title: [Regression analysis of idiopathic endothelial cell loss after perforating normal risk keratoplasty: basic principles for long-term analysis of endothelial risk factors in a retrospective clinical study].
abstract: BACKGROUND
  For the characterisation of influencing factors on chronic endothelial cell loss after penetrating keratoplasty by means of multivariate statistics, a mathematical description of the course of the individual postoperative endothelial cell density is a prerequisite. This mathematical description should result in a standardized index value describing course and amount of the postoperative endothelial cell loss over time in a canonical way. The slopes of the linear regression lines for each individual scatter plot of a) the endothelial cell density values plotted against the respective postoperative time directly (linear regression), and b) after logarithmic transformation (exponential regression) are evaluated, respectively.
  
  
  METHODS
  58 patients after normal-risk keratoplasty (26x keratokonus, 22x Fuchs-dystrophy and 10 cases of corneal decompensation after cataract surgery) with 5 or more postoperatively acquired endothelial density values and without any episodes of graft rejection were included in this study. Mean follow up was 2.9 +/- 1.1 years. The postoperative endothelial cell density values were plotted against the respective time for each patient individually. The coefficients of variation (R2) derived from the linear and the exponential regression models were calculated for each of these scatter plots. The pairs of R2 values (linear vs. exponential) were compared statistically. A dependence of the difference of linear and exponential R2-values on the ophthalmologic diagnosis was tested as well.
  
  
  RESULTS
  The linear model is able to declare 83% the total variance of the course of the endothelial cell density. The exponential model even declares 86%. This small difference was statistically significant. Since both methods of regression describe the course of the cell density well, intra/and extrapolation of missing endothelial values is possible with both models. No dependence of the difference of linear and exponential R2-values on the ophthalmologic diagnosis could be demonstrated.
  
  
  CONCLUSIONS
  Both, the intuitively understandable slope of the linear regression line and the constant of decay of the exponential regression curve, are suitable for describing the amount of the postoperative loss of endothelial cells after normal-risk keratoplasty independent of the ophthalmologic diagnosis. Both can thus be used as target variable in forthcoming statistical analyses for chronic endothelial cell loss.
authors.affiliation: Augenklinik, Heinrich-Heine Universität, Moorenstr. 5, 40225 Düsseldorf. daniel.boehringer@uni-duesseldorf.de
authors.forename: D
authors.initials: D
authors.lastname: Böhringer
authors.forename: T
authors.initials: T
authors.lastname: Reinhard
authors.forename: E
authors.initials: E
authors.lastname: Godehardt
authors.forename: R
authors.initials: R
authors.lastname: Sundmacher
mesh_terms: D000328:Adult; D000368:Aged; D002452:Cell Count; D002470:Cell Survival / Q000502:physiology*; D019781:Corneal Topography; D004728:Endothelium, Corneal / Q000473:pathology*; D005260:Female; D005500:Follow-Up Studies; D006801:Humans; D015948:Keratoplasty, Penetrating; D008297:Male; D008875:Middle Aged; D011183:Postoperative Complications / Q000473:pathology*; D012044:Regression Analysis; D012189:Retrospective Studies; D012307:Risk Factors