrid mixtures and among parallel-process mixtures are emphasized. Third, the combination of both extensions is motivated and illustrated by means of an example on oppositional defiant and depressive symptoms. By clarifying how existing mixture models relate and can be combined, this article bridges past and current developments and provides a foundation for understanding new developments.