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Ordinal Logic Regression: A classifier for discovering combinations of binary markers for ordinal outcomes.

ABSTRACT: In medicine, it is often useful to stratify patients according to disease risk, severity, or response to therapy. Since many diseases arise from complex gene-gene and gene-environment interactions, patient strata may be defined by combinations of genetic and environmental factors. Traditional statistical methods require specifying interactions a priori making it difficult to identify high order interactions. Alternatively, machine learning methods can model complex interactions, however these models are often difficult to interpret in a clinical setting. Logic regression (LR) enables modeling a binary outcome using logical combinations of binary predictors yielding easily interpretable models. However LR, as currently available, cannot model ordinal responses. This paper extends LR to model an ordinal response and the resulting method is called Ordinal Logic Regression (OLR). Several simulations comparing OLR and Classification and Regression Trees (CART) demonstrate that OLR is superior to CART for identifying variable interactions associated with an ordinal response. OLR is applied to data from a study to determine associations between genetic and health factors with severity of adult periodontitis.

SUBMITTER: Wolf BJ

PROVIDER: S-EPMC4397503 | biostudies-literature | 2015 Feb

REPOSITORIES: biostudies-literature

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Ordinal Logic Regression: A classifier for discovering combinations of binary markers for ordinal outcomes.

Wolf Bethany J BJ Slate Elizabeth H EH Hill Elizabeth G EG

Computational statistics & data analysis 20150201

In medicine, it is often useful to stratify patients according to disease risk, severity, or response to therapy. Since many diseases arise from complex gene-gene and gene-environment interactions, patient strata may be defined by combinations of genetic and environmental factors. Traditional statistical methods require specifying interactions <i>a priori</i> making it difficult to identify high order interactions. Alternatively, machine learning methods can model complex interactions, however t ...[more]

PMID: 25892835

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Project description:BackgroundLogistic random effects models are a popular tool to analyze multilevel also called hierarchical data with a binary or ordinal outcome. Here, we aim to compare different statistical software implementations of these models.MethodsWe used individual patient data from 8509 patients in 231 centers with moderate and severe Traumatic Brain Injury (TBI) enrolled in eight Randomized Controlled Trials (RCTs) and three observational studies. We fitted logistic random effects regression models with the 5-point Glasgow Outcome Scale (GOS) as outcome, both dichotomized as well as ordinal, with center and/or trial as random effects, and as covariates age, motor score, pupil reactivity or trial. We then compared the implementations of frequentist and Bayesian methods to estimate the fixed and random effects. Frequentist approaches included R (lme4), Stata (GLLAMM), SAS (GLIMMIX and NLMIXED), MLwiN ([R]IGLS) and MIXOR, Bayesian approaches included WinBUGS, MLwiN (MCMC), R package MCMCglmm and SAS experimental procedure MCMC.Three data sets (the full data set and two sub-datasets) were analysed using basically two logistic random effects models with either one random effect for the center or two random effects for center and trial. For the ordinal outcome in the full data set also a proportional odds model with a random center effect was fitted.ResultsThe packages gave similar parameter estimates for both the fixed and random effects and for the binary (and ordinal) models for the main study and when based on a relatively large number of level-1 (patient level) data compared to the number of level-2 (hospital level) data. However, when based on relatively sparse data set, i.e. when the numbers of level-1 and level-2 data units were about the same, the frequentist and Bayesian approaches showed somewhat different results. The software implementations differ considerably in flexibility, computation time, and usability. There are also differences in the availability of additional tools for model evaluation, such as diagnostic plots. The experimental SAS (version 9.2) procedure MCMC appeared to be inefficient.ConclusionsOn relatively large data sets, the different software implementations of logistic random effects regression models produced similar results. Thus, for a large data set there seems to be no explicit preference (of course if there is no preference from a philosophical point of view) for either a frequentist or Bayesian approach (if based on vague priors). The choice for a particular implementation may largely depend on the desired flexibility, and the usability of the package. For small data sets the random effects variances are difficult to estimate. In the frequentist approaches the MLE of this variance was often estimated zero with a standard error that is either zero or could not be determined, while for Bayesian methods the estimates could depend on the chosen "non-informative" prior of the variance parameter. The starting value for the variance parameter may be also critical for the convergence of the Markov chain.

Dataset Information

Ordinal Logic Regression: A classifier for discovering combinations of binary markers for ordinal outcomes.

Publications

Ordinal Logic Regression: A classifier for discovering combinations of binary markers for ordinal outcomes.

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