Estimates and test procedures in connection with stochastic models for deaths, recoveries and transfers between different states of health

Abstract This paper deals with statistical situations which are typical of many planned experiments in medical statistics where the effect of certain treatments are measured by mortality, recurrence of attacks, recovery etc. The classical methods in mortality statistics developed by actuaries and demographers are predominantly concerned with the problem of obtaining unbiased estimates in face of varying duration of exposure to risk and several causes of departure. In recent litterature this situation with departure for other reasons than the one with which the investigation is concerned, is sometimes referred to as “missing observations”. Now, it is obvious that if the rates of death, rates of recovery etc. (with corrected denominators to achieve unbiasedness) are used and if the corresponding probabilities are high, there will be a loss of information due to the fact that the time which elapse to deaths and recoveries are wholly or partially disregarded. To overcome the difficulties of several causes of departure and different exposure to risk in a rational manner J. Karup 1 in a paper from 1893 introduces the forces of death, disablement etc. and he estimates these forces in principle by the “central” rates of mortality, disablement etc. (See also E. Zwingi 2 (1945) and P. Spangenberg 3 (1911).) Although these central rates are very efficient (i. e. with little loss of information) if the denominators are accurately computed, the main argument for their introduction was certainly that of achieving unbiasedness.