Incorporating Additional Information to Normal Linear Discriminant Rules

Statistical Applications in Genetics and Molecular Biology

Salvador

Rueda

et al. 2013

Self Cite

Classification rules that incorporate additional information usually present in discrimination problems are receiving certain attention during the last years as they perform better than the usual rules in poor discrimination problems. Fernández et al (2006) proved that these rules have a lower unconditional misclassification probability than the usual Fisher's rule but they did not consider the estimation of the conditional error probability when a training sample is given (the so-called true error rate) which is a very interesting parameter in practice.In this paper we consider the problem of estimating the true error rate of these classification rules in the classical topic of discrimination among two normal populations. We prove theoretical results on the apparent error rate of the rules that expose the need of new estimators of their true error rate. Our proposal is to also consider the additional information in the definition of the true error rate estimators. We propose four such new estimators. Two of them are defined incorporating the additional information into the leave-one-out-bootstrap. The other two are the corresponding cross-validation after bootstrap versions. We compare these new estimators with the usual ones in a simulation study and in a cancer trial application, showing the very good behavior, in terms of mean square error, of the leave-one-out bootstrap estimators that incorporate the available additional information.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In Section ? ?, we start reviewing the restricted rules defined in Fernández et al (2006). In Section ?…”

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

See 3 more Smart Citations

Performance and estimation of the true error rate of classification rules built with additional information. An application to a cancer trial

Statistical Applications in Genetics and Molecular Biology

Salvador

Rueda

et al. 2013

Self Cite

Classification of samples into two or more ordered populations with application to a cancer trial

Fernández

Rueda

et al. 2012

Statistics in Medicine

In many applications, especially in cancer treatment and diagnosis, investigators are interested in classifying patients into various diagnosis groups on the basis of molecular data such as gene expression or proteomic data. Often, some of the diagnosis groups are known to be related to higher or lower values of some of the predictors. The standard methods of classifying patients into various groups do not take into account the underlying order. This could potentially result in high misclassification rates, especially when the number of groups is larger than two. In this article, we develop classification procedures that exploit the underlying order among the mean values of the predictor variables and the diagnostic groups by using ideas from order-restricted inference. We generalize the existing methodology on discrimination under restrictions and provide empirical evidence to demonstrate that the proposed methodology improves over the existing unrestricted methodology. The proposed methodology is applied to a bladder cancer data set where the researchers are interested in classifying patients into various groups.

Classification of Samples with Order-Restricted Discriminant Rules

Methods in Molecular Biology

Fernández

Salvador

et al. 2016

In recent years, mass spectrometry techniques have helped proteomics to become a powerful tool for the early diagnosis of cancer, as they help to discover protein profiles specific to each pathological state. One of the questions where proteomics is giving useful practical results is that of classifying patients into one of the possible severity levels of an illness, based on some features measured on the patient. This classification is usually made using one of the many discrimination procedures available in statistical literature. We present in this chapter recently developed restricted discriminant rules that use additional information in terms of orderings on the means, and we illustrate how to apply them to mass spectrometry data using R package dawai. Specifically, we use proteomic prostate cancer data, and we describe all steps needed, including data preprocessing and feature extraction, to build a discriminant rule that classifies samples in one of several disease stages, thus helping diagnosis. The restricted discriminant rules are compared with some standard classifiers that do not take into account the additional information, showing better performance in terms of error rates.