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Original Articles: Adult Cardiac

Prediction of Survival After Coronary Revascularization: Modeling Short-Term, Mid-Term, and Long-Term Survival

^a Department of Medicine, Dartmouth Medical School, Hanover, New Hampshire
^b Department of Community and Family Medicine, Dartmouth-Hitchcock Medical Center, Lebanon, New Hampshire
^c Section of Cardiology, Dartmouth-Hitchcock Medical Center, Lebanon, New Hampshire

Accepted for publication September 16, 2008.

^_* Address correspondence to Dr MacKenzie, Dartmouth-Hitchcock Medical Center, 1 Medical Center Dr, Lebanon, NH 03756 (Email: todd.a.mackenzie{at}hitchcock.org).

	Abstract

Top Abstract Introduction Patients and Methods Results Comment Acknowledgments References

 
Background: Many clinical prediction rules for short-term mortality after coronary revascularization have been developed, validated, and introduced into routine clinical practice. Few rules exist for predicting long-term survival in the modern era of coronary revascularization. We report on the development and validation of models for predicting long-term survival after coronary artery bypass graft surgery and percutaneous coronary intervention on the basis of recent experience.

Methods: We linked 1987 through 2001 coronary artery bypass graft surgery and 1992 through 2001 percutaneous coronary intervention data from our northern New England registries on 35,000 patients with complete data on risk factors to the National Death Index, ascertaining 7,000 deaths. We partitioned time after revascularization into three periods on the basis of exploratory analysis using generalizations of Cox's semiparametric model to nonproportional hazards and nonlinear log-hazards. These periods were 0 to 3 months, 4 to 18 months, and 19 months and later. For each period, Cox's regression model was used to regress survival on risk factors yielding three models, which were then combined to make long-term predictions.

Results: These models were incorporated into easy-to-use software that yields predicted survival for up to 8 years after revascularization. The Harrell concordance statistic ranged from 72% to 83% for these models.

Conclusions: We developed and internally validated models that accurately predict long-term survival after coronary artery bypass graft surgery and percutaneous coronary intervention as currently performed. These models using routine clinical data, can be solved with available software, and could be used to enhance informed, patient-centered clinical decision making on the choice of revascularization procedure.

	Introduction

Top Abstract Introduction Patients and Methods Results Comment Acknowledgments References

 
Patients with multivessel coronary artery disease often choose to undergo revascularization with percutaneous coronary intervention (PCI) or coronary artery bypass grafting surgery (CABG) to improve their quality of life or survival. The choice of procedure should depend on a full consideration by the patient of the risks and benefits of the alternative revascularization strategies.

We and others have developed clinical prediction rules for short-term outcomes that make use of past experience to more fully inform current decision making by providing patient-specific estimates of short-term adverse event rates after PCI and CABG [1–4]. However, the choice of revascularization strategy should also incorporate information on long-term outcomes.

The Northern New England Cardiovascular Disease Study Group (NNECDSG) has maintained clinical registries of consecutive coronary revascularization since 1987. We recently linked our data to the National Death Index (NDI). These data were used to develop clinical prediction rules for survival up to 8 years after CABG and PCI.

	Patients and Methods

Top Abstract Introduction Patients and Methods Results Comment Acknowledgments References

 
Patients
The patient cohort used for this study was drawn from the PCI and CABG registries of the NNECDSG, a voluntary research consortium composed of clinicians, research scientists, and hospital administrators at the institutions in Maine, New Hampshire, and Vermont. The intent of this group is to foster continuous improvement in the quality of care of patients with cardiovascular disease in northern New England [1, 2]. Hospital-based data on all PCIs and CABGs in the region are prospectively collected and periodically validated. Data are collected on patient demographics, comorbid conditions, cardiac anatomy and function, procedural priority and indication, procedural process, and in-hospital outcomes. Each patient is represented no more than once in the data used for analysis. (The data collection instruments and data definitions are available on-line at www.nnecdsg.org.) The NNECDSG received institutional review board approval for its registries, and patients gave consent.

