The Use of Kernel Density Estimators to Monitor Protocol Compliance

The use of kernel density estimation to develop instrument panels will be demonstrated in the continuous monitoring of medical outcomes. Kernel density functions can be quickly derived using SAS/QC®, and can be used to examine conditional probabilities. In version 7, SAS/STAT® contains PROC KDE that can also be used to estimate the kernel density. Specifically, kernel density functions were used to determine whether a new protocol was being implemented properly and whether the intervention had impact upon the patients it was intended to serve. The purpose of this protocol was to systematically monitor and control glucose levels in diabetic patients undergoing open heart surgery. The motivation for the protocol was to reduce infection rates, and average length of stay. Kernel density was used to determine the distributions of glucose levels, and to determine whether protocol interventions at high patient glucose levels resulted in a subsequent reduction. After analysis, it was concluded that the protocol was being properly implemented and that glucose levels were more likely to decrease once they climbed above 150 mg/dL. Initial results also indicated a reduction in the infection rate for diabetic patients. INTRODUCTION The protocol under investigation was designed to reduce infection rates in open heart surgery for diabetic patients. It was initiated in January, 1999 and subsequently modified in March and July. In January, all patients who were known diabetic patients were placed on the protocol. In March, all patients with an initial glucose reading greater than 180 were added to the protocol. In July, the protocol was extended to three days past surgery. As the requirements for monitoring and intervention were quite stringent, there was an initial question of protocol compliance that had to be answered prior to any examination of the impact on infection rates. It was successfully demonstrated that hospital personnel were complying with protocol. The protocol called for the patient’s glucose levels to be monitored every hour before and after surgery, and every 30 minutes during surgery. The monitoring began at 5:30 am regardless of the scheduled time of surgery. As soon as the glucose level climbed above 150 mg/dL, a combination insulin-glucose drip was initiated. The amount of insulin and glucose was determined by the level of blood glucose. The amount increased by preset increments if the glucose level continued to increase; it was decreased once the glucose level peaked and began to decrease. Complicating the issue is the fact that glucose levels routinely climb above 150 mg/dL during the use of the heart-lung bypass machine. Therefore, patients identified as diabetic were routinely put on an insulin-glucose IV drip. After postoperative recovery, the patient was moved to the nursing floor and the monitoring continued every hour until the patient was stabilized and removed from IV nourishment. At that point, glucose was monitored by stick approximately every 4 hours until discharge. In March, the protocol was expanded to include all patients who might be diabetic even if not diagnosed. All patients were tested prior to surgery, and if the sugar level was high (ie above 150 mg/ dL), patients were also placed on the protocol. In July, patients were continued on the IV insulin-glucose drip for 3 days after surgery with continued hourly monitoring. Data Collection PROTOCOL COMPLIANCE Initial examination of the data took place after 60 patients had completed the protocol. The data were collected from several sources. A general database was used to gather information concerning surgery: types of procedures, length of surgery, complications, etc. A second database contained information about infection rates. The third database used in the protocol contained the monitored glucose levels. The three databases had to be merged by patient identification number prior to analysis. The glucose levels for each patient are recorded as a time series as shown in Figure 1. It is somewhat questionable whether the use of averages could be used to examine the protocol since it was primarily concerned with high levels of glucose. Contrast the time series of patient#6 with that of patient#1 (Figure 2). Patient #1 has an initial spike that quickly returns to normal range while patient #6 has a serious and long-lasting spike. According to the protocol, patient #6 requires much more aggressive intervention than patient #1. The data were complicated in that Figure 1. Time Series Curve for Patient #6 0 100 200 300 400 500 1 4 7 10 13 16 19 22 25 28 31 34 Reading Number G lu co se L ev el Figure 2. Time Series Curve for Patient #1