Fig 1.
Study flowchart.
Table 1.
Inpatient stays characteristics per quarter.
Fig 2.
Histograms of observed outcomes and the related curves of expected trends with classical or enhanced adjustments.
Expected rates of complications per quarter were calculated from the GEEs models initially fitted on the training dataset and then applied to the testing dataset. Models used for the construction of classical control charts were adjusted for case-mix variables only (age, gender, socioeconomic status, medical accessibility, emergency admission, hospital status, surgical procedure complexity, primary diagnosis, and comorbidities in dummies from the Elixhauser score). Models used for the construction of enhanced case-mix and time adjusted control charts were adjusted with the same set of variables, in addition to the year as a proxy for secular trends and the quarter as a proxy of seasonal variations.
Fig 3.
Example of classical and enhanced control charts for two hospitals.
Crude observed rates (dotted black line) were monitored over 20 quarters for all three surgical outcomes. 2-SD warning limits (light green/red lines) and 3-SD control limits (bold green/red lines) were based on the central line (blue line) computed through the GEE models. A special cause variation related to a deterioration of surgical outcomes was detected in case of one single point beyond the 3-SD upper control limit (3-SD UCL), or 2 out of 3 consecutive points beyond the 2-SD upper warning limit (2-SD UWL). Conversely, a special cause variation related to an improvement of surgical outcomes was detected in case of one single point below the 3-SD lower control limit (3-SD LCL), or 2 out of 3 consecutive points below the 2-SD lower warning limit (2-SD LWL). The signal detection was considered at the first point beyond the limit when using the 2 out of 3 consecutive points rule. The two selected hospitals demonstrated discordances (encircled in pink) in interpretation of surgical outcome variations between classical and enhanced charts. Hospital A detected a special cause variation of increased mortality during the second quarter of 2018 using the time-adjusted chart (1 point above the 3-SD upper control limit, chart A2) but not the case-mix only adjusted chart (chart A1). Similarly, hospital B detected a special cause variation of decreased reoperation rate during the second quarter of 2015 using the time-adjusted chart (2 points out of 3 below the 2-SD lower warning limit, chart B6) but not the classical one (only 1 point out of 3 below the 2-SD warning limit, chart B5).
Table 2.
Comparison of special cause variations detection between classical and enhanced control charts.