Methods

The design of the EURopean trial On reduction of cardiac events with Perindopril in stable coronary Artery disease (EUROPA) study has been previously reported. In brief, this randomized, double-blind, placebo-controlled trial investigated the efficacy of perindopril in the reduction of cardiovascular events in 12,218 patients. Each patient provided informed consent, and the study protocol conformed to the ethical guidelines of the Declaration of Helsinki.

The study participants consisted of men and women aged ≥18 years, with evidence of coronary heart disease documented by previous MI (>3 months before screening), percutaneous or surgical coronary revascularization (>6 months before screening), angiographic evidence of ≥70% narrowing of ≥1 major coronary artery, or, in men, a history of typical chest pain with abnormal stress test findings. All patients provided informed consent. The exclusion criteria included clinically evident (New York Heart Association class II or greater) heart failure, planned revascularization procedure, hypotension (sitting systolic blood pressure <110 mm Hg), uncontrolled hypertension (systolic blood pressure >180 mm Hg and/or diastolic blood pressure >100 mm Hg), use of angiotensin-converting enzyme inhibitors or angiotensin 2 receptor blockers in the past month, renal insufficiency (serum creatinine >150 μmol/L or 1.5 mg/dl), and serum potassium >5.5 mmol/L. The patients were randomly assigned to perindopril 8 mg or placebo once daily for ≥3 years. The first patient was enrolled in October 1997.

At baseline, exposure data were collected for age, current smoking (patients who were current smokers or had smoked in the previous month), diastolic blood pressure, systolic blood pressure, heart rate, diabetes (known history of diabetes or the use of antidiabetic agents), total cholesterol, body mass index, family history of CAD, history of congestive heart failure, history of peripheral vessel disease, history of previous MI, history of previous revascularization, and previous stroke.

The patients were followed up for cardiovascular mortality, noncardiovascular mortality, MI, CABG, PCI, and resuscitated cardiac arrest until March 2003. Intensive monitoring and end point validation was done by a clinical event committee. The median follow-up period was 4.1 years (interquartile range 4.0 to 4.5).

For the development of risk prediction models with subsequent internal validation, several techniques are available, including the split-sample and bootstrap methods. According to the split-sample method, the original sample is randomly divided into 2 parts: a training set for model development and a testing set for model validation. Bootstrap replicates the process of sample generation from an underlying population by drawing “bootstrap samples,” with replacement from the original sample. The bootstrap samples usually have the same size as the original. According to the bootstrap method, risk prediction models are developed on the original sample and validated in the set of bootstrap samples. The bootstrap method is preferred for small data sets. Our original sample was large; thus, we were confident to apply the split-sample method. The original sample was randomly divided into a training set of 8,144 patients (2/3 of the original sample) and a testing set of 4,074 patients.

To develop the optimal risk prediction model, multivariate Cox proportional hazards analysis was applied in the training set. All available predictors were considered as potential determinants of the outcomes we studied. Backward stepwise selection was used for variable selection, because this has been argued to render reliable predictors. Variable exclusion was performed using a 5% significance level as a stopping criterion.

We examined the end points of cardiovascular mortality, noncardiovascular mortality, nonfatal MI, CABG, and PCI. Moreover, we examined the combination of cardiovascular mortality, nonfatal MI, and resuscitated cardiac arrest, which was originally the primary end point of the EUROPA study (combined end point 1), and the combination of cardiovascular mortality, noncardiovascular mortality, nonfatal MI, CABG, PCI, and resuscitated cardiac arrest (combined end point 2). In the analysis of the combined end points, we applied censoring at the first moment that any 1 of the end point components occurred in a patient. In the analysis of the separate outcomes, we used time-dependent covariates to account for other nonfatal end points. For instance, when CABG was the end point of interest, we used nonfatal MI and PCI as time-dependent variables.

Complete information was available for most variables. The values for total cholesterol, heart rate, history of MI and revascularization, and body mass index were missing in <5% of participants. Missing values were managed using expectation maximization, an iterative method for finding maximum likelihood estimates of parameters in statistical models, in which the model depends on unobserved latent variables. The Statistical Package for Social Sciences, version 17.0, for Windows (SPSS, Chicago, Illinois) was used for these analyses.