Follow-Up
Survival data were obtained through linkage to the NDI using a probabilistic algorithm based on name, social security number, date of birth, sex, date last known alive, and state of last known residence. The index procedure only was used, so that no patient is represented more than once. The sensitivity of this process for correctly identifying deaths ranges from 83% to 92%, with a specificity of 92% to 100%, depending on which patient identifiers are available [5–7].

Statistical Analysis
Separate models were developed for CABG and PCI. Candidate risk factors included sex, age, body mass index (BMI), diabetes mellitus (DM), peripheral vascular disease (PVD), chronic obstructive pulmonary disease (COPD), cancer, preprocedure creatinine (CR), preprocedure white blood cell count (WBC), renal insufficiency (CR > 2 mg/dL) or failure, history of a prior myocardial infarction (MI), time from prior MI, congestive heart failure (CHF), prior CABG or PCI, procedural priority (elective, urgent, emergent), ejection fraction (EF), number of diseased (70% stenosis) coronary vessels (VD), and procedural indication (chronic stable angina, acute coronary syndrome, MI, cardiogenic shock).

The initial phase of modeling used regression splines [8] and smoothing splines [9] for Cox's model to estimate the hazard ratio (HR) as a function of time. It revealed significant time-dependence of the HR (ie, violations of proportionality of hazards) for multiple risk factors. Therefore the follow-up was partitioned into three intervals; short-term (0 to 90 days), mid-term (90 days to 18 months), and long-term (19 months and up) to facilitate risk prediction models that did not require numerical integration of the estimated HR as a function of time (which would be the case if a continuous nonconstant HR was adopted). Within each of these intervals, the risk prediction models described below assume a constant HR. Cox's regression was performed separately in each of the three follow-up intervals and for both types of revascularization. (Note: This is equivalent to using one Cox model with a step-function time-dependent HR.)

The functional form of continuous risk factors was investigated using regression splines and smoothing splines [9]. These analyses revealed that the effect of age and EF on the log-hazard of survival after CABG was linear. For mortality after PCI, each increment of 1 year in age had a constant increment in the log-hazard except at ages younger than 50, for which there was no effect of age. Each decrease of 0.01 in EF in PCI patients increased the log-hazard by a constant amount except for EFs of 0.70 or greater, for which a change had no effect on the log-hazard. For the sake of parsimony and ease of interpretation, the decision was made to treat age and EF as linear effects because their departures from linearity, although significant, were too small to meaningfully modify measures of calibration and discrimination. The functional form of WBC was determined to be approximately logarithmic, so WBC was log-transformed. The functional form of BMI index was determined to be well fitted by a straight line broken at the point where BMI equals 25. Serum CR was combined with the renal dialysis variable to create a single risk factor with the following three categories: renal failure or CR of 2 mg/dL or greater, no renal failure but CR between 1.5 and 2 mg/dL, and no renal failure and CR less than 1.5 mg/dL.

All two-variable interactions were tested for but included only if they were significant at the level of 0.1%. This was roughly equivalent to keeping the overall type 1 error rate for all of the approximately 50 interactions at 5%. To handle missing data we considered imputation by the mean, multiple imputation (ie, aggregate analysis of data sets constructed from Monte Carlo simulation of missing covariates conditional on nonmissing covariates), and complete records analysis, and compared these results. We found that model fit was better using the complete records approach except that we imputed BMI and WBC using the mean, which we found yielded almost identical results as multiple imputation. Site of revascularization was considered both as a fixed effect and as a random effect or frailty [9], but had a negligible effect on each of the risk models (for either gamma or log-normal frailties).

Model discrimination was determined using Harrell's concordance (C) statistic [10] as well as a C statistic for specific points in follow-up, with cross-validation to correct for overfitting bias [11]. The C statistic was calculated for estimated survival at a specific time t (eg, 3 months, 1 year, 5 years), as follows: A pair of subjects, with survival predictions at that time of S₁(t) and S₂(t), and right-censored survival times (₁, t₁) and (₂, t₂), are considered concordant with respect to time t if S₁ is less than S₂, ₁ equals 1, and t₁ is less than t and t₂ is greater than t. They are considered discordant if S₁ is less than S₂, ₂ equals 1, and t₂ is less than t and t₁ is greater than t. Model calibration was assessed using Kent and O'Quigley's R² [10] and by comparing observed survival (calculated using the Kaplan–Meier statistic) with the predicted survival (mean of predicted survival probabilities) by quantiles of predicted risk (as in a Hosmer-Lemeshow plot).

