In a series of two papers, this paper and the one by Ozkok et al. (Modelling critical illness claim diagnosis rates II: results), we develop statistical models to be used as a framework for estimating, and graduating, Critical Illness (CI) insurance diagnosis rates. We use UK data for 1999-2005 supplied by the Continuous Mortality Investigation (CMI) to illustrate their use. In this paper, we set out the basic methodology. In particular, we set out some models, we describe the data available to us and we discuss the statistical distribution of estimators proposed for CI diagnosis inception rates. A feature of CI insurance is the delay, on average about 6 months but in some cases much longer, between the diagnosis of an illness and the settlement of the subsequent claim. Modelling this delay, the so-called Claim Delay Distribution, is a necessary first step in the estimation of the claim diagnosis rates and this is discussed in the present paper. In the subsequent paper, we derive and discuss diagnosis rates for CI claims from 'all causes' and also from specific causes.