The Distribution of Risk Across Healthcare Providers and Reducing Misclassification

Abstract

Four linear multilevel mixed-risk models were compared using model assumption tests and predictions. Models varied by the number of random intercepts from 1 to 4, producing 2-level through 5-level models of the same measure, operative time. Normality of the dependent variable and residuals, variance homoscedasticity, level-1, and level-2 exogeneity were tested using the robust test of the level-1 residuals variance by surgeon, estimates of density, skew, and the Hausman test. Measure (operative time by hospital and surgeon) aberrancy and risk classification were evaluated using traditional methods and used to assess distribution measures. The dependent variable and the level-1 residuals required transformation for linearity and variance stabilization, respectively. Normality criteria were met for both level-1 and level-2 residuals and standardized residuals. The likelihood ratio comparing the four models was significantly larger for the 5-level (1016.1; P<0.00005) model than the likelihood ratio for the four-level and other models. Shrinkage was greatest for the 2-level model (0.039; P<0.00005) and least for the 5-level model (0.028; P<0.00005). Level-1 variance homoscedasticity was confirmed by the robust variance test across all models (P>F=1). Aberrant value detection did not require the exclusion of any observations, while prediction intervals revealed low or high risk for 54.2% of surgeons for the 2-level model and 8.6% for the 5-level model. The traditional (c2 = -11.01; P=1) and instrumental variable (c2 = 21.06; P=1) Hausman tests show that the null hypothesis cannot be rejected for level-1 or level-2 exogeneity. Once level-1 and level-2 exogeneity was confirmed, and since deconfounding was a model consideration, causal inferential capacity was assumed. The likelihood ratio, residual variance, shrinkage, and predictions show that the 5-level model is preferred to the other models.