Logistic and Cox Regression, Markov Models, Laplace Transformations

Abstract

Data modeling can be applied for improving precision of clinical studies. Multiple regression modeling is often used for that purpose. Relevant papers on this topic have recently been published (Breithaupt-Grogler et al. 1997; Debord et al. 1998; Kato et al. 1994; Mahmood and Mahayni 1999; Sabot et al. 1995; Ulrich et al. 2003; Vrecer et al. 2003). Although multiple regression modeling, generally, does not influence the magnitude of the treatment effect versus control, it may reduce overall variances in the treatment comparison and thus increase sensitivity or power of statistical testing. It tries to fit experimental data in a mathematical model, and, subsequently, tests how far distant the data are from the model. A statistically significant correlation indicates that the data are closer to the model than will happen with random sampling. The very model-principle is at the same time its largest limitation: biological processes are full of variations and will not allow for a perfect fit. In addition, the decision about the appropriate model is not well founded on statistical arguments. The current chapter assesses uncertainties and risks of misinterpretations commonly encountered with regression analyses and rarely communicated in research papers. Simple regression models and real data examples are used for assessment.