	Results

Top Abstract Introduction Patients and Methods Results Comment Acknowledgments References

 
Characteristics of Patients
Between 1987 and 2001, 47,917 unique patients underwent CABG in northern New England, of whom 15,245 had complete information for all risk factors except possibly CR and BMI (which were imputed) and became the study cohort. As shown in Table 1, the mean age in this group was 66, 27% were female, 30% had DM, 14% had a history of CHF, 50% had 3-VD, 5.5% underwent emergency procedures, and 76% had CABG in 1998 through 2001. From 1988 to 2001, 47,589 patients were added to the PCI registry, of whom 19,806 had complete data for the risk factors we modeled, except for BMI (which was imputed). The mean age of this group was 62, 33% were female, 22% had DM, 8% had CHF, 34% had 2- or 3-VD, 11% had emergent procedures, and 65% had PCI from 1998 through 2001.

View larger version (18K): [in this window] [in a new window]   Fig 1. (A) Overall survival of subjects in the cohorts selected for modeling from the coronary artery bypass graft surgery (CABG) and percutaneous coronary intervention (PCI) registries of the Northern New England Cardiovascular Disease Study Group. The cohorts were chosen from patients having no missing data for the risk factors used in the prediction models we develop. The numbers below the time axis are the number of subjects (in the thousands) still alive (at risk) at each year after revascularization. The row CABG w WBC is the number of patients at risk for which none of the risk factors was missing. The row CABG is the number of subjects at risk for which WBC might be missing. The short-term and mid-term prediction models are based on CABG w WBC, whereas the long-term model is based on the larger CABG cohort because WBC was irrelevant to long-term predictions. (B) Survival in the CABG and percutaneous coronary intervention cohorts adjusted for case-mix using the methods similar to Ghali [12]. (WBC = white blood cells.)

Discrimination and Calibration of the Model for Survival After Coronary Artery Bypass Graft Surgery
The C statistic measure of discriminatory ability of the short-term risk model was 80%. The C-indices of the mid-term and long-term prediction models were 77% and 72%, respectively. The prediction of survival from 3 to 18 months combines predictions from the short-term (where the greatest mortality is) and the mid-term. As reported in Table 3 the C statistic of predictions at 1 year is 80%, and the C statistic of predictions at 5 years (which combines the short-term, mid-term, and long-term models) is also 80%. Table 3 compares observed versus predicted survival for all patients and for clinically relevant patient subgroups at 3 months, 1 year, and 5 years, with the related C statistic. There is excellent agreement between observed and predicted mortality rates.

View larger version (29K): [in this window] [in a new window]   Fig 2. The calibration of each the prediction models, short-term (A), mid-term (B) and long-term (C) for survival after coronary artery bypass graft surgery is illustrated in these plots of observed survival versus expected survival. For each model the patients used to build that prediction model are divided into 25 groups of equal size according to quantiles of their expected survival. Each point of the calibration plot shows observed proportion surviving calculated using the Kaplan–Meier statistic against expected survival calculated as the mean expected survival proportion for subjects in that quantile. The points used for calculating survival were 90 days, 18 months, and 5 years for the short-term, mid-term, and long-term prediction models. Note that each of these models is a conditional model based on survival up to the beginning of that time frame (eg, the mid-term is built on all subjects who survived 90 days).

View larger version (29K): [in this window] [in a new window]   Fig 3. Calibration plots for the short-term (A), mid-term (B), and long-term (C) prediction models for survival after percutaneous coronary intervention. For each model the patients used to build that prediction model are divided into 25 groups of equal size according to quantiles of their expected survival. Each point of the calibration plot shows observed proportion surviving calculated using the Kaplan–Meier statistic against expected survival calculated as the mean expected survival proportion for subjects in that quantile. The points used for calculating survival were 90 days, 18 months, and 5 years for the short-term, mid-term, and long-term prediction models. Note that each of these models is a conditional model based on survival up to the beginning of that time frame (eg, the mid-term is built on all subjects who survived 90 days).

