Recent Advances in Group-Based Trajectory Modeling for Clinical Research.

Group-based trajectory modeling (GBTM) identifies groups of individuals following similar trajectories of one or more repeated measures. The categorical nature of GBTM is particularly well suited to clinical psychology and medicine, where patients are often classified into discrete diagnostic categories. This review highlights recent advances in GBTM and key capabilities that remain underappreciated in clinical research. These include accounting for nonrandom subject attrition, joint trajectory and multitrajectory modeling, the addition of the beta distribution to modeling options, associating trajectories with future outcomes, and estimating the probability of future outcomes. Also discussed is an approach to selecting the number of trajectory groups. Expected final online publication date for the Annual Review of Clinical Psychology, Volume 20 is May 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Cohort bias in predictive risk assessments of future criminal justice system involvement.

Risk assessment instruments (RAIs) are widely used to aid high-stakes decision-making in criminal justice settings and other areas such as health care and child welfare. These tools, whether using machine learning or simpler algorithms, typically assume a time-invariant relationship between predictors and outcome. Because societies are themselves changing and not just individuals, this assumption may be violated in many behavioral settings, generating what we call cohort bias. Analyzing criminal histories in a cohort-sequential longitudinal study of children, we demonstrate that regardless of model type or predictor sets, a tool trained to predict the likelihood of arrest between the ages of 17 and 24 y on older birth cohorts systematically overpredicts the likelihood of arrest for younger birth cohorts over the period 1995 to 2020. Cohort bias is found for both relative and absolute risks, and it persists for all racial groups and within groups at highest risk for arrest. The results imply that cohort bias is an underappreciated mechanism generating inequality in contacts with the criminal legal system that is distinct from racial bias. Cohort bias is a challenge not only for predictive instruments with respect to crime and justice, but also for RAIs more broadly.

Mortality Risk in Pediatric Sepsis Based on C-reactive Protein and Ferritin Levels.

OBJECTIVES: Interest in using bedside C-reactive protein (CRP) and ferritin levels to identify patients with hyperinflammatory sepsis who might benefit from anti-inflammatory therapies has piqued with the COVID-19 pandemic experience. Our first objective was to identify patterns in CRP and ferritin trajectory among critically ill pediatric sepsis patients. We then examined the association between these different groups of patients in their inflammatory cytokine responses, systemic inflammation, and mortality risks. DATA SOURCES: A prospective, observational cohort study. STUDY SELECTION: Children with sepsis and organ failure in nine pediatric intensive care units in the United States. DATA EXTRACTION: Two hundred and fifty-five children were enrolled. Five distinct clinical multi-trajectory groups were identified. Plasma CRP (mg/dL), ferritin (ng/mL), and 31 cytokine levels were measured at two timepoints during sepsis (median Day 2 and Day 5). Group-based multi-trajectory models (GBMTM) identified groups of children with distinct patterns of CRP and ferritin. DATA SYNTHESIS: Group 1 had normal CRP and ferritin levels ( n = 8; 0% mortality); Group 2 had high CRP levels that became normal, with normal ferritin levels throughout ( n = 80; 5% mortality); Group 3 had high ferritin levels alone ( n = 16; 6% mortality); Group 4 had very high CRP levels, and high ferritin levels ( n = 121; 11% mortality); and Group 5 had very high CRP and very high ferritin levels ( n = 30; 40% mortality). Cytokine responses differed across the five groups, with ferritin levels correlated with macrophage inflammatory protein 1α levels and CRP levels reflective of many cytokines. CONCLUSIONS: Bedside CRP and ferritin levels can be used together to distinguish groups of children with sepsis who have different systemic inflammation cytokine responses and mortality risks. These data suggest future potential value in personalized clinical trials with specific targets for anti-inflammatory therapies.

Bayesian Outcome Prediction After Resuscitation From Cardiac Arrest.

