title: The Box-Cox power transformation on nursing sensitive indicators: does it matter if structural effects are omitted during the estimation of the transformation parameter?
abstract: BACKGROUND
  Many 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.
  
  
  METHODS
  Simulation 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.
  
  
  RESULTS
  Linear 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.
  
  
  CONCLUSIONS
  The 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.
authors.affiliation: Department of Biostatistics, University of Kansas Medical Center, Kansas City, KS 66160, USA. qhou@kumc.edu
authors.forename: Qingjiang
authors.initials: Q
authors.lastname: Hou
authors.forename: Jonathan D
authors.initials: JD
authors.lastname: Mahnken
authors.forename: Byron J
authors.initials: BJ
authors.lastname: Gajewski
authors.forename: Nancy
authors.initials: N
authors.lastname: Dunton
mesh_terms: D000058:Accidental Falls / Q000706:statistics & numerical data; D000465:Algorithms; D000704:Analysis of Variance; D003627:Data Interpretation, Statistical; D006801:Humans; D007902:Length of Stay; D015233:Models, Statistical; D009010:Monte Carlo Method; D009732:Nursing Care / Q000592:standards*; D014481:United States