title: Presenting simulation results in a nested loop plot.
abstract: BACKGROUND
  Statisticians investigate new methods in simulations to evaluate their properties for future real data applications. Results are often presented in a number of figures, e.g., Trellis plots. We had conducted a simulation study on six statistical methods for estimating the treatment effect in binary outcome meta-analyses, where selection bias (e.g., publication bias) was suspected because of apparent funnel plot asymmetry. We varied five simulation parameters: true treatment effect, extent of selection, event proportion in control group, heterogeneity parameter, and number of studies in meta-analysis. In combination, this yielded a total number of 768 scenarios. To present all results using Trellis plots, 12 figures were needed.
  
  
  METHODS
  Choosing bias as criterion of interest, we present a 'nested loop plot', a diagram type that aims to have all simulation results in one plot. The idea was to bring all scenarios into a lexicographical order and arrange them consecutively on the horizontal axis of a plot, whereas the treatment effect estimate is presented on the vertical axis.
  
  
  RESULTS
  The plot illustrates how parameters simultaneously influenced the estimate. It can be combined with a Trellis plot in a so-called hybrid plot. Nested loop plots may also be applied to other criteria such as the variance of estimation.
  
  
  CONCLUSIONS
  The nested loop plot, similar to a time series graph, summarizes all information about the results of a simulation study with respect to a chosen criterion in one picture and provides a suitable alternative or an addition to Trellis plots.
authors.affiliation: Institute for Medical Biometry and Statistics, Medical Center - University of Freiburg, Stefan-Meier-Strasse 26, 79104 Freiburg, Germany. ruecker@imbi.uni-freiburg.de.
authors.forename: Gerta
authors.initials: G
authors.lastname: Rücker
authors.forename: Guido
authors.initials: G
authors.lastname: Schwarzer
mesh_terms: D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D015201:Meta-Analysis as Topic; D017594:Publication Bias; D012044:Regression Analysis; D015983:Selection Bias