BACKGROUND AND OBJECTIVES: Postarrest prognostication research does not typically account for the sequential nature of real-life data acquisition and interpretation and reports nonintuitive estimates of uncertainty. Bayesian approaches offer advantages well suited to prognostication. We used Bayesian regression to explore the usefulness of sequential prognostic indicators in the context of prior knowledge and compared this with a guideline-concordant algorithm. METHODS: We included patients hospitalized at a single center after cardiac arrest. We extracted prospective data and assumed these data accrued over time as in routine practice. We considered predictors demographic and arrest characteristics, initial and daily neurologic examination, laboratory results, therapeutic interventions, brain imaging, and EEG. We fit Bayesian hierarchical generalized linear multivariate models predicting discharge Cerebral Performance Category (CPC) 4 or 5 (poor outcomes) vs 1-3 including sequential clinical and prognostic data. We explored outcome posterior probability distributions (PPDs) for individual patients and overall. As a comparator, we applied the 2021 European Resuscitation Council and European Society of Intensive Care Medicine (ERC/ESICM) guidelines. RESULTS: We included 2,692 patients of whom 864 (35%) were discharged with a CPC 1-3. Patients' outcome PPDs became narrow and shifted toward 0 or 1 as sequentially acquired information was added to models. These changes were largest after arrest characteristics and initial neurologic examination were included. Using information typically available at or before intensive care unit admission, sensitivity predicting poor outcome was 51% with a 0.6% false-positive rate. In our most comprehensive model, sensitivity for poor outcome prediction was 76% with 0.6% false-positive rate (FPR). The ERC/ESICM algorithm applied to 547 of 2,692 patients and yielded 36% sensitivity with 0% FPR. DISCUSSION: Bayesian models offer advantages well suited to prognostication research. On balance, our findings support the view that in expert hands, accurate neurologic prognostication is possible in many cases before 72 hours postarrest. Although we caution against early withdrawal of life-sustaining therapies, rapid outcome prediction can inform clinical decision making and future clinical trials.

Social change and cohort differences in group-based arrest trajectories over the last quarter-century.

This article draws on official criminal histories for multiple birth cohorts spanning a 17-y difference in birth year to study how social change can alter our understanding of influential theories and policies about criminal offender groups. Arrest histories are linked to comprehensive longitudinal measurement on over 1,000 individuals originally from Chicago. Using group-based trajectory modeling, we investigated the magnitude and type of cohort differences in trajectories of arrest over the period 1995 to 2020. Our results show that trajectory group membership varies strongly by birth cohort. Membership in the nonoffender group is nearly 15 percentage points higher for cohorts born in the mid-1990s as compared to those born in the 1980s; conversely, older cohorts are more likely to be members of adolescent-limited and chronic-offender groups. Large cohort differences in trajectory group membership persist after controlling for a wide-ranging set of demographic characteristics and early-life risk factors that vary by cohort and that prior research has identified as important influences on crime. Not only does the effect of social change on cohort differentiation persist, but its magnitude is comparable to-indeed larger than-differences in trajectory group membership associated with varying levels of self-control or by whether individuals grew up in high-poverty households. These results suggest that changes in the broader social environment shared by members of the same birth cohort are as powerful in shaping their trajectory group membership as classic predictors identified in prior research, a finding that carries implications for crime-control policies that rely on prediction.

Comparison of parametric and nonparametric methods for outcome prediction using longitudinal data after cardiac arrest.

