Terence A. Etchells

Partial Logistic Artificial Neural Network for Competing Risks Regularized With Automatic Relevance Determination

Time-to-event analysis is important in a wide range of applications from clinical prognosis to risk modeling for credit scoring and insurance. In risk modeling, it is sometimes required to make a simultaneous assessment of the hazard arising from two or more mutually exclusive factors. This paper applies to an existing neural network model for competing risks (PLANNCR), a Bayesian regularization with the standard approximation of the evidence to implement automatic relevance determination (PLANNCR-ARD). The theoretical framework for the model is described and its application is illustrated with reference to local and distal recurrence of breast cancer, using the data set of Veronesi (1995).

How to find simple and accurate rules for viral protease cleavage specificities

BackgroundProteases of human pathogens are becoming increasingly important drug targets, hence it is necessary to understand their substrate specificity and to interpret this knowledge in practically useful ways. New methods are being developed that produce large amounts of cleavage information for individual proteases and some have been applied to extract cleavage rules from data. However, the hitherto proposed methods for extracting rules have been neither easy to understand nor very accurate. To be practically useful, cleavage rules should be accurate, compact, and expressed in an easily understandable way.ResultsA new method is presented for producing cleavage rules for viral proteases with seemingly complex cleavage profiles. The method is based on orthogonal search-based rule extraction (OSRE) combined with spectral clustering. It is demonstrated on substrate data sets for human immunodeficiency virus type 1 (HIV-1) protease and hepatitis C (HCV) NS3/4A protease, showing excellent prediction performance for both HIV-1 cleavage and HCV NS3/4A cleavage, agreeing with observed HCV genotype differences. New cleavage rules (consensus sequences) are suggested for HIV-1 and HCV NS3/4A cleavages. The practical usability of the method is also demonstrated by using it to predict the location of an internal cleavage site in the HCV NS3 protease and to correct the location of a previously reported internal cleavage site in the HCV NS3 protease. The method is fast to converge and yields accurate rules, on par with previous results for HIV-1 protease and better than previous state-of-the-art for HCV NS3/4A protease. Moreover, the rules are fewer and simpler than previously obtained with rule extraction methods.ConclusionA rule extraction methodology by searching for multivariate low-order predicates yields results that significantly outperform existing rule bases on out-of-sample data, but are more transparent to expert users. The approach yields rules that are easy to use and useful for interpreting experimental data.

Time-to-event analysis with artificial neural networks: An integrated analytical and rule-based study for breast cancer

This paper presents an analysis of censored survival data for breast cancer specific mortality and disease-free survival. There are three stages to the process, namely time-to-event modelling, risk stratification by predicted outcome and model interpretation using rule extraction. Model selection was carried out using the benchmark linear model, Cox regression but risk staging was derived with Cox regression and with Partial Logistic Regression Artificial Neural Networks regularised with Automatic Relevance Determination (PLANN-ARD). This analysis compares the two approaches showing the benefit of using the neural network framework especially for patients at high risk. The neural network model also has results in a smooth model of the hazard without the need for limiting assumptions of proportionality. The model predictions were verified using out-of-sample testing with the mortality model also compared with two other prognostic models called TNG and the NPI rule model. Further verification was carried out by comparing marginal estimates of the predicted and actual cumulative hazards. It was also observed that doctors seem to treat mortality and disease-free models as equivalent, so a further analysis was performed to observe if this was the case. The analysis was extended with automatic rule generation using Orthogonal Search Rule Extraction (OSRE). This methodology translates analytical risk scores into the language of the clinical domain, enabling direct validation of the operation of the Cox or neural network model. This paper extends the existing OSRE methodology to data sets that include continuous-valued variables.

An integrated framework for risk profiling of breast cancer patients following surgery

OBJECTIVE An integrated decision support framework is proposed for clinical oncologists making prognostic assessments of patients with operable breast cancer. The framework may be delivered over a web interface. It comprises a triangulation of prognostic modelling, visualisation of historical patient data and an explanatory facility to interpret risk group assignments using empirically derived Boolean rules expressed directly in clinical terms. METHODS AND MATERIALS The prognostic inferences in the interface are validated in a multicentre longitudinal cohort study by modelling retrospective data from 917 patients recruited at Christie Hospital, Wilmslow between 1983 and 1989 and predicting for 931 patients recruited in the same centre during 1990-1993. There were also 291 patients recruited between 1984 and 1998 at the Clatterbridge Centre for Oncology and the Linda McCartney Centre, Liverpool, UK. RESULTS AND CONCLUSIONS There are three novel contributions relating this paper to breast cancer cases. First, the widely used Nottingham prognostic index (NPI) is enhanced with additional clinical features from which prognostic assessments can be made more specific for patients in need of adjuvant treatment. This is shown with a cross matching of the NPI and a new prognostic index which also provides a two-dimensional visualisation of the complete patient database by risk of negative outcome. Second, a principled rule-extraction method, orthogonal search rule extraction, generates readily interpretable explanations of risk group allocations derived from a partial logistic artificial neural network with automatic relevance determination (PLANN-ARD). Third, 95% confidence intervals for individual predictions of survival are obtained by Monte Carlo sampling from the PLANN-ARD model.

