Possible benefits of the "logistic flip" in discerning between two logistic regression models Public
Masalovich, Svetlana E. (2010)
Published
Abstract
Abstract
We investigated the relationship between and
properties of odds ratio estimates in two logistic regression
models: the model for a dichotomous outcome (Y) and
dichotomous predictor (X) including an auxiliary continuous
covariate, and the "flipped" model where X and Y are
interchanged. The odds ratio is invariant to flipping when no
additional covariates are considered. However, its estimates
yielded by the two models in the presence of covariates are
generally different unless some finer adjustments for covariate
effects on the outcome in the flipped model are made (e.g.,
involving polynomial terms). The reason is appearing in the flipped
model a non-linear function of the covariates and the model
parameters and a function of the conditional probability of the
predictor given the covariates are introduced. We demonstrated that
the odds ratio estimates from the two models can be similar without
adjustment if the function of the covariate in the flipped model is
approximately linear and the predictor and covariate in the initial
model are independent or related through a logistic regression.
When the model for the predictor and covariate is not logistic,
nonparametric approaches (such as LOESS) can be employed to
estimate the conditional probability of X given the
covariates.
We found that the extent of the equivalence of odds ratio estimates in initial and flipped models can be useful in data sets with covariates when it is not known which outcome is more appropriate, Y or X . We hypothesized that the difference between the odds ratio estimates yielded by the initial and "flipped' models with Y as the outcome in the initial model, and that difference when, instead, X is the outcome, can be used to discern between the correct and incorrect models. It was expected that the estimates based on the initial and reversed correct model would tend be closer to one another than the corresponding estimates based on the incorrect model. The simulation study confirmed this hypothesis in general. This approach can be useful in studies where it is not clear which model is more appropriate.
Table of Contents
Table of Contents
Introduction……………………………………………………………………………...1
Objectives…………………………………………………………………………….…..6
Methodology……………………………………………………………………………..7
I. Invariance of Odds
Ratio……………………………………………………...7
II. Logistic flip in discerning between two logistic
models……….14
Simulation
study……………………………………………………………………….15
Discussion……………………………………………………………………………....
22
Tables and
Figures…………………………………………………………………...28
References……………………………………………………………………………....30
Appendix……………………………………………………………………………….....32
I. The condition for linearity of
alpha*……………………………….…...32
II. Example of SAS
output…………………………………………………......35
III. SAS partial
code…………………………………………………………….....40
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