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Title: Probabilistic index models for flexible and efficient rank based inference Authors:  Jan De Neve - Ghent University (Belgium)
Stijn Vansteelandt - Ghent University and London School of Hygiene and Tropical Medicine (Belgium)
Karel Vermeulen - Ghent University (Belgium)
Olivier Thas - Ghent University (Belgium) [presenting]
Gustavo Amorim - Ghent University (Belgium)
Joris Meys - Ghent University (Belgium)
Abstract: Probabilistic Index Models (PIM) are as a class of semiparametric models for the conditional probabilistic index (PI) which is defined as the probability that $Y_2$ exceeds $Y_1$ given $X_1$ and $X_2$, where $X_1$ and $X_2$ are the covariates corresponding to the outcomes $Y_1$ and $Y_2$, respectively. PIMs are related to semiparametric transformation models, but can be considered as more flexible since PIMs impose weaker restrictions on the conditional outcome distribution. The PIM methodology generates many of the classical rank tests for factorial designs, but the flexibility of the model allows to generate rank-type tests for many more complicated designs, including correcting for continuous covariate effects. The original PIM estimators were not efficient and simulation studies showed slow convergence. The focus is now on the construction of efficient estimators and on improved inference in small samples. A further development makes use of PIMs for increasing the power of the Wilcoxon test by using covariate information. This approach lends itself to permutation inference. We start with an introduction to the PIM with a focus on its flexibility for rank test generation, and on efficient parameter estimation and small sample inference. The relation with the Wilcoxon test and covariate adjustment will also be included. The methods are implemented in the PIM R package, which will be illustrated on several examples.