Statistica Sinica 10(2000), 999-1010

ON THE EXACT DISTRIBUTION OF SECON AND

ITS APPLICATION

James C. Fu and W. Y. Wendy Lou

University of Manitoba and Mount Sinai School of Medicine

Abstract: 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 measure the sequential continuity of stationary Markov-dependent $m$-state trials $\{X_t\}$, where $Y_t$ is defined as 1 if $X_{t-1} = X_t$ 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 the standard estimate of the sequential nature of continuity of care, an important health policy aim that drives many of the changes underway in the current US health care market. After almost two decades of application, however, the exact distribution of $SECON$ is still unknown except for the case where the $X_t$ are i.i.d. with equal probabilities for each state. In this article, the distribution problem is cast into a finite Markov chain setting via the imbedding technique developed by Fu and Koutras (1994), and the exact probabilities under one-step Markov dependence can be obtained either directly 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.

Key words and phrases: Ergodic distribution, Markov dependence, sequential continuity.