On the exact distribution of SECON and its application

The index for SEquential CONtinuity of care (SECON, Steinwachs (1979)) can be defined as the average of a sequence of random variables {Y-t} which mea sure the sequential continuity of stationary Markov-dependent m-state trial s {X-t}, where Y-t is defined as 1 if Xt-1 = X-t and as 0 otherwise. In the health care sector, SECON is usually applied as the fraction of sequential patient-visit pairs at which the same provider was seen, and represents th e standard estimate of the sequential nature of continuity of care, an impo rtant health policy aim that drives many of the changes underway in the cur rent US health care market. After almost two decades of application, howeve r, the exact distribution of SECON is still unknown except for the case whe re the X-t are i.i.d. with equal probabilities for each state. In this arti cle, the distribution problem is cast into a finite Markov chain setting vi a the imbedding technique developed by Fu and Koutras (1994), and the exact probabilities under one-step Markov dependence can be obtained either dire ctly or via recursive equations. It is also shown that SECON is the minimum variance unbiased estimator, and the maximum likelihood estimator, for the sequential continuity measure. Numerical and real-data examples are given to illustrate the theoretical results.