Factor scoring methods affected by response shift in patient-reported outcomes
Objective: Patient-reported outcomes (PROs) are measures collected from a patient to determine how he/she feels or functions in regards to a health condition. Longitudinal PROs, which are collected at multiple occasions from the same individual, may be affected by response shift (RS). RS is a change in a person’s self-evaluation of a target construct. Latent variable models (LVMs) are statistical models that relate observed variables to latent variables (LV). LVMs are used to analyze PROs and detect RS. LVs are random variables whose realizations are not observable. Factor scores are estimates of LVs for each individual and can be estimated from parameter estimates of LVMs. Factor scoring methods to estimate factor scores include: Thurstone, Bartlett, and sum scores. This simulation study examines the effects of RS on factor scores used to test for change in the LV means and recommend a factor scoring method least affected by RS. Methods: Data from two time points were fit to three confirmatory factor analysis (CFA) models. CFA models are a type of LVM. Each CFA model had different sets of parameters that were invariant over time. The unconstrained (Uncon) CFA model had no invariant parameters, the constrained (Con) model had all the parameters invariant, and the partially constrained (Pcon) model had some of the parameters invariant over time. Factor scores were estimated and tested for change over time via paired t-test. The Type I error, power, and factor loading (the regression coefficient between an observed and LV) and factor score bias were estimated to determine if RS influenced the test of change over time and factor score estimation. Results: The results depended on the true LV mean. The Type I error and power were similar for all factor scoring methods and CFA models when the LV mean was 0 at time 1. For LV mean of 0.5 at time 1 the Type I error and power increased as RS increased for all factor scores except for scores estimated from the Uncon model and Bartlett method. The biases of the factor loadings were unaffected by RS when estimated from an Uncon model. The factor scores estimated from the Uncon model and the Bartlett and sum scores method had the smallest factor score biases. Conclusion: The factor scores estimated from the Uncon model and the Bartlett method was least affected by RS and performed best in all measures of Type I error, statistical power, factor loading and factor score bias. Estimating factor scores from PROs data that ignores RS may result in erroneous (or biased) estimates.
DegreeMaster of Science (M.Sc.)
DepartmentMathematics and Statistics
SupervisorLix, Lisa; Liu, Juxin
CommitteeLi, Longhai; Sarty, Gordon; Martin, John
Copyright DateJuly 2014