# A multinomial change-point theory in the context of diagnosis code searching

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## Abstract

Change-point theory can be described as follows. Consider a sequence of independent random variables, X1, X2,.. Xr, Xr+1,., Xn, in which X1,.., Xr-1 are independently, identically distributed as F1 with parameter Ã¸1, and Xr,...,Xn are distributed as F1 with parameter Ã¸2. The variable r is the change-point. The objective is to determine if a change has occurred and possibly estimate the change-point. The scope of change-point theory is very broad, including essentially all problems in which the stationarity of a sequence of random variables is tested against the possible abrupt change in location, scale or shape of the distributions.

In this research, Bayesian change-point theory is extended to multinomial random variables. Using this theory, decision rules are developed for a variety of applications.

The major application of multinomial change-point theory discussed in this research is in diagnosis codes searching of the database of the International Classification of Diseases. Ninth Revision, Clinical Modification (ICD-9-CM). This database contains approximately 10,000 diagnosis codes. A hierarchical menu-driven search has been developed to find the correct code. To avoid repeated searches for commonly-used diagnoses, a dynamically changing cache set of the current, most frequently used codes is constructed, and multinomial change-point theory is applied to provide dynamic maintenance of the cache set.