Another way to deal with day-of-week variations is to use the sickness availability method to smooth the time series by removing noise due to the day-of-week effect. This algorithm transforms the daily counts in the time series into a daily sickness value, which is defined as the number of people getting sick every day irrespective of whether they seek health care or not. The term availability refers to the probability that a patient will seek health care during a specific day of the week; hence, there are a total of seven values of availability, one for each day of the week. The availability of a day can be thought of as the fraction of a weeks-worth of visits that get assigned to the given day. The sickness availability method is based on the intuitive assumptions that the expected count is the product of the true amount of sickness and the current day's availability.
We can estimate the expected availability for a specific day of week (dow) using the average of the availabilities on that day for the past m weeks. We can calculate the expected availability Adow as:
In Eq. 9, Adow refers to the expected availability for the day of week specified by the variable dow, which takes on seven different values ranging from 0 to 6. The term Ci(dow) is the actual number of patients that visited the ED on the particular day of week dow during the ith week in the past. Since national holidays affect the number of patients visiting the ED, weeks containing holidays are ignored completely in the availability calculations. Finally, the parameter m controls the smoothness of the sickness curve.
Since sickness is defined as the total number of people in the city getting sick on a particular day, we can calculate it as follows:
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