Targeted use of growth mixture modeling: a learning perspective

From the statistical learning perspective, this paper shows a new direction for the use of growth mixture modeling (GMM), a method of identifying latent subpopulations that manifest heterogeneous outcome trajectories. In the proposed approach, we utilize the benefits of the conventional use of GMM for the purpose of generating potential candidate models based on empirical model fitting, which can be viewed as unsupervised learning. We then evaluate candidate GMM models on the basis of a direct measure of success; how well the trajectory types are predicted by clinically and demographically relevant baseline features, which can be viewed as supervised learning. We examine the proposed approach focusing on a particular utility of latent trajectory classes, as outcomes that can be used as valid prediction targets in clinical prognostic models. Our approach is illustrated using data from the Longitudinal Assessment of Manic Symptoms study. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  M. Thase,et al.  Differential effects of treatments for chronic depression: a latent growth model reanalysis. , 2010, Journal of consulting and clinical psychology.

[2]  M. A. Tanner,et al.  Tools for Statistical Inference: Methods for the Exploration of Posterior Distributions and Likelihood Functions, 3rd Edition , 1998 .

[3]  Daniel J Bauer,et al.  Distributional assumptions of growth mixture models: implications for overextraction of latent trajectory classes. , 2003, Psychological methods.

[4]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[5]  J. Audrain-McGovern,et al.  Team sport participation and smoking: analysis with general growth mixture modeling. , 2004, Journal of pediatric psychology.

[6]  J. Neuhaus,et al.  Identification of distinct depressive symptom trajectories in women following surgery for breast cancer. , 2011, Health psychology : official journal of the Division of Health Psychology, American Psychological Association.

[7]  N. Ryan,et al.  Characteristics of children with elevated symptoms of mania: the Longitudinal Assessment of Manic Symptoms (LAMS) study. , 2010, The Journal of clinical psychiatry.

[8]  B. Muthén,et al.  Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm , 1999, Biometrics.

[9]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[10]  Scott L. Zeger,et al.  Latent Variable Regression for Multiple Discrete Outcomes , 1997 .

[11]  Booil Jo,et al.  Construction of longitudinal prediction targets using semisupervised learning , 2018, Statistical methods in medical research.

[12]  Katherine E. Masyn,et al.  Latent Class Analysis and Finite Mixture Modeling , 2013 .

[13]  B. Muthén,et al.  Preventing disruptive behavior in elementary schoolchildren: impact of a universal classroom-based intervention. , 2004, Journal of consulting and clinical psychology.

[14]  D. Axelson,et al.  Longitudinal Assessment of Manic Symptoms (LAMS) study: background, design, and initial screening results. , 2010, The Journal of clinical psychiatry.

[15]  B. Muthén,et al.  Estimating drug effects in the presence of placebo response: Causal inference using growth mixture modeling , 2009, Statistics in medicine.

[16]  Katherine E. Masyn,et al.  General growth mixture modeling for randomized preventive interventions. , 2001, Biostatistics.

[17]  Karen Bandeen-Roche,et al.  Residual Diagnostics for Growth Mixture Models , 2005 .

[18]  Bengt Muthén,et al.  Latent Variable Analysis: Growth Mixture Modeling and Related Techniques for Longitudinal Data , 2004 .

[19]  N. Ryan,et al.  The 24‐month course of manic symptoms in children , 2013, Bipolar disorders.

[20]  N. Ialongo,et al.  Using latent outcome trajectory classes in causal inference. , 2009, Statistics and its interface.

[21]  B. Birmaher,et al.  Pediatric bipolar disorder: validity, phenomenology, and recommendations for diagnosis. , 2008, Bipolar disorders.

[22]  M. Stone An Asymptotic Equivalence of Choice of Model by Cross‐Validation and Akaike's Criterion , 1977 .

[23]  B. Jo,et al.  Causal inference in longitudinal comparative effectiveness studies with repeated measures of a continuous intermediate variable , 2014, Statistics in Medicine.

[24]  Richard E. Tremblay,et al.  DEVELOPMENTAL TRAJECTORY GROUPS: FACT OR A USEFUL STATISTICAL FICTION?* , 2005 .

[25]  Trevor Hastie,et al.  An Introduction to Statistical Learning , 2013, Springer Texts in Statistics.

[26]  Bengt Muthén,et al.  Second-generation structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class–latent growth modeling. , 2001 .

[27]  M. Stone Cross‐Validatory Choice and Assessment of Statistical Predictions , 1976 .

[28]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[29]  B. Muthén,et al.  Deciding on the Number of Classes in Latent Class Analysis and Growth Mixture Modeling: A Monte Carlo Simulation Study , 2007 .

[30]  Robert Tibshirani,et al.  The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition , 2001, Springer Series in Statistics.

[31]  J. Krystal,et al.  Trajectories of depression severity in clinical trials of duloxetine: insights into antidepressant and placebo responses. , 2011, Archives of general psychiatry.

[32]  K. Jordan,et al.  Characterizing the course of low back pain: a latent class analysis. , 2006, American journal of epidemiology.

[33]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[34]  Wei Wang,et al.  Effects of a universal classroom behavior management program in first and second grades on young adult behavioral, psychiatric, and social outcomes. , 2008, Drug and alcohol dependence.

[35]  D. Rubin,et al.  Statistical Analysis with Missing Data , 1988 .

[36]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[37]  Katherine E. Masyn,et al.  General Growth Mixture Analysis with Antecedents and Consequences of Change , 2010 .

[38]  Bengt Muthén,et al.  Statistical and substantive checking in growth mixture modeling: comment on Bauer and Curran (2003). , 2003, Psychological methods.