Statistical Analysis

The meta-analysis of the reported proportions of graft occlusion in eligible studies was carried out using a random effects model using the method of DerSimonian and Laird,⁵⁷ with the estimate of heterogeneity being taken from the inverse-variance random-effect model (metaprop command; Stata Statistical Software, Release 13; StataCorp LP, College Station, Tex). Subgroup and meta-regression analysis were carried out to identify predictors of reported graft occlusion rates (metareg command; Stata). To explore the association between the period of patient enrollment and graft occlusion in meta-regression, a “chronological rank” was assigned to all studies. A random-effects model was used to obtain the pooled incidence of SVG occlusion (and 95% confidence intervals [CIs]) and illustrated in forest plots. Subgroup analyses were performed for the time of graft patency assessment postsurgery (<1 month, 1 to <3 months, 3 to 6 months, or 12 months), the type of surgery performed (on-pump vs off-pump surgery), period of patient enrollment, study location, and study size. The presence of statistical heterogeneity was explored using the I².

The shared IPD contributed to the formation of a database of 1864 patients (2925 SVGs) with complete angiographic follow-up data on early SVG occlusion. The collected demographic characteristics were examined for the extent of missingness. Missing values occurred for several predictors in our dataset, and some variables were systematically missing, meaning they were not collected within specific studies. We therefore applied a multilevel multiple imputation (MLMI) model, which uses generalized linear mixed effect model to simultaneously impute sporadically and systematically missing variables in the setting of IPD meta-analysis. MLMI also fully accounts for between-study heterogeneity within the imputation model.⁵⁸ Simulation studies have shown that MLMI is associated with less bias in predictor effects compared with a complete case analysis—where studies with systematically missing variables are excluded—and MLMI is also associated with less bias than traditional multiple imputation, which ignores heterogeneity across studies.⁵⁸ All variables that were available in at least 70% of participants across all studies combined were considered for inclusion in the multiple imputation model. Five imputation data sets were generated.

The population of the SAFINOUS-CABG Consortium was split using a random seed into a derivation (80%, n = 1492 patients) and validation (20%, n = 372 patients) cohort for prediction of SVG occlusion (caret package, R project). The derivation cohort was used for model development and internal 10-fold cross-validation (and an optimism-adjusted c-index was also calculated), whereas the validation cohort served for the validation of the developed model. All variables included in the imputation model were included in a generalized logistic random effects model (lme4 R package) as predictors for graft occlusion within the 1st year post surgery (using a random effect for individual cohorts, ie, surgical sites). A random effects model assumes that patient level observations are not independent as in the case of samples drawn from multiple sites. All remaining predictor variables were introduced as fixed effects. The model included demographic variables (age, sex, body mass index), cardiovascular risk factors (hypertension, dyslipidemia, diabetes mellitus, smoking), clinical scores (ie, New York Heart Association class), laboratory/diagnostic (preoperative serum creatinine levels, left ventricular ejection fraction, number of diseased vessels), and procedural characteristics (endoscopic vein harvesting, on/off-pump operation, use of complex, ie, composite or sequential, grafts, number of grafts, and target vessel type). All continuous predictors were included as linear terms in the regression model because this was found to be a good approximation based on assessment for nonlinearity using fractional polynomials. The discriminatory performance of prediction models was assessed using the c-index. Model calibration was assessed graphically using a calibration plot and a smoothed loess estimator.

The final model was used for the construction of the SAFINOUS risk score by following the method described by Sullivan and colleagues⁵⁹ previously used in the development of the Framingham risk score system. To summarize in brief, points were assigned to each variable using as 1 point the risk related with a 10-year increment in age (constant B = 10 × 0.015 = 0.15) and rounded to the nearest integer. Continuous variables were categorized, and each category was assigned point scores based on the distance of each category from the reference one. Points were assigned to each variable by considering the beta coefficients of the final model. The performance of the model across patient subgroups was explored using ipdover and ipdmetan commands in Stata All analyses were completed with R (www.r-project.org; version 3.2.4) and Stata version 13.0 (StataCorp LP).