The Economics of the Maternity Service †

The relationship between the size of a hospital, as measured by its average daily census, and the percentage occupancy of its beds has fascinated students in hospital planning and administration for many years. A further extension of this relationship to include the cost of operating that bed reveals the importance of this inter-connection. If, indeed, the factor of the size in small hospitals results of itself in a low percentage of occupancy and consequently, in high operating costs, then this relationship is not only fascinating but should be understood as a basic determinant of hospital economics. One of the first major discussions of this relationship appeared in Hospital Care In The United States where C. H. Hamilton not only isolated and described the occurrence of lower occupancy in smaller hospitals but advanced a theory to explain it.' When Dr. Hamilton stated, "Both statistical theory and study of individual hospital data indicate that the extreme limit of occupied beds will not be greater or less than the average daily census plus or minus approximately four times the square root of the average daily census," he assumed the year's daily census followed a Poisson distribution. This inference can be drawn even though it was stated that "the daily number of beds occupied will follow the normal curve." The reason for this inference is that for a Poisson distribution the mean is equal to the variance and since the square root of the variance is the standard deviation, the above formula puts the limits of occupancy at four standard deviations from the average daily census. In accepting the Poisson distribution of daily census, we are accepting a whole series of suppositions but weakly demonstrated by the Commission