	Comment

Top Abstract Introduction Patients and Methods Results Comment Acknowledgments References

 
We have developed rules for predicting short-term, mid-term, and long-term survival in patients undergoing CABG and patients undergoing PCI. The rules were developed using models that are sensitive to departures from the usual assumptions (ie, proportionality of hazards and log-linear continuous effects). These rules are well calibrated and discriminate well overall (C indices of 77% to 83%, corrected for overfitting bias) and for a range of patient subtypes.

A variety of models have been developed and validated to predict in-hospital or 30-day mortality after CABG [2, 13–15] and PCI [16–20], but to our knowledge only a few models have been developed for predicting 90-day or longer-term survival [21–24]. Only one group [22–24] has systematically explored how risk factors might differ as a function of the time from procedure. Gardner and associates [22] used stratified follow-up and Gao and colleagues [23, 24] used B-splines to identify risk factors for survival after CABG whose predictive ability either significantly increased (acuity, DM, age, renal disease, and COPD) or decreased (prior heart surgery, prior MI) with time since CABG. If a time-dependent HR is modeled using proportional hazards the impact is to bias predicted survival. For instance, an elective CABG patient would have a predicted survival that is lower than observed in the short-term and higher than observed in the long-term if priority is modeled using proportional hazards because the proportional hazards model would average out the advantage that elective patients have (relative to emergency and urgent patients) in the first 90 days over the entire 8 years. In contrast, the predicted survival for an emergency patient would be higher than observed in the short-term and lower than observed in the long-term. For instance, the predicted 6-month mortality for a 70-year-old woman with an EF of 0.50 and no comorbidities is 2.8% if the patient is elective and 7.8% if she is an emergency patient. In contrast a proportional hazards model predicts 6-month mortality of 3.3% and 6.1%. This is why it is important to relax the assumption of proportional hazard just as Gardner and coworkers [22], Gao and associates [23, 24], and our group has done.

We partitioned follow-up into three periods, estimated patient-specific conditional survival in each interval, and combined the survival estimates from each interval into one curve. Although flexible regression methods such as splines [8, 23–25] are ideal for modeling associations, it is difficult to convert a model containing time-dependent spline estimates into patient-specific survival curves because it is then necessary to use methods for numerical integration to obtain predictions that would prohibit implementation of the prediction models into spreadsheets. Our partitioning of follow-up into three intervals is similar to the multiphase survival models proposed by Blackstone and colleagues [26], but the Blackstone model is fully parametric whereas ours makes no assumptions about the shape of the baseline hazard. We chose the cut points of 3 and 18 months for partitioning follow-up on the basis of the shape of the estimated time-dependent HRs [8, 9, 25] and on the distribution of death times. Our model for survival after CABG in the short-term period was restricted to those who had complete information including WBC, whereas the mid-term and long-term models were based on larger cohorts that may have had a missing WBC. We do not believe this led to any bias because there was no significant different in survival for any of the three periods between those with complete data and those without.

The usual approach to modeling the association of continuous risk factors with mortality is categorization. This approach makes the implicit assumption that there is no association of the risk factor and mortality within a category. This forces a discontinuous step function shape onto what is almost certainly a smooth shape. For instance, a model that has a category of "EF less than 0.40" is making the assumption that patients with EFs of 0.20 are at the same risk as patients with EFs of 0.39. As a consequence any prediction based on this model will give the same survival curves for these two patients. We chose to smoothly model the association and in so doing identified that the effects of age and EF on survival after CABG and PCI,can be modeled appropriately using the usual log-linear model. We also determined that if WBC is log-transformed it has a log-linear association with the log-hazard of mortality.

These prediction rules could be used in practice to help patients and their clinicians choose between CABG and PCI. For instance, consider the following patients. The first is a 65-year-old man with no comorbidities, an EF of 0.55, and 2-VD. Survival after CABG and PCI are very similar in the short-term, intermediate-term, and long-term (Fig 4A). However, for a similar middle-aged man with DM and 3-VD, survival is similar for CABG and PCI out to 6 months but separates thereafter and favors CABG (Fig 4B). If this latter patient has a depressed EF of 0.35, survival for CABG and PCI are similar only out to 3 months (Fig 4C), at which time CABG begins to offer a small survival advantage that grows to 12% at 5 years.

View larger version (19K): [in this window] [in a new window]   Fig 4. Estimated survival probabilities with time for patients undergoing coronary artery bypass graft surgery (CABG) and patients undergoing percutaneous coronary intervention (PCI) applied to a 65-year-old man with no comorbidities, an ejection fraction of 0.55, and two-vessel disease (A). For such a man who also has diabetes mellitus and three-vessel disease, the survival curves are shown in B. (C) Survival curves for this man if in addition he has an ejection fraction of only 0.35.

We have performed internal validations only. We used cross-validation to calculate measures of discrimination and calibration corrected for overfitting bias. It remains to be determined whether our prediction rules will perform as well when applied to other populations.

One limitation of any long-term survival analysis for which there may be changes in long-term survival over calendar time (owing to improvements in treatment) is estimation of long-term survival for the most recent subjects in the dataset. For the most recent subjects there is no long-term survival. We make our survival predictions reflect the most recent survival experience by including year in our models and by substituting the year 2000 in all survival predictions.

There may be clinical information not routinely collected in the registries that could improve the performance of the clinical prediction rules. Our risk prediction model for CABG uses WBC, whereas our risk predictions for PCI do not. This was because of its availability in the registries. As WBC predicts survival up to 18 months, survival predictions for a patient with poor WBC may look better for PCI only because the PCI prediction is not based on WBC.

Our models cannot be used to predict survival for patients receiving planned concurrent CABG and PCI. The Northern New England registry did not record any planned concurrent procedures during the study period ending in 2001. Between the years 2003 and 2007, the proportion of PCI patients who also received a planned CABG was 0.15% (59 of 39,965).

Summary
We have developed and internally validated a clinical rule for predicting long-term survival after CABG or PCI. These prediction rules can be used to provide a stronger evidence base for patients and providers faced with choosing a strategy for coronary revascularization. We have embedded these (and other) prediction rules into a spreadsheet that prompts users for the relevant list of preoperative risk factors and displays the estimated probability of survival after CABG or PCI, for persons with the same risk factor profile. Our plan is to encourage the use of this tool for decision support throughout the region.

	Appendix

 
Approximate Formulas for Predicted Survival
A formula (approximation based on use of a Weibull distribution in each period) for the estimated probability of survival for a CABG patient with covariates x₁, x₂, x₃, ... (eg, age, male, BMI, ...) is exp[–0.00013 x (time)^0.49 x HR₁] for the first period, where time is measured in years, and HR₁ equals exp(β₁₁x₁ + β₁₂x₂ + β₁₃x₃ + ...) where β₁₁, β₁₂, β₁₃ are the logarithm of the hazard ratios for period 1 appearing in Table 2. In the second period this formula is exp[–0.000069 x HR₁ – 0.00063 x (time – 0.25)^0.85 x HR₂], where HR₂, similar to HR₁, is calculated using the period 2 entries from Table 2. In the third period the probability of survival is exp[–0.000069 x HR₁ – 0.00076 x HR₂ – 0.00034 x (time – 1.5)^1.31 x HR₃] where HR₃ is calculated using the period 3 entries from Table 2. The corresponding probabilities for a PCI patient, based on the logarithm of the hazard ratios found in Table 2 are exp[–0.0090 x (time)^0.37 x HR₁] for the first period, exp[–0.0054 x HR₁ – 0.0023 x (time – 0.25)^0.85 x HR₂] for the second period, and exp[–0.0054 x HR₁ – 0.0027 x HR₂ – 0.0021 x (time – 1.5)^1.2 x HR₃] for period 3.

	Acknowledgments

Top Abstract Introduction Patients and Methods Results Comment Acknowledgments References

 
This study was funded by the Northern New England Cardiovascular Disease Study Group, Lebanon, NH.

	References

Top Abstract Introduction Patients and Methods Results Comment Acknowledgments References

 

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This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to Personal Folders Download to citation manager Permission Requests Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by MacKenzie, T. A. Search for Related Content PubMed Articles by MacKenzie, T. A. Related Collections Coronary disease Related Article