An application of Lasso Poisson Regression in configural frequency analysis for breast cancer analysis

Abstract

Configural Frequency Analysis (CFA) refers to a method which is used to detect patterns of categorical data (referred to as configurations) that occur more often (types) or less often (antitypes) than expected. These types and antitypes give us information regarding which groups of attributes are likely or unlikely to be present in the sample. The classic CFA method, which assumes all variables to be independent and is also referred to as first order CFA, is the most popular method and is sometimes considered as the only CFA method. However, different developments such as second order CFA, prediction CFA,and two sample CFA have been proposed and are more useful than their counterpart in certain situations. The one thing in common that all these methods share is that so far they have only been applied to datasets with a small number of variables and this is most probably because the methods work better in those scenarios. In this dissertation we considered a breast cancer dataset with a large number of variables and when we implemented CFA to this dataset in order to detect risk factors for breast cancer we encountered some issues, e.g. types and antitypes were not emerging due to the nature of the data. The idea put forth in this dissertation as an attempt to solve the aforementioned problem is to use Lasso regression for its variable selection properties before carrying out any kind of CFA analysis. Therefore we will familiarize ourselves with Poisson Lasso Regression and propose applying it to CFA through the breast cancer application.