Cranial Morphology Associated With Syndromic Craniosynostosis: A Potential Detection of Abnormality in Patient's Cranial Growth Using Angular Statistics.

INTRODUCTION: Apert, Crouzon, and Pfeiffer syndromes are common genetic syndromes related to syndromic craniosynostosis (SC), whereby it is a congenital defect that occurs when the cranial growth is distorted. Identifying cranial angles associated with these 3 syndromes may assist the surgical team to focus on a specific cranial part during the intervention planning, thus optimizing surgical outcomes and reducing potential morbidity. OBJECTIVE: The aim of this study is to identify the cranial angles, which are associated with Apert, Crouzon, and Pfeiffer syndromes. METHODS: The cranial computed tomography scan images of 17 patients with SC and 22 control groups aged 0 to 12 years who were treated in the University Malaya Medical Centre were obtained, while 12 angular measurements were attained using the Mimics software. The angular data were then divided into 2 groups (patients aged 0 to 24 months and >24 months). This work proposes a 95% confidence interval (CI) for angular mean to detect the abnormality in patient's cranial growth for the SC syndromes. RESULTS: The 95% CI of angular mean for the control group was calculated and used as an indicator to confirm the abnormality in patient's cranial growth that is associated with the 3 syndromes. The results showed that there are different cranial angles associated with these 3 syndromes. CONCLUSIONS: All cranial angles of the patients with these syndromes lie outside the 95% CI of angular mean of control group, indicating the reliability of the proposed CI in the identification of abnormality in the patient's cranial growth.

A new outlier detection method for spherical data.

In this study, we propose a new method to detect outlying observations in spherical data. The method is based on the k-nearest neighbours distance theory. The proposed method is a good alternative to the existing tests of discordancy for detecting outliers in spherical data. In addition, the new method can be generalized to identify a patch of outliers in the data. We obtain the cut-off points and investigate the performance of the test statistic via simulation. The proposed test performs well in detecting a single and a patch of outliers in spherical data. As an illustration, we apply the method on an eye data set.

Procedure for Detecting Outliers in a Circular Regression Model.

A number of circular regression models have been proposed in the literature. In recent years, there is a strong interest shown on the subject of outlier detection in circular regression. An outlier detection procedure can be developed by defining a new statistic in terms of the circular residuals. In this paper, we propose a new measure which transforms the circular residuals into linear measures using a trigonometric function. We then employ the row deletion approach to identify observations that affect the measure the most, a candidate of outlier. The corresponding cut-off points and the performance of the detection procedure when applied on Down and Mardia's model are studied via simulations. For illustration, we apply the procedure on circadian data.