Finding reproducible cluster partitions for the k-means algorithm

K-means clustering is widely used for exploratory data analysis. While its dependence on initialisation is well-known, it is common practice to assume that the partition with lowest sum-of-squares (SSQ) total i.e. within cluster variance, is both reproducible under repeated initialisations and also the closest that k-means can provide to true structure, when applied to synthetic data. We show that this is generally the case for small numbers of clusters, but for values of k that are still of theoretical and practical interest, similar values of SSQ can correspond to markedly different cluster partitions.This paper extends stability measures previously presented in the context of finding optimal values of cluster number, into a component of a 2-d map of the local minima found by the k-means algorithm, from which not only can values of k be identified for further analysis but, more importantly, it is made clear whether the best SSQ is a suitable solution or whether obtaining a consistently good partition requires further application of the stability index. The proposed method is illustrated by application to five synthetic datasets replicating a real world breast cancer dataset with varying data density, and a large bioinformatics dataset.

Patient stratification with competing risks by multivariate Fisher distance

Early characterization of patients with respect to their predicted response to treatment is a fundamental step towards the delivery of effective, personalized care. Starting from the results of a time-to-event model with competing risks using the framework of partial logistic artificial neural networks with automatic relevance determination (PLANNCR-ARD), we discuss an effective semi-supervised approach to patient stratification with application to Acute Myeloid Leukaemia (AML) data (n = 509) acquired prospectively by the GIMEMA consortium. Multiple prognostic indices provided by the survival model are exploited to build a metric based on the Fisher information matrix. Cluster number estimation is then performed in the Fisher-induced affine space, yielding to the discovery of a stratification of the patients into groups characterized by significantly different mortality risks following induction therapy in AML. The proposed model is shown to be able to cluster the input data, while promoting specificity of both target outcomes, namely Complete Remission (CR) and Induction Death (ID). This generic clustering methodology generates an affine transformation of the data space that is coherent with the prognostic information predicted by the PLANNCR-ARD model.

Missing Data Imputation in Longitudinal Cohort Studies: Application of PLANN-ARD in Breast Cancer Survival

Missing values are common in medical datasets and may be amenable to data imputation when modelling a given data set or validating on an external cohort. This paper discusses model averaging over samples of the imputed distribution and extends this approach to generic non-linear modelling with the Partial Logistic Artificial Neural Network (PLANN) regularised within the evidence-based framework with Automatic Relevance Determination (ARD). The study then applies the imputation to external validation over new patient cohorts, considering also the case of predictions made for individual patients. A prognostic index is defined for the non-linear model and validation results show that 4 statistically significant risk groups identified at the 95% level of confidence from the modelling data, from Christie Hospital (n=931), retain good separation during external validation with data from the British Columbia Cancer Agency (n=4,083).

Stratification of Severity of Illness Indices: A Case Study for Breast Cancer Prognosis

Prognostic modelling involves grouping patients by risk of adverse outcome, typically by stratifying a severity of illness index obtained from a classifier or survival model. The assignment of thresholds on the risk index depends of pairwise statistical significance tests, notably the log-rank test. This paper proposes a new methodology to substantially improve the robustness of the stratification algorithm, by reference to a statistical and neural network prognostic study of longitudinal data from patients with operable breast cancer.

Minimal MLPs do not model the XOR logic

Abstract Fitting the continuous valid logic of the exclusive OR (XOR) problem requires more than a minimal neural network configuration. This letter shows that the simplest logic to fit the XOR problem involves boundaries that cannot be mapped by a multi-layer perceptron with just two hidden nodes. This observation calls into question rule extraction methodologies based on pruning, since this practice can lock the network into a subspace of achievable continuous valued logic functions that prevent it from mapping the simplest logic to explain the data.

Comparing Analytical Decision Support Models Through Boolean Rule Extraction: A Case Study of Ovarian Tumour Malignancy

The relative performances of different classifiers applied to the same data are typically analyzed using the Receiver Operator Characteristic framework (ROC). This paper proposes a further analysis by explaining the operation of classifiers using low-order Boolean rules to fit the predicted response surfaces using the Orthogonal Search Based Rule Extraction algorithm (OSRE). Four classifiers of malignant or benign ovarian tumours are considered. The models analyzed are two Logistic Regression models and two Multi-Layer Perceptrons with Automatic Relevance Determination (MLP-ARD) each applied to a specific alternative covariate subset. While all models have comparable classification rates by Area Under ROC (AUC) the classification varies for individual cases and so do the resulting explanatory rules. Two sets of clinically plausible rules are obtained which account for over one half of the malignancy cases, with near-perfect specificity. These rules are simple, explicit and can be prospectively validated in future studies.