A meta-analytic approach to growth curve analysis

A meta-analytic approach to growth curve analysis is described and illustra ted by applying it to the evaluation of the Arizona Pilot Project, an exper imental project for financing the treatment of the severely mentally ill. I n this approach to longitudinal data analysis, each individual subject for which repeated measures are obtained is initially treated as a separate cas e study for analysis. This approach has at least two distinct advantages. F irst, it does not assume a balanced design (equal numbers of repeated obser vations) across all subjects; to accommodate a variable number of observati ons for each subject, individual growth curve parameters are differentially weighted by the number of repeated measures on which they are based. Secon d, it does not assume homogeneity of treatment effects (equal slopes) acros s all subjects. Individual differences in growth curve parameters represent ing potentially unequal developmental rates through rime are explicitly mod eled. A meta-analytic approach to growth curve analysis may be the optimal analytical strategy for longitudinal studies where either (1) a balanced de sign is not feasible or (2) an assumption of homogeneity of treatment effec ts across ail individuals is theoretically indefensible. In our evaluation of the Arizona Pilot Project, individual growth curve parameters were obtai ned for each of the 13 rationally derived subscales of the New York Functio nal Assessment Survey, over time, by linear regression analysis. The slopes , intercepts, and residuals obtained for each individual were then subjecte d to meta-analytic causal modeling. Using factor analytic models and then g eneral linear models for the latent constructs, the growth curve parameters of all individuals were systematically related to each other via common fa ctors and predicted based on hypothesized exogenous causal factors. The sam e two highly correlated common factors were found for all three growth curv e parameters analyzed, a general psychological factor and a general functio nal factor. The factor patterns were found to be nearly identical across th e separate analyses of individual intercepts, slopes. and residuals. Direct effects on the unique factors of each subscale of the New York Functional Assessment Sun ey were tested for each growth curve parameter by including the common factors as hierarchically prior predictors in the structural mod el for each of the indicator variables, thus statistically controlling for any indirect effect produced on the indicator through the common factors. T he exogenous, predictors modeled mere theoretically specified orthogonal co ntrasts for Method of Payment (comparing Arizona Pilot Project treatment or "capitation" to traditional or "fee-for-service" care as a control), Treat ment Administration Site (comparing Various locations within treatment or c ontrol groups), Pretreatment Assessment (comparing general functional level at intake as assigned by an Outside Assessment Team), and various interact ions among these main effects. The intercepts, representing the initial sta tus of individual subjects on both the two common factors and the 13 unique factors of the subscales of the New York Functional Assessment Survey. wer e found ro vary significantly across many of the various different treatmen t conditions, treatment administration sites, and pretreatment functional l evels. This indicated a severe threat to the validity of the originally int ended design of the Arizona Pilot Project as a randomized experiment. When the systematic variations were statistically controlled by including i ntercepts as hierarchically prior predictors in the structural models for s lopes, recasting the experiment as a nonequivalent groups design, the effec ts of the intercepts on the slopes were found to be both statistically sign ificant and substantial in magnitude. Furthermore. the contrasts for Pretre atment Assessment scores also predicted statistically significant proportio ns of Variance in both the two common factors and che 13 unique factors of the subscales of the New York Functional Assessment Survey for all three gr owth curve parameters, confirming an influence of the initial status of ind ividual subjects on treatment effect. This empirical example illustrates bo th the mechanics and the many practical benefits of a meta-analytic approac h to growth curve analysis in program evaluation.