Statistics and Its Interface

Volume 2 (2009)

Number 4

Using latent outcome trajectory classes in causal inference

Pages: 403 – 412



Nicholas S. Ialongo (Department of Mental Health, Johns Hopkins University)

Booil Jo (Department of Psychiatry & Behavioral Sciences, Stanford University, Stanford, Calif., U.S.A.)

Chen-Pin Wang (Department of Epidemiology & Biostatistics, University of Texas Health Science Center)


In longitudinal studies, outcome trajectories can provide important information about substantively and clinically meaningful underlying subpopulations who may also respond differently to treatments or interventions. Growth mixture analysis is an efficient way of identifying heterogeneous trajectory classes. However, given its exploratory nature, it is unclear how involvement of latent classes should be handled in the analysis when estimating causal treatment effects. In this paper, we propose a 2-step approach, where formulation of trajectory strata and identification of causal effects are separated. In Step 1, we stratify individuals in one of the assignment conditions (reference condition) into trajectory strata on the basis of growth mixture analysis. In Step 2, we estimate treatment effects for different trajectory strata, treating the stratum membership as partly known (known for individuals assigned to the reference condition and missing for the rest). The results can be interpreted as how subpopulations that differ in terms of outcome prognosis under one treatment condition would change their prognosis differently when exposed to another treatment condition. Causal effect estimation in Step 2 is consistent with that in the principal stratification approach (Frangakis and Rubin, 2002) in the sense that clarified identifying assumptions can be employed and therefore systematic sensitivity analyses are possible. Longitudinal development of attention deficit among children from the Johns Hopkins School Intervention Trial (Ialongo et al., 1999) will be presented as an example.


causal inference, latent trajectory class, longitudinal outcome prognosis, growth mixture modeling, principal stratification, reference stratification

Published 1 January 2009