Interval control charts for rare events

If a "rare" event is roughly defined as something that occurs with a frequency of less than 10%, then there are many examples in healthcare including medication errors, patient falls, nosocomial infections, surgical complications and VAP. If non-rare event, rate-based, control charts are used to monitor these adverse events, they have the following problems:

• The majority of points is equal to zero
• It is not clear, just by looking, what it means (is it acceptable or not)?
• Statistically not useful
• Two type of situations can occur (Figure 1):
  1. Periodic rare events: "mountain range" appearance where the zeros are the valleys
  2. Prolonged periods with no events. Which raises the quesion: How long before we can say with confidence that the process has shown significant improvement?

Often compliance with a related process is used to indirectly assess a clinical outcome. Some examples:

• Antibiotic timing for surgical prophylaxis, which is assumed to correlate with the SSI rate (Figure 2).
• Compliance with WHO Surgical Safety Checklist, compared to perioperative adverse events (POAE).

Solutions are based on measuring the event interval:

• Number of cases between events (g chart): for example, the number of surgical operations between surgical site infections
  • Number of open heart surgeries between sternal wound infections.
  • Number of CABG procedures between adverse events.
• Time between (interval) events (T-chart): This is used because it is not always practical to measure the exact number between events. Some examples:
  • Days between needle sticks.
  • Number of inpatient days between patient falls.

This data is relatively easy to collect: you only need to record the dates that events occurred. However, evaluating the interval control needs a change in thinking.

Identifying process changes.

1. A higher value on the chart means that the rate of the event occurring has actually decreased because the time between events is longer (Figure 3). For adverse events this is a good thing. Similarly, a smaller value plotted on the chart means that the rate of the event occurring has increased.
2. Runs above or below baseline median
   • 3 ~ 5 points = Possible improvement
   • 5 ~ 6 points = Probable improvement
   • 8 or more points = Near-certain improvement
3. Simple rule {3:x-bar rule}:
   • Time-between:
     • Plot the time or number between events. Compute baseline average time-between (can be overall, which is more conservative, or before changes).
     • Check if the plotted datapoint > 3 times the average? If so, improvement (reduction in rate) at approximately 0.05 significance level (Figure 2, last two points on the right). Alternatively use 4 x baseline for approximately 0.02 significance (Figure 2, last point on right).
   • Number of consecutive months with zero cases.
     • Plot the number of cases per month. Calculate the monthly baseline average.
     • Divide 3 by the monthly baseline average. Is the number of consecutive months with zero > 3 times the average? If so, improvement (reduction in rate) at approximately 0.05 significance level.
     • The lower the rate (rare event), the longer the period of consecutive zeros required to confirm improvement (Table 1). For example, if an event occurs each month (12/year), thens 3 consecutive months of zeros are required, whereas a rate of 1 event per year would need 3 years of zeros for confirmation.