We extracted data on all admissions in England for isolated coronary artery bypass graft (CABG, OPCS4 codes K40-K46), repair of abdominal aortic aneurysm (OPCS4 codes L18-L21), and colorectal excision (OPCS4 H06-H11, H33) for cancer (ICD10 C18-C20) for the period 1996-7 to 2003-4. After we linked episodes belonging to the same admission, we excluded records with invalid date of birth, sex, length of stay, or method of admission and duplicated records. We also excluded records for CABG if the procedure was preceded in the same admission by an angioplasty because we then considered it to be a “rescue” rather than the primary intended procedure. We divided repairs of abdominal aortic aneurysm into ruptured and non-ruptured (according to whether the primary diagnosis was I710, I711, I713, I715, or I718) to enable comparison with published results. We divided colorectal excisions into procedure subgroups by OPCS code. Data extracts were split randomly and equally into training sets and validation sets. Within HES, death in hospital in the same admission or after transfer to another unit was taken as the outcome.
Operations were classified as elective (admission method (ADMIMETH) 11 to 13) or non-elective (all other ADMIMETH values) as HES does not have an “urgent” category, unlike US admissions data or those from the Society of Cardiothoracic Surgeons. Age was divided into five year bands to ≥85, but with those aged <45 combined. We used secondary diagnosis fields to create comorbidity variables used to make up the Charlson index.15
Further factors considered specific to each index procedure group were also considered (tables 1 and 2). The two variables we used that were not adjusted for in the models from the clinical databases were financial year and socioeconomic deprivation. Our measure of deprivation was the index of multiple deprivation for 2004 at super output area, linked through the patient's postcode.
Table 1 Odds ratios (95% confidence intervals) for mortality in hospital for isolated coronary artery bypass (CABG), repair of ruptured abdominal aortic aneurysm (AAA), repair of unruptured AAA, and colorectal excision procedures for cancer for variables (more ...)
Table 2 Odds ratios (95% confidence intervals) for mortality in hospital for isolated coronary artery bypass (CABG), repair of ruptured abdominal aortic aneurysm (AAA), repair of unruptured AAA, and colorectal excision procedures for cancer for variables (more ...)
We plotted each variable against the death rate to determine whether the relation, if any, was linear or if the variable should be categorised (age group and all dichotomous variables were automatically fitted as factors—that is, as categorical variables rather than as continuous covariates). We then used logistic regression to fit three models for each index procedure: a simple model—year, age, and sex only; an intermediate model—year, age, sex, method of admission, diagnostic, or operation subgroup; and a complex model—all appropriate variables in tables 1 and 2.
We compared these HES based models with the best published predictive risk model based on data from the clinical databases. For CABG and abdominal aortic aneurysms we used the most recent society reports available.6 8
For colorectal resection we used the published model in the report on risk adjusted outcomes from the Association of Coloproctology of Great Britain and Ireland.9 16
We compared models using receiver operating characteristic (ROC) curve scores (c statistics). The c statistic is the probability of assigning a greater risk of death to a randomly selected patient who died compared with a randomly selected patient who survived. A value of 0.5 suggests that the model is no better than random chance in predicting death. A value of 1.0 suggests perfect discrimination. In general, values less than 0.7 are considered to show poor discrimination, values of 0.7-0.8 can be described as reasonable, and values above 0.8 suggest good discrimination. The models were calibrated by plotting observed versus predicted numbers of deaths by tenth based on risk. A model that closely fits the observed outcome is desirable, and this can be tested using a χ2
type statistic developed by Hosmer and Lemeshow measuring goodness of fit.17
This test compares the number of observed cases with the number of predicted cases for each tenth of risk. As the performance of this test depends on sample size, we also inspected the proportion of residuals whose absolute values were greater than 1.96 (5% are expected to be greater than this value). We also checked for influential data points via their Cook's statistic, which have values greater than 1.18