After deriving the models in the training set, we assessed their performance in the testing set. We used Nagelkerke’s R ² to assess global model performance. R ² is a likelihood-based measure that provides information about the goodness of fit of the model (i.e., how well the regression line estimates the real survival). There are several different definitions of R ² . The definition proposed by Nagelkerke can be readily applied to survival outcomes and has the advantage of being scaled from 1% to 100%. Of note is that the value of R ² depends in part on incidence of the outcome. A lower incidence results in lower values of R ² , which thus should be interpreted in their appropriate context. Subsequently, we assessed model discrimination for every end point by calculating area under the receiver operating characteristic curve (AUC). Model discrimination is the ability of the model to rank persons appropriately, from low to high risk. We calculated time-dependent AUCs using the statistical program R. This approach takes into account the follow-up time until event occurrence. Standard errors were calculated by bootstrapping.

To assess differences in model discrimination between the training and testing sets, we compared the AUCs using chi-square tests. A 2-tailed probability <0.05 was considered a statistically significant result.

Moreover, we investigated calibration, or how closely the predicted probabilities reflected actual risk. For this purpose, we compared observed survival, derived from Kaplan-Meier curves, with predicted survival, calculated from the Cox proportional hazards models. We constructed calibration plots according to the categories defined by deciles of predicted risk.

Results

The baseline characteristics are summarized in Table 1 . The mean age was 60 years, and 85% were men. No significant differences were present between the training and testing sets. The incidence of the end points is listed in Table 2 . The incidence of cardiovascular mortality was 9.6/1,000 person-years in the training set.

In the training set, 16 potential variables were evaluated for model inclusion. The variables included in the best-fitting prediction model for cardiovascular mortality after backward selection were age, current smoking, diabetes mellitus, total cholesterol, body mass index, previous MI, a history of congestive heart failure, peripheral vessel disease, previous revascularization, and previous stroke ( Table 3 ). The hazard ratios for the variables in this model are listed in Table 4 . A smaller number of variables were included in the predictive model for noncardiovascular mortality after backward selection (i.e., age, current smoking, and heart rate). The variables included in the prediction models for MI, CABG, PCI, and the combined end points are also listed in Table 3 .

Table 3

Prognostic models resulting from backward stepwise selection, with corresponding area under receiver operating characteristic curve (AUC) and Nagelkerke’s R ² in training and testing sets

End Point	Full Model from Backward Stepwise Selection	Training Set		Testing Set		p Value for Difference in AUC Between Training and Testing Sets
		AUC (95% CI)	Nagelkerke R 2 (%)	AUC (95% CI)	Nagelkerke R 2 (%)
Cardiovascular mortality	Age, smoking, DM, cholesterol, BMI, HF, previous MI, PVD, revascularization, stroke	0.70 (0.69–0.71)	10	0.73 (0.70–0.77)	12	0.12
Noncardiovascular mortality	Age, smoking, and heart rate	0.69 (0.67–0.71)	5	0.71 (0.69–0.73)	8	<0.001
Nonfatal MI	Age, smoking, DM, cholesterol, previous MI, family history of CAD, PVD	0.60 (0.58–0.62)	2	0.59 (0.56–0.62)	2	0.42
CABG	Age, gender, DM, cholesterol, BMI, previous MI, family history of CAD, revascularization	0.67 (0.64–0.68)	5	0.65 (0.62–0.68)	4	0.12
PCI	DM, renal function, revascularization	0.55 (0.54–0.56)	1	0.57 (0.53–0.59)	1	0.08
Combined end point 1 ∗	Age, gender, smoking, DM, cholesterol, DBP, renal function, previous MI, PVD, revascularization, stroke	0.64 (0.63–0.66)	5	0.63 (0.61–0.66)	6	0.36
Combined end point 2 †	Age, gender, smoking, DM, cholesterol, family history of CAD, PVD, revascularization, stroke	0.62 (0.60–0.63)	4	0.61 (0.59–0.63)	4	0.56

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