ESTIMATION OF MEAN SOJOURN TIME IN BREAST-CANCER SCREENING USING A MARKOV-CHAIN MODEL OF BOTH ENTRY TO AND EXIT FROM THE PRECLINICAL DETECTABLE PHASE

The sojourn time, time spent in the preclinical detectable phase (PCDP ) for chronic diseases, for example, breast cancer, plays an important role in the design and assessment of screening programmes. Traditiona l methods to estimate it usually assume a uniform incidence rate of pr eclinical disease from a randomized control group or historical data. In this paper, a two-parameter Markov chain model is proposed and deve loped to explicitly estimate the preclinical incidence rate (lambda(1) ) and the rate of transition from preclinical to clinical state (lambd a(2), equivalent to the inverse of mean sojourn time) without using co ntrol data. A new estimate of sensitivity is proposed, based on the es timated parameters of the Markov process. When this method is applied to the data from the Swedish two-county study of breast cancer screeni ng in the age group 70-74, the estimate of MST is 2.3 with 95 per cent CI ranging from 2.1 to 2.5, which is close to the result based on the traditional method but the 95 per cent CI is narrower using the Marko v model. The reason for the greater precision of the latter is the ful ler use of all temporal data, since the continuous exact times to even ts are used in our method instead of grouping them as in the tradition al method. Ongoing and future researches should extend this model to i nclude, for example, the tumour size, nodal status and malignancy grad e, along with methods of simultaneously estimating sensitivity and the transition rates in the Markov process.