Post date: Jun 11, 2015 8:41:29 PM
Title: Functional data analysis in characterizing bacterial vaginosis patterns and identifying pattern-specific risk factors
Speaker: Rahul Biswas, Indian Statistical Institute
Abstract: Functional data analysis extends the methods of multivariate statistics to infinite dimensional function spaces. In this project, with an initial aim to characterize bacterial vaginosis (BV) infection patterns using fairly high dimensional BV score time series observed in adolescent girls in Rural Uganda, we employ functional clustering methodology, considering the data as discrete realisations of random functions or, random variables taking values in an infinite dimensional function space. We discuss reduction of that data to finite dimensions by means of functional principal components, making it amenable to the usage of multivariate clustering methods. We then extended Ferraty et al's clustering methodology to obtain comparatively more detailed results.
The second aim was to identify risk factors for each BV pattern. In that regard, we modelled the response BV score time series by considering parameters varying over classes for the expectation, with covariance matrix modelled to be varying over classes too. An autoregressive process over the BV scores time points was used as a detailed model for the covariance matrix as in Pourahmadi (1999). The objective could now be precisely framed in terms of hypothesis tests, and likelihood ratio test (LRT) was employed to test the hypotheses. The values of the LRT statistic or equivalently p-values of the tests also gave us an order of significance of the variables in separating between the classes. We recorded results as mentioned above for determining the required significance of variables in differentiating between BV infection patterns.