SEQUENTIAL PATHOGENIC COMPONENTS OF RATES

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Abstract
Overall measures of disease development for a total population incidence-and mortality-rates are based on events which are the results of a pathogenic sequence. Overall rates depend on the rates of transition from each stage of the pathogenic process to the next. In this paper, a relationship is derived between rates of sequential pathogenic transitions and the corresponding overall rate. The average duration of the entire natural history of a disease Is the sum of the average durations of all its stages. The rate of termination of each stage Is inversely related to the duration of the stage; the overall rate for a disease with multiple stages Is the reciprocal of the total average duration of the natural history. The overall rate for multiple stages must be less than the lowest component transition rate. Thus, for any particular disease, the mortality rate is less than both the incidence rate among the well and the rate of death among the diseased. The incidence rate is less than both the rate of preclinical disease development and the rate of transition from preclinical disease to clinical. A change in the rate of one transition, such as that of cancer initiation, will be underestimated by the corresponding change In an overall rate such as the incidence rate. Similarly, a change in an incidence rate will be underestimated by the respective change in the overall mortality rate. The maximum change in an overall rate due to any degree of change In one transition rate is limited by the size of other rates in the sequence. These relationships may be helpful for predicting changes in morbidity or mortality due to factors which affect early stages of disease development, for Interpreting differences in overall rates with respect to the natural history of disease, and for separating the effects of real benefit, lead time, and length bias on the survival of patients detected by screening.

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