A nonparametric method of comparing the partial areas under two correlated receiver operating characteristic curves

A non-parametric method was developed and tested to compare the partial areas under two correlated Receiver Operating Characteristic curves. Based on the theory of generalized U-statistics the mathematical formulas have been derived for computing ROC area, and the variance and covariance between the portions of two ROC curves. A practical SAS application also has been developed to facilitate the calculations. The accuracy of the non-parametric method was evaluated by comparing it to other methods. By applying our method to the data from a published ROC analysis of CT image, our results are very close to theirs. A hypothetical example was used to demonstrate the effects of two crossed ROC curves. The two ROC areas are the same. However each portion of the area between two ROC curves were found to be significantly different by the partial ROC curve analysis. For computation of ROC curves with large scales, such as a logistic regression model, we applied our method to the breast cancer study with Medicare claims data. It yielded the same ROC area computation as the SAS Logistic procedure. Our method also provides an alternative to the global summary of ROC area comparison by directly comparing the true-positive rates for two regression models and by determining the range of false-positive values where the models differ. ^

STUDY OF THE EFFECTS OF TOTAL MODULATION TRANSFER FUNCTION CHANGES ON OBSERVER PERFORMANCE USING CLINICAL MAMMOGRAMS

The main goal of this study was to relate physical changes in image quality measured by Modulation Transfer Function (MTF) to diagnostic accuracy.^ One Hundred and Fifty Kodak Min-R screen/film combination conventional craniocaudal mammograms obtained with the Pfizer Microfocus Mammographic system were selected from the files of the Department of Radiology, at M.D. Anderson Hospital and Tumor Institute.^ The mammograms included 88 cases with a variety of benign diagnosis and 62 cases with a variety of malignant biopsy diagnosis. The average age of the patient population was 55 years old. 70 cases presented calcifications with 30 cases having calcifications smaller than 0.5mm. 46 cases presented irregular bordered masses larger than 1 cm. 30 cases presented smooth bordered masses with 20 larger than 1 cm.^ Four separated copies of the original images were made each having a different change in the MTF using a defocusing technique whereby copies of the original were obtained by light exposure through different thicknesses (spacing) of transparent film base.^ The mammograms were randomized, and evaluated by three experienced mammographers for the degree of visibility of various anatomical breast structures and pathological lesions (masses and calicifications), subjective image quality, and mammographic interpretation.^ 3,000 separate evaluations were anayzed by several statistical techniques including Receiver Operating Characteristic curve analysis, McNemar test for differences between proportions and the Landis et al. method of agreement weighted kappa for ordinal categorical data.^ Results from the statistical analysis show: (1) There were no statistical significant differences in the diagnostic accuracy of the observers when diagnosing from mammograms with the same MTF. (2) There were no statistically significant differences in diagnostic accuracy for each observer when diagnosing from mammograms with the different MTF's used in the study. (3) There statistical significant differences in detail visibility between the copies and the originals. Detail visibility was better in the originals. (4) Feature interpretations were not significantly different between the originals and the copies. (5) Perception of image quality did not affect image interpretation.^ Continuation and improvement of this research ca be accomplished by: using a case population more sensitive to MTF changes, i.e., asymptomatic women with minimum breast cancer, more observers (including less experienced radiologists and experienced technologists) must collaborate in the study, and using a minimum of 200 benign and 200 malignant cases.^

Bayesian and survival model for tumor relapse status and disease-specific survival, with applications to breast cancer

Breast cancer is the most common non-skin cancer and the second leading cause of cancer-related death in women in the United States. Studies on ipsilateral breast tumor relapse (IBTR) status and disease-specific survival will help guide clinic treatment and predict patient prognosis.^ After breast conservation therapy, patients with breast cancer may experience breast tumor relapse. This relapse is classified into two distinct types: true local recurrence (TR) and new ipsilateral primary tumor (NP). However, the methods used to classify the relapse types are imperfect and are prone to misclassification. In addition, some observed survival data (e.g., time to relapse and time from relapse to death)are strongly correlated with relapse types. The first part of this dissertation presents a Bayesian approach to (1) modeling the potentially misclassified relapse status and the correlated survival information, (2) estimating the sensitivity and specificity of the diagnostic methods, and (3) quantify the covariate effects on event probabilities. A shared frailty was used to account for the within-subject correlation between survival times. The inference was conducted using a Bayesian framework via Markov Chain Monte Carlo simulation implemented in softwareWinBUGS. Simulation was used to validate the Bayesian method and assess its frequentist properties. The new model has two important innovations: (1) it utilizes the additional survival times correlated with the relapse status to improve the parameter estimation, and (2) it provides tools to address the correlation between the two diagnostic methods conditional to the true relapse types.^ Prediction of patients at highest risk for IBTR after local excision of ductal carcinoma in situ (DCIS) remains a clinical concern. The goals of the second part of this dissertation were to evaluate a published nomogram from Memorial Sloan-Kettering Cancer Center, to determine the risk of IBTR in patients with DCIS treated with local excision, and to determine whether there is a subset of patients at low risk of IBTR. Patients who had undergone local excision from 1990 through 2007 at MD Anderson Cancer Center with a final diagnosis of DCIS (n=794) were included in this part. Clinicopathologic factors and the performance of the Memorial Sloan-Kettering Cancer Center nomogram for prediction of IBTR were assessed for 734 patients with complete data. Nomogram for prediction of 5- and 10-year IBTR probabilities were found to demonstrate imperfect calibration and discrimination, with an area under the receiver operating characteristic curve of .63 and a concordance index of .63. In conclusion, predictive models for IBTR in DCIS patients treated with local excision are imperfect. Our current ability to accurately predict recurrence based on clinical parameters is limited.^ The American Joint Committee on Cancer (AJCC) staging of breