Modeling major lung resection outcomes using classification trees and multiple imputation techniques

Transcription

1 European Journal of Cardio-thoracic Surgery 34 (2008) Modeling major lung resection outcomes using classification trees and multiple imputation techniques Mark K. Ferguson a, *, Juned Siddique b, Theodore Karrison b a Department of Surgery, The University of Chicago, 5841 South Maryland Avenue, MC5035, Chicago, IL USA b Department of Health Studies, The University of Chicago, Chicago, IL USA Received 5 June 2008; received in revised form 14 July 2008; accepted 21 July 2008; Available online 29 August 2008 Abstract Objective: Modeling of operative risks associated with major lung resection is potentially inaccurate and inefficient because of incomplete observations for predictor variables (covariates). Missing values do not usually occur randomly, potentially introducing an important source of bias in modeling. Deletion of cases with missing data also results in loss of precision. The current study analyzes incomplete variables as potential predictors of outcomes after major lung resection using imputation techniques. Methods: We analyzed major lung resection patients treated from 1980 to 2006 for predictors of pulmonary, cardiovascular, and overall complications, as well as mortality. Predictive variables were initially determined using classification and regression tree (CART) methods. Imputation models were developed and variables with missing values were multiply imputed. We fit a logistic regression model for each outcome using CART variables and any covariates that were of interest clinically. Results: Of 1046 resected patients, serum albumin and diffusing capacity (DLCO%) had a large number of missing values (32% and 13% missing, respectively). Models included 10 covariates for pulmonary complications ( p < 0.05 for DLCO% and forced expiratory volume in the first second [FEV1%]), 12 covariates for cardiovascular complications ( p < 0.05 for FEV1%, extent of resection, year of operation, and age), 15 covariates for overall complications ( p < 0.05 for DLCO%, performance status, serum albumin, and FEV1/FVC ratio), and 12 covariates for death ( p < 0.05 for DLCO%, extent of resection, and operation year). Conclusions: We identified serum albumin as a previously under-reported and strong predictor of overall complications. Serum albumin was marginally significantly related to pulmonary and cardiovascular outcomes after major lung surgery. Use of imputation techniques for modeling surgical risks has potential value in identifying important predictive variables that may ordinarily be eliminated from analysis or not identified as predictors because of incomplete observations in clinical databases. # 2008 European Association for Cardio-Thoracic Surgery. Published by Elsevier B.V. All rights reserved. Keywords: Neoplasm; Lung; Surgical risk; Serum albumin; Imputation; Diffusing capacity; Classification and regression tree 1. Introduction Major lung surgery is associated with rates of morbidity and mortality that are not trivial. Risks for pulmonary complications or cardiovascular complications exceed 15%, and mortality rates range from 2% for lobectomy to as high as 8% for pneumonectomy. Patients undergoing major lung resection often have multiple comorbid factors such as hypertension, coronary artery disease, diabetes, and chronic obstructive pulmonary disease. Data on these factors are easily recorded and have been used in risk assessment estimates for decades. Formal modeling of risks for morbidity and mortality is important in appropriate patient selection for surgery, counseling patients as part of the surgical consent process, stratifying outcomes for research purposes, and assessment * Corresponding author. Tel.: ; fax: address: mferguso@surgery.bsd.uchicago.edu (M.K. Ferguson). of resource utilization. Previous studies from our institution have demonstrated the importance of pulmonary function, age, and performance status in predicting the risk of major lung resection [1 6]. Recent analyses of our database as part of a longitudinal study of outcomes demonstrated a possible important effect of serum albumin on estimations of outcomes such as mortality and cardiopulmonary complications [7]. However, there were too many missing data points for that parameter to include it in the development of a generalized risk model using routine methodology. Standard statistical techniques and software routines automatically eliminate patients with missing values from risk analyses. This is problematic because missing values do not usually occur randomly, potentially introducing an important source of bias in any such analyses. Deleting observations can also reduce the precision of parameter estimates. New techniques for imputing missing values are currently being advocated for more accurate modeling of outcomes using large datasets [8 10]. In fact, some clinical medicine journals strongly encourage the use of imputation /$ see front matter # 2008 European Association for Cardio-Thoracic Surgery. Published by Elsevier B.V. All rights reserved. doi: /j.ejcts

2 1086 M.K. Ferguson et al. / European Journal of Cardio-thoracic Surgery 34 (2008) techniques in data analyses so that potentially relevant relationships are not overlooked and to avoid potential bias in results reporting. The purpose of the current study is to analyze serum albumin and other incomplete variables as potential predictors of outcomes after major lung resection using imputation techniques. 2. Methods We analyzed our database of patients who underwent major lung resection from 1980 through The data include demographic information, preoperative laboratory values, type of operation, cancer staging information where appropriate, and operative outcomes including specific complications. This study was approved by our institutional review board and specific patient consent was waived. Predictive variables for specific outcomes including mortality, overall complications, pulmonary morbidity (initial ventilatory support >24 h, reintubation for respiratory insufficiency, pneumonia, lobar collapse) and cardiovascular morbidity (myocardial infarction, arrhythmia, pulmonary embolism, cardiovascular instability requiring intravenous vasoactive agents) were determined using classification and regression tree (CART) methods [11]. Classification trees are a computationally intensive nonparametric approach to classification often used in medical decision-making. Tree construction consists of searching through the predictive variables and choosing the one variable that best subsets the data into two groups in which the distribution of the variable to be classified is more pure (i.e., homogenous with respect to the outcome, resulting in lower misclassification rates) than before the split. If a predictive variable is not already binary, the algorithm identifies the cut-off that provides the best split. Once the data have been subset into two nodes, the algorithm then considers each node separately. If a node is sufficiently pure, no more classification is necessary. Otherwise, the algorithm, using the cases in that node, searches through the remaining variables to identify the variable that best splits the node into two additional nodes of increased purity. This construction process continues until all nodes are sufficiently pure and no more splitting is necessary. A final pruning step may also be performed to avoid over fitting. By incorporating a loss function into the tree algorithm, one can grow trees that maximize sensitivity or specificity. In order to identify all variables associated with our outcomes, we grew two trees for each outcome; one that maximized sensitivity, and one that maximized specificity. We then developed an imputation model that incorporated the following: our outcome variables, the variables that were identified in the classification trees, and any additional variables that appeared in our regression models or were correlated with those variables with missing values. All variables with missing values were multiply imputed under a multivariate normal model [12]. Once the data were imputed, we fit a logistic regression model for each outcome again using those variables identified by the classification trees as well as any covariates that were of interest clinically. All models included the variables DLCO% (diffusing capacity of the lung for carbon monoxide, expressed as a percent of predicted), gender, performance status, induction therapy, cancer stage, FEV1% (forced expiratory volume in the first second, expressed as a percent predicted), serum albumin, and fraction of lung volume, whether or not they were identified in the classification trees. While we considered all two-way interactions among the covariates, for the sake of parsimony, the regression models only included covariate main effects [13]. Models were fit on each of the five imputed datasets and results were combined using the methods described in Rubin [14]. Data are expressed as mean standard deviation (SD). 3. Results A total of 1046 patients underwent major lung resection during the study period. Their demographic information, laboratory values, diagnoses, preoperative therapy, operations, and outcomes are listed in Table 1. Among the variables that had the largest number of missing values were serum albumin and diffusing capacity (32% and 13% missing, respectively). There were substantial differences between groups with and without these measurements, indicating the importance of complete datasets in modeling outcomes (Table 2). After CART identification of predictive variables and multiple imputation for missing values, the resultant models included 10 covariates for pulmonary complications ( p < 0.05 for DLCO% and FEV1%; Table 3); 12 covariates for cardiovascular complications ( p < 0.05 for FEV1%, extent of resection, year of operation, and age; Table 4); 15 covariates for overall complications ( p < 0.05 for DLCO%, performance status, serum albumin, and FEV1/FVC ratio; Table 5); and 12 covariates for death ( p < 0.05 for DLCO%, extent of resection, and operation year; Table 6). Serum albumin was marginally significantly related to pulmonary and cardiovascular outcomes. 4. Discussion The prediction of the risk of complications after major lung resection is important for a number of reasons. It assists in selecting patients for surgery, obtaining informed consent, determining the utility of preoperative risk-reducing interventions, selecting alternative therapies if the risk is deemed to be excessive, and in assigning resources for postoperative care. Formal preoperative assessment of risk by clinicians using rating algorithms is uncommon in major lung surgery. This is likely because the predictive ability of such algorithms is generally only moderately good, a variety of systems have been published that are not consistent in their recommendations, and many surgeons believe that the risk of a resection for cancer is often a better option than the high risk a patient faces if curative cancer therapy in the form of surgery is not offered. Inconsistency among risk models exists in part because of differing patient populations, clinical management, and methods of outcome assessment. In addition, potentially useful indicators may not be measured routinely or their

3 M.K. Ferguson et al. / European Journal of Cardio-thoracic Surgery 34 (2008) Table 1 Demographic, laboratory, and surgical data for patients who underwent major lung resection Category Patients assessed Value or number affected Range Age (years; mean SD) Male gender (54.8%) Diabetes mellitus (14.1%) Hypertension (39.1%) Serum creatinine (mg/dl) Serum hemoglobin (g/dl) Serum albumin (g/dl) Prior myocardial infarction (10.0%) (84.0%) Current cigarette smoker (43.5%) Body mass index (BMI) FVC% FEV1% FEV1/FVC ratio DLCO% Lung cancer diagnosis (82.8%) Induction chemotherapy or radiotherapy (10.4%) Year of operation Extent of resection 1046 Lobectomy 780 (74.6%) Bilobectomy 89 (8.5%) Pneumonectomy 177 (16.9%) Fraction of lung volume Cancer stage 858 0orI 472 (55.0%) II 166 (19.4%) III 207 (24.1%) IV 13 (1.5%) Pulmonary complications (14.6%) Cardiovascular complications (15.1%) Any complication (31.7%) Operative mortality (6.2%) FVC%: forced vital capacity expressed as a percent of predicted; FEV1%: forced expiratory volume in the first second expressed as a percent of predicted; DLCO%: diffusing capacity of the lung for carbon monoxide expressed as a percent of predicted. values may not be collected for database purposes. An example is diffusing capacity, which has been shown to be a strong, independent determinant of pulmonary complications and operative mortality after major lung resection. In the European Thoracic Surgery Database fewer than 25% of patients had values for diffusing capacity recorded [15]. In our own database we also found in statistical analyses that serum albumin was a potentially important determinant of Table 2 Comparison of variables between groups with and without accompanying key covariate measurements Variable No DLCO group DLCO group No albumin group Albumin group Age (years) Male 61.1% 53.8% % 57.2% 0.02 Diabetes mellitus 11.0% 14.5% % 15.0% 0.23 Hypertension 33.8% 40.0% % 39.5% 0.73 Prior myocardial infarction 11.2% 9.8% % 10.7% 0.23 Induction therapy 11.3% 10.2% % 12.1% % 84.1% % 17.3% 0.10 Serum creatinine (mg/dl) Serum hemoglobin (g/dl) FVC% FEV1% < FEV1/FVC ratio DLCO% Fraction of lung volume Current smoker 54.1% 41.9% % 47.5% <0.001 Body mass index (BMI) Cancer stage I or II 66.1% 75.6% % 72.7% 0.10 Serum albumin (g/dl) Year of operation < <0.001 FVC%: forced vital capacity expressed as a percent of predicted; FEV1%: forced expiratory volume in the first second expressed as a percent of predicted; DLCO%: diffusing capacity of the lung for carbon monoxide expressed as a percent of predicted.

4 1088 M.K. Ferguson et al. / European Journal of Cardio-thoracic Surgery 34 (2008) Table 3 Covariates for pulmonary complications Table 5 Covariates for overall complications DLCO% (10% change) < FEV1% (10% change) Female Induction therapy Early cancer stage (I or II) Late cancer stage (III or IV) Serum albumin Fraction of lung volume Year of operation (5 years change) FEV1%: forced expiratory volume in the first second expressed as a percent of predicted; DLCO%: diffusing capacity of the lung for carbon monoxide expressed as a percent of predicted. Table 4 Covariates for cardiovascular complications DLCO% (10% change) FEV1% (10% change) Female Induction therapy Early cancer stage (I or II) Late cancer stage (III or IV) Serum albumin Fraction of lung volume Body mass index (BMI) Year of operation (5 years change) Age (10 years change) < FEV1%: forced expiratory volume in the first second expressed as a percent of predicted; DLCO%: diffusing capacity of the lung for carbon monoxide expressed as a percent of predicted. risk, but because many patients did not have serum albumin values measured or recorded, this variable was often not considered in risk models. In this study we explored newer techniques for improving risk assessment, including CART methodology and multiple imputation techniques for assigning values to variables that were frequently missing. The need for this type of analysis is clearly indicated in Table 2, in which numerous important statistical and clinical differences are evident between groups with and without measurements for two of the most common missing variables, diffusing capacity and serum albumin. In addition, because most statistical software drops observations with missing values, any statistical model including both DLCO and serum albumin would result in 432 (41%) of our observations being dropped from the analysis. CART methodology previously has been used sparingly in modeling lung resection outcomes [16] and is not generally familiar to the thoracic surgical community. Its primary advantage is the development of more rigorous DLCO% (10% change) FEV1% (10% change) Female Induction therapy Early cancer stage (I or II) Late cancer stage (III or IV) Serum albumin Fraction of lung volume FVC% (10% change) Body mass index (BMI) FEV1/FVC ratio > Non-small cell lung cancer Small cell lung cancer Carcinoid tumor Other lung pathology FVC%: forced vital capacity expressed as a percent of predicted; FEV1%: forced expiratory volume in the first second expressed as a percent of predicted; DLCO%: diffusing capacity of the lung for carbon monoxide expressed as a percent of predicted. Table 6 Covariates for operative mortality DLCO% (10% change) FEV1% (10% change) Female Induction therapy Early cancer stage (I or II) Late cancer stage (III or IV) Serum albumin Fraction of lung volume FVC% (10% change) Year of operation (5 years change) Age (10 years change) FVC%: forced vital capacity expressed as a percent of predicted; FEV1%: forced expiratory volume in the first second expressed as a percent of predicted; DLCO%: diffusing capacity of the lung for carbon monoxide expressed as a percent of predicted. models through nonparametric recursive partitioning of data, including interactions, permitting identification of potentially influential variables that might not be obvious in simple univariate or even multivariable analyses. Multiple imputation techniques, which replace missing values with two or more plausible values, strengthens modeling efforts by enabling inclusion of more patients whose data ordinarily would be eliminated from model generation because of missing values. It should be noted, however, that the validity of post-imputation estimates depends on the assumption that the missing data are missing at random (MAR), i.e., the probability that an observation is missing can depend on the values of observed items but not on the value of the missing item itself. Thus, for example, if the probability that a value

5 M.K. Ferguson et al. / European Journal of Cardio-thoracic Surgery 34 (2008) is missing is greater in males than females and gender is recorded, then the data satisfy the MAR assumption. On the other hand, if a value is more likely to be missing when the true (but unobserved) value of the variable itself is large, then the data would not satisfy the MAR assumption. Our findings are similar to some previously published findings, in which diffusing capacity was identified as the single strongest predictor of complications (pulmonary, overall, mortality) following major lung resection [17 19]. Additional previously reported determinants of complications that approached or achieved statistical significance in this analysis included FEV1% (pulmonary, cardiovascular), performance status (overall, mortality), age (cardiovascular, mortality), the extent of surgery (cardiovascular, mortality), chronic obstructive lung disease (COPD, defined as FEV1/FVC ratio <0.7; overall complications), and year of operation (cardiovascular, mortality). In addition, as suspected in our preliminary review of these data, serum albumin approached or achieved statistical significance as a predictor of outcomes including pulmonary, cardiovascular, and overall complications. That serum albumin is an important predictor of complications after major lung surgery is not surprising. Weight loss and low body cell mass are correlated with low serum albumin in patients with lung cancer, and are associated with systemic inflammation that may contribute to an increased risk of postoperative complications [20]. Other authors have reported an association between low serum albumin and postoperative pulmonary complications, ascribing the utility of serum albumin as a determinant of outcomes to its value as a surrogate for overall nutritional and/or immune status [21,22]. Because multiple imputation incorporates additional variability into parameter estimates to account for the uncertainty due to missing values being unknown, standard errors of parameter estimates tend to be larger than in analyses with no missing values. As a result, the importance of serum albumin in our models is likely to be understated. In summary, in addition to confirming the role of diffusing capacity in predicting postoperative complications after major lung resection, we report that serum albumin is also a strong predictor of such complications. Its routine measurement may improve estimates of risk in patients who are candidates for lung resection. 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