Lynette A. Hunt

Mixture model clustering for mixed data with missing information

One difficulty with classification studies is unobserved or missing observations that often occur in multivariate datasets. The mixture likelihood approach to clustering has been well developed and is much used, particularly for mixtures where the component distributions are multivariate normal. It is shown that this approach can be extended to analyse data with mixed categorical and continuous attributes and where some of the data are missing at random in the sense of Little and Rubin (Statistical Analysis with Mixing Data, Wiley, New York).

Theory & Methods: Mixture model clustering using the MULTIMIX program

Hunt (1996) implemented the finite mixture model approach to clustering in a program called MULTIMIX. The program is designed to cluster multivariate data that have categorical and continuous variables and that possibly contain missing values. This paper describes the approach taken to design MULTIMIX and how some of the statistical problems were dealt with. As an example, the program is used to cluster a large medical dataset.

Posterior sloping angle as a predictor of contralateral slip in slipped capital femoral epiphysis.

BACKGROUND Slipped capital femoral epiphysis is a condition with potentially severe complications. Controversy remains as to when to undertake prophylactic pinning. We aimed to assess the utility of the posterior sloping angle as a predictor for contralateral slip in a large, multi-ethnic cohort including Polynesian children with a high incidence of slipped capital femoral epiphysis. METHODS All patients presenting to our hospital between 2000 and 2009 were identified and records were reviewed to determine demographic data and determine whether they subsequently developed a contralateral slip. The presenting radiographs were reviewed and the posterior sloping angle was measured. Patients with bilateral slips at presentation and those without initial radiographs were excluded. RESULTS Records and radiographs of 132 patients were analyzed for the posterior sloping angle in the unaffected hip. Forty-two patients who had subsequently developed a contralateral slip had a mean posterior sloping angle (and standard deviation) of 17.2° ± 5.6°, which was significantly higher (p < 0.001) than that of 10.8° ± 4.2° for the ninety patients who had had a unilateral slip. Children who had developed a subsequent contralateral slip were significantly younger (11.1 years) than those who had developed a unilateral slip (12.2 years) (p < 0.001). If a posterior sloping angle of 14° were used as an indication for prophylactic fixation in this population, thirty-five (83.3%) of forty-two contralateral slips would have been prevented, and nineteen (21.1%) of ninety hips would have been pinned unnecessarily. The number needed to treat to prevent one subsequent contralateral slip is 1.79. CONCLUSIONS To our knowledge, this is the largest study to date that confirms that the posterior sloping angle is a reliable predictor of contralateral slip and can be used to guide prophylactic pinning. The posterior sloping angle is applicable in the high-risk Polynesian population and could be useful in preventing future slips in populations that are difficult to follow up.

Clustering mixed data

Mixture model clustering proceeds by fitting a finite mixture of multivariate distributions to data, the fitted mixture density then being used to allocate the data to one of the components. Common model formulations assume that either all the attributes are continuous or all the attributes are categorical. In this paper, we consider options for model formulation in the more practical case of mixed data: multivariate data sets that contain both continuous and categorical attributes.

Fitting a mixture model to three-mode three-way data with missing information

When the data consist of certain attributes measured on the same set of items in different situations, they would be described as a three-mode three-way array. A mixture likelihood approach can be implemented to cluster the items (i.e., one of the modes) on the basis of both of the other modes simultaneously (i.e,, the attributes measured in different situations). In this paper, it is shown that this approach can be extended to handle three-mode three-way arrays where some of the data values are missing at random in the sense of Little and Rubin (1987). The methodology is illustrated by clustering the genotypes in a three-way soybean data set where various attributes were measured on genotypes grown in several environments.

Arthroscopic, open and mini‐open approach for rotator cuff repair: no difference in pain or function at 24 months

The New Zealand Rotator Cuff Registry was established in 2009 to collect prospective functional, pain and outcome data on patients undergoing rotator cuff repair (RCR).

Missing Data Imputation and Its Effect on the Accuracy of Classification

Multivariate data sets frequently have missing observations scattered throughout the data set. Many machine learning algorithms assume that there is no particular significance in the fact that a particular observation has an attribute value missing. A common approach in coping with these missing values is to replace the missing value using some plausible value, and the resulting completed data set is analysed using standard methods. We evaluate the effect that some commonly used imputation methods have on the accuracy of classifiers in supervised leaning. The effect is assessed in simulations performed on several classical datasets where observations have been made missing at random in different proportions. Our analysis finds that missing data imputation using hot deck, iterative robust model-based imputation (IRMI), factorial analysis for mixed data (FAMD) and Random Forest Imputation (MissForest) perform in a similar manner regardless of the amount of missing data and have the highest mean percentage of observations correctly classified. Other methods investigated did not perform as well.

Comparing classical criteria for selecting intra-class correlated features in Multimix

The mixture approach to clustering requires the user to specify both the number of components to be fitted to the model and the form of the component distributions. In the Multimix class of models, the user also has to decide on the correlation structure to be introduced into the model. The behaviour of some commonly used model selection criteria is investigated when using the finite mixture model to cluster data containing mixed categorical and continuous attributes. The performance of these criteria in selecting both the number of components in the model and the form of the correlation structure amongst the attributes when fitting the Multimix class of models is illustrated using simulated data and a real medical data set. It is found that criteria based on the integrated classification likelihood have the best performance in detecting the number of clusters to be fitted to the model and in selecting the form of the component distributions. The performance of the Bayesian information criterion in detecting the correct model depends on the partitioning structure among the attributes while the Akaike information criterion and classification likelihood criterion perform in a less satisfactory way.