General linear contrasts on latent variable means: structural equation hypothesis tests for multivariate clinical trials.

Abstract

Structural equation models articulate the assumed measurement and causal relations among variables, imposing discipline on otherwise unstructured and redundant associations that arise in correlational studies. Biomedical research has eschewed such methods, relying on the generally superior causal inference afforded by randomized controlled trials. Increasingly, however, clinical trials incorporate numerous covariates that are measured but unmanipulated. Most clinical trials now also include multiple correlated endpoints, which can generate ambiguous outcome patterns refractory to simple statistical analysis and interpretation. Modern clinical trials are really multivariate longitudinal studies with at best a component of randomized control; as such, structural equation approaches can add rigour and clarity. The analysis of latent variance (LANOVA) conception combines structural equation and experimental analysis of variance legacies. It allows, for any design that can be decomposed into between-group and within-person models, tests on latent means (that is, the means of the unobserved factors) that are directly analogous to their analysis of variance counterparts. LANOVA variables are either outcomes (which may have a time structure), varying covariates (which may have a time structure), or background covariates (which are static). Allowable causal relations are set-recursive: background covariates can affect all other variables; varying covariates can affect current outcomes and later outcomes and covariates; outcomes can affect only later outcomes. All standard ANOVA and ANCOVA hypotheses can then be tested by proper restrictions among the means and intercepts of these latent variables. Structural equation modelling programs can be used to estimate the models and test the hypotheses. I demonstrate the approach by expressing and testing hypotheses appropriate for two clinical studies that evaluate patient-reported outcomes in populations with solid and haematological malignancies.