INTRODUCTION: Predicting outcome after cardiac arrest is challenging. We previously tested group-based trajectory modeling (GBTM) for prognostication based on baseline characteristics and quantitative electroencephalographic (EEG) trajectories. Here, we describe implementation of this method in a freely available software package and test its performance against alternative options. METHODS: We included comatose patients admitted to a single center after resuscitation from cardiac arrest from April 2010 to April 2019 who underwent ≥6 h of EEG monitoring. We abstracted clinical information from our prospective registry and summarized suppression ratio in 48 hourly epochs. We tested three classes of longitudinal models: frequentist, statistically based GBTMs; non-parametric (i.e. machine learning) k-means models; and Bayesian regression. Our primary outcome of interest was discharge CPC 1-3 (vs unconsciousness or death). We compared sensitivity for detecting poor outcome at a false positive rate (FPR) <1%. RESULTS: Of 1,010 included subjects, 250 (25%) were awake and alive at hospital discharge. GBTM and k-means derived trajectories, group sizes and group-specific outcomes were comparable. Conditional on an FPR < 1%, GBTMs yielded optimal sensitivity (38%) over 48 h. More sensitive methods had 2-3 % FPRs. CONCLUSION: We explored fundamentally different tools for patient-level predictions based on longitudinal and time-invariant patient data. Of the evaluated methods, GBTM resulted in optimal sensitivity while maintaining a false positive rate <1%. The provided code and software of this method provides an easy-to-use implementation for outcome prediction based on GBTMs.

Using the Beta distribution in group-based trajectory models.

BACKGROUND: We demonstrate an application of Group-Based Trajectory Modeling (GBTM) based on the beta distribution. It is offered as an alternative to the normal distribution for modeling continuous longitudinal data that are poorly fit by the normal distribution even with censoring. The primary advantage of the beta distribution is the flexibility of the shape of the density function. METHODS: GBTM is a specialized application of finite mixture modeling designed to identify clusters of individuals who follow similar trajectories. Like all finite mixture models, GBTM requires that the distribution of the data composing the mixture be specified. To our knowledge this is the first demonstration of the use of the beta distribution in GBTM. A case study of a beta-based GBTM analyzes data on the neurological activity of comatose cardiac arrest patients. RESULTS: The case study shows that the summary measure of neurological activity, the suppression ratio, is not well fit by the normal distribution but due to the flexibility of the shape of the beta density function, the distribution of the suppression ratio by trajectory appears to be well matched by the estimated beta distribution by group. CONCLUSIONS: The addition of the beta distribution to the already available distributional alternatives in software for estimating GBTM is a valuable augmentation to extant distributional alternatives.

Group-based multi-trajectory modeling.

Identifying and monitoring multiple disease biomarkers and other clinically important factors affecting the course of a disease, behavior or health status is of great clinical relevance. Yet conventional statistical practice generally falls far short of taking full advantage of the information available in multivariate longitudinal data for tracking the course of the outcome of interest. We demonstrate a method called multi-trajectory modeling that is designed to overcome this limitation. The method is a generalization of group-based trajectory modeling. Group-based trajectory modeling is designed to identify clusters of individuals who are following similar trajectories of a single indicator of interest such as post-operative fever or body mass index. Multi-trajectory modeling identifies latent clusters of individuals following similar trajectories across multiple indicators of an outcome of interest (e.g., the health status of chronic kidney disease patients as measured by their eGFR, hemoglobin, blood CO2 levels). Multi-trajectory modeling is an application of finite mixture modeling. We lay out the underlying likelihood function of the multi-trajectory model and demonstrate its use with two examples.

Risk Factors Associated With Boys' and Girls' Developmental Trajectories of Physical Aggression From Early Childhood Through Early Adolescence.

