The logistic transform for bounded outcome scores

• DOI: 10.1093/biostatistics/kxj034
• Publication Date: 2006-04-06T13:55:14Z
• Authors: E. Lesaffre; D. Rizopoulos; R. Tsonaka
• Keywords: Logistic distribution

The logistic transformation, originally suggested by Johnson (1949), is applied to analyze responses that are restricted a finite interval (e.g. (0,1)⁠), so-called bounded outcome scores. Bounded scores often have non-standard distribution, e.g. J- or U-shaped, precluding classical parametric statistical approaches for analysis. Applying the transformation on normally distributed random variable, gives rise logit-normal (LN) distribution. This distribution can take variety of shapes (0,1)⁠. Further, model be extended correct (baseline) covariates. Therefore, method could useful comparative clinical trials. outcomes found in many research areas, drug compliance research, quality-of-life studies, and pain (and relief) studies using visual analog scores, but all these attain boundary values 0 1. A natural extension above approach therefore assume latent score (0,1) having LN Two cases considered: (a) proportion where true probabilities (b) [0,1] coarsened version with We also allow variance (on transformed scale) depend treatment. usefulness our trials will assessed this paper. It turns out important distinguish case equal unequal variances. For second type variances, comes close ordinal probit (OP) regression. However, ignoring inequality variances lead highly biased parameter estimates. simulation study compares performance two-sample Wilcoxon test OP Finally, different methods illustrated two data sets.