Abstract
BackgroundMany nursing and health related research studies have continuous outcome measures that are inherently non-normal in distribution. The Box-Cox transformation provides a powerful tool for developing a parsimonious model for data representation and interpretation when the distribution of the dependent variable, or outcome measure, of interest deviates from the normal distribution. The objectives of this study was to contrast the effect of obtaining the Box-Cox power transformation parameter and subsequent analysis of variance with or without a priori knowledge of predictor variables under the classic linear or linear mixed model settings.MethodsSimulation data from a 3 × 4 factorial treatments design, along with the Patient Falls and Patient Injury Falls from the National Database of Nursing Quality Indicators (NDNQI®) for the 3rd quarter of 2007 from a convenience sample of over one thousand US hospitals were analyzed. The effect of the nonlinear monotonic transformation was contrasted in two ways: a) estimating the transformation parameter along with factors with potential structural effects, and b) estimating the transformation parameter first and then conducting analysis of variance for the structural effect.ResultsLinear model ANOVA with Monte Carlo simulation and mixed models with correlated error terms with NDNQI examples showed no substantial differences on statistical tests for structural effects if the factors with structural effects were omitted during the estimation of the transformation parameter.ConclusionsThe Box-Cox power transformation can still be an effective tool for validating statistical inferences with large observational, cross-sectional, and hierarchical or repeated measure studies under the linear or the mixed model settings without prior knowledge of all the factors with potential structural effects.
Highlights
Many nursing and health related research studies have continuous outcome measures that are inherently non-normal in distribution
This study contrasted the effect of obtaining the Box-Cox power transformation parameter and subsequent analysis with or without a priori knowledge of predictor variable under the classic Analysis of Variance (ANOVA) model with simulation, and illustrated such effects by extending the Box-Cox transformation into hierarchical analysis with the mixed model on two National Database of Nursing Quality Indicators (NDNQI) nursing sensitive indicators
We first ignored the within hospital intra class correlation (ICC) and extended the Box-Cox power transformation into the linear mixed model framework [26] and analyzed NDNQI Patient Falls and Patient Injury Falls with mixed models assuming compound symmetric covariance structure [28] to contrast the effect of Box-Cox transformations when predictor variable (Hospital Teaching and Magnet Status) were included in the transformation model with when they were ignored
Summary
Many nursing and health related research studies have continuous outcome measures that are inherently non-normal in distribution. The objectives of this study was to contrast the effect of obtaining the Box-Cox power transformation parameter and subsequent analysis of variance with or without a priori knowledge of predictor variables under the classic linear or linear mixed model settings. Under the linear model framework, the parameter estimate for l with the power transformation family, by definition, is obtained along with the structural effect such that the error term is normally distributed, ε ~ N (0, s2), with the model y(l) = Xθ + ε, where y(l), X, and θ represents the transformed response, the design matrix of structural effects, and the vector of parameter estimates, respectively This implies one should know a priori what the structure is before estimating the parameter for transformation (l). This study contrasted the effect of obtaining the Box-Cox power transformation parameter and subsequent analysis with or without a priori knowledge of predictor variable under the classic ANOVA model with simulation, and illustrated such effects by extending the Box-Cox transformation into hierarchical analysis with the mixed model on two NDNQI nursing sensitive indicators
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