Importance: This study used multitrajectory modeling to identify distinct trajectories of physical aggression from ages 1.5 to 13 years for boys and girls. Objectives: To trace the development of boys' and girls' physical aggression problems from infancy to adolescence using mother ratings, teacher ratings, and self-ratings and to identify early family predictors of children on the high physical aggression trajectories. Design, Setting, and Participants: This cohort study used data from the Quebec Longitudinal Study of Child Development (QLSCD), a study of a representative, population-based sample of 2223 infants born in 1997 and 1998 in the Canadian province of Quebec. The dates of analysis were January 2017 to January 2018. Main Outcomes and Measures: Trained research assistants conducted 7 interviews (at child ages 1.5, 2.5, 3.5, 4.5, 5, 6, and 8 years) with the person most knowledgeable about the child (mothers in 99.6% [2214 of 2223] of cases). Teachers assessed the child's behavior at ages 6, 7, 8, 10, 12, and 13 years. Self-reports of behavior problems were obtained from the child at ages 10, 12, and 13 years. Results: The sample included 2223 participants, 51.2% of whom were boys and 91.2% of whom were of white race/ethnicity. The mean response rate for mother ratings of physical aggression during the first 8 years of life was 80.9% (range, 65.1%-91.7%). For teacher ratings of physical aggression from ages 6 to 13 years, the mean response rate was 45.7% (range, 35.4%-56.9%), while the mean response rate of physical aggression assessment from self-ratings between ages 10 and 13 years was 57.9% (range, 55.2%-60.5%). Attrition was higher among families with low socioeconomic status and single-parent families, as well as among young mothers and mothers who were not fluent in French or English. A statistical analysis to examine the consequences of attrition was included. For boys and girls, the frequency of physical aggressions increased from age 1.5 years (2039 [91.7%]) to age 3.5 years (1941 [87.3%]) and then substantially decreased until age 13 years (1228 [55.2%]). Three distinct developmental trajectories of physical aggression were observed for girls and 5 for boys. Most family characteristics measured at 5 months after the child's birth were associated with a high physical aggression trajectory for boys and girls. Conclusions and Relevance: Family characteristics at 5 months after the child's birth could be used to target preschool interventions aimed at preventing the development of boys' and girls' chronic physical aggression problems.

Assessing benefits, costs, and disparate racial impacts of confrontational proactive policing.

Effective policing in a democratic society must balance the sometime conflicting objectives of public safety and community trust. This paper uses a formal model of optimal policing to explore how society might reasonably resolve the tension between these two objectives as well as evaluate disparate racial impacts. We do so by considering the social benefits and costs of confrontational types of proactive policing, such as stop, question, and frisk. Three features of the optimum that are particularly relevant to policy choices are explored: (i) the cost of enforcement against the innocent, (ii) the baseline level of crime rate without confrontational enforcement, and (iii) differences across demographic groups in the optimal rate of enforcement.

Depressive Trajectories and Risk of Disability and Mortality in Older Adults: Longitudinal Findings From the Health, Aging, and Body Composition Study.

BACKGROUND: Depression and disability are closely linked. Less is known regarding clinical and subclinical depressive symptoms over time and risk of disability and mortality. METHODS: Responses to the Center for Epidemiologic Studies Short Depression scale (CES-D10) were assessed over a 4-year period in men (n = 1032) and women (n = 1070) aged 70-79 years initially free from disability. Depressive symptom trajectories were defined with group-based models. Disability (2 consecutive reports of severe difficulty walking one-quarter mile or climbing 10 steps) and mortality were determined for 9 subsequent years. Hazard ratios (HRs) were estimated using Cox proportional hazards adjusted for covariates. RESULTS: Three trajectories were identified: persistently nondepressed (54% of men, 54% of women, mean baseline CES-D10: 1.16 and 1.46), mildly depressed and increasing (40% of men, 38% of women, mean baseline CES-D10: 3.60 and 4.35), and depressed and increasing (6% of men, 8% of women, mean baseline CES-D10: 7.44 and 9.61). Disability and mortality rates per 1,000 person years were 41.4 and 60.3 in men and 45.8 and 41.9 in women. Relative to nondepressed, men in the mildly depressed (HR = 1.45, 95% confidence interval [CI] 1.11-1.89) and depressed trajectories (HR = 2.12, 95% CI 1.33-3.38) had increased disability; women in the depressed trajectory had increased disability (HR = 2.02, 95% CI 1.37-2.96). Men in the mildly depressed (HR = 1.24, 95% CI 1.01-1.52) and depressed trajectories (HR = 1.63, 95% CI 1.10-2.41) had elevated mortality risk; women exhibited no mortality risk. CONCLUSIONS: Trajectories of depressive symptoms without recovery may predict disability and mortality in apparently healthy older populations, thus underscoring the importance of monitoring depressive symptoms in geriatric care.

Multi-Trajectory Models of Chronic Kidney Disease Progression.

An ever increasing number of people are affected by chronic kidney disease (CKD). A better understanding of the progression ofCKD and its complications is needed to address what is becoming a major burden for health-care systems worldwide. Utilizing a rich data set consisting of the Electronic Health Records (EHRs) of more than 33,000 patients from a leading community nephrology practice in Western Pennsylvania, we applied group-based trajectory modeling (GBTM) in order to detect patient risk groups and uncover typical progressions of CKD and related comorbidities and complications. We have found distinct risk groups with differing trajectories and are able to classify new patients into these groups with high accuracy (up to ≈ 90%). Our results suggest that multitrajectory modeling via GBTM can shed light on the developmental course ofCKD and the interactions between related complications.

Body Mass Index Trajectories in Relation to Change in Lean Mass and Physical Function: The Health, Aging and Body Composition Study.

OBJECTIVES: To examine body mass index (BMI) trajectories with change in lean mass and physical function in old age. DESIGN: Prospective cohort study. SETTING: Health, Aging and Body Composition Study. PARTICIPANTS: Black and white men (n = 482) and women (n = 516) aged 73.1 ± 2.7 and initially free of disability. MEASUREMENTS: A group-based trajectory model was used to determine BMI trajectories, the path a person's BMI followed over 9 years. Lean mass, gait speed, grip strength, and knee extension strength were assessed at baseline and after 9 years, and relative changes were calculated. Multivariable linear regression was used to determine associations between trajectories and relative change in lean mass and physical function. RESULTS: Four BMI trajectories were identified for men and four for women. Although all demonstrated a decline in BMI, the rate of decline differed according to trajectory for women only. Men in Trajectory 4 (mean BMI at baseline 33.9 ± 2.3 kg/m(2) ) declined more than those in Trajectory 1 (mean BMI at baseline 22.9 ± 1.6 kg/m(2) ) in gait speed (-9.91%, 95% confidence interval (CI) = -15.15% to -4.67%) and leg strength (-8.63%, 95% CI = -15.62% to -1.64%). Women in Trajectory 4 (mean BMI at baseline 34.9 ± 3.0 kg/m(2) ) had greater losses than those in Trajectory 1 (mean BMI at baseline 20.5 ± 1.6 kg/m(2) ) in lean mass in the arms (-3.19%, 95% CI = -6.16% to -0.23%). No other associations were observed. CONCLUSION: Obese men had the highest risk of decline in physical function despite similar weight loss between trajectories, whereas overweight and obese women who lost the most weight had the greatest risk of lean mass loss. The weight at which a person enters old age is informative for predicting loss in lean mass and physical function, illustrating the importance of monitoring weight.

Group-based trajectory modeling: an overview.

This article provides an overview of a group-based statistical methodology for analyzing developmental trajectories - the evolution of an outcome over age or time. Across all application domains, this group-based statistical method lends itself to the presentation of findings in the form of easily understood graphical and tabular data summaries. In so doing, the method provides statistical researchers with a tool for figuratively painting a statistical portrait of the predictors and consequences of distinct trajectories of development. Data summaries of this form have the great advantage of being accessible to nontechnical audiences and quickly comprehensible to audiences that are technically sophisticated. Examples of the application of the method are provided. A detailed account of the statistical underpinnings of the method and a full range of applications are provided by the author in a previous study.

Examining late-life functional limitation trajectories and their associations with underlying onset, recovery, and mortality.

OBJECTIVES: Identify common trajectories of physical functional limitation and mortality among Taiwanese 50 and older as they age, link these to underlying transitions in onset, recovery, and mortality, and assess associations between trajectories and a set of risk factors. METHOD: Longitudinal data from 4 waves of the Survey of Health and Living Status of the Middle-Aged and Elderly in Taiwan, collected between 1996 and 2007, are analyzed using a summary measure indicating difficulty with one or more of 7 physical functions. A group-based trajectory model identifies common trajectories. Shorter term transition probabilities that underlie multiperiod trajectories are examined. Multinomial regression associates risk factors with trajectory group membership. RESULTS: Best fitting the data is a model with 3 groups characterized as early, mid, and late onset of limitation. Roughly half the population follows the trajectory of mid onset and a quarter each of the other 2. Females and those least educated are most likely to belong to the early-onset group. DISCUSSION: The analysis advances understanding of late-life functioning by focusing on the heterogeneity of functional limitation experience, appropriately accounting for the relation between functional limitation and mortality and linking long-term patterns with short-term changes in functional limitation.

Modeling disability trajectories and mortality of the oldest-old in China.

This article uses a group-based modeling approach to jointly estimate disability and mortality trajectories over time based on data from the population aged 80 and older in China, and explores relations of demographic, socioeconomic, and early-life characteristics to membership in gender-specific trajectory groups. A three-group model best fits the data for both males and females. For most groups, predicted numbers of limitations in activities of daily living (ADLs) increase with age, but the pace is gradual in some cases and rapid in others. For each gender, the estimated mortality probability trajectories for the three groups follow a hierarchy that is related to the predicted ADL counts at age 80. Only a few characteristics predict trajectory-group membership. Prior nonagricultural occupation is associated with less favorable disability trajectories for both genders. For females, rural residence, a greater number of children ever born, and having a father who did not work in agriculture are associated with more favorable trajectories. For a small group of males who received education, disability is moderate but changes little with age. Findings may reflect heterogeneity of survival among the least advantaged, as well as a possible expansion of morbidity among a small advantaged group.

The neurocognition of conduct disorder behaviors: specificity to physical aggression and theft after controlling for ADHD symptoms.

There is growing evidence that among the different conduct disorder (CD) behaviors, physical aggression, but not theft, links to low neurocognitive abilities. Specifically, physical aggression has consistently been found to be negatively related to neurocognitive abilities, whereas theft has been shown to be either positively or not related to neurocognition. The specificity of these links needs further examination because attention deficit hyperactivity disorder (ADHD) links to both physical aggression and neurocognitive variation. The development of self-reported physical aggression and theft, from age 11 to 17 years, was studied in a prospective at-risk male cohort via a dual process latent growth curve model. Seven neurocognitive tests at age 20 were regressed on the growth parameters of physical aggression and theft. The links between neurocognition and the growth parameters of physical aggression and theft were adjusted for ADHD symptoms at ages 11 and 15 (parent, child and teacher reports). Results indicated that verbal abilities were negatively related to physical aggression while they were positively associated with theft. However, inductive reasoning was negatively associated with increases in theft across adolescence. Symptoms of ADHD accounted for part of the neurocognitive test links with physical aggression but did not account for the associations with theft. These differences emphasize the importance of examining specific CD behaviors to better understand their neurodevelopmental mechanisms. They also suggest that youth who engage in different levels of physical aggression or theft behaviors may require different preventive and corrective interventions.

Trajectories of childhood sexual abuse and early adolescent HIV/AIDS risk behaviors: the role of other maltreatment, witnessed violence, and child gender.

Childhood sexual abuse (CSA) has been associated with HIV/AIDS risk behavior; however, much of this work is retrospective and focuses on women. The current study used semi-parametric mixture modeling with youth (n = 844; 48.8% boys) from the Longitudinal Studies of Child Abuse and Neglect (LONGSCAN) to examine the link between trajectories of CSA (2 to 12 years old) and HIV/AIDS risk behavior at age 14 (i.e., sexual intercourse & alcohol use). Trajectory analyses revealed a link between a history of CSA and the development of risky behavior. In addition, trajectories for physical and emotional abuse, but not neglect or witnessed violence, contributed to risky behavior over and above the role of CSA. Child gender did not moderate the findings. Findings highlight the significance of CSA histories, as well as the broader context of maltreatment, for better understanding the development of risk behaviors in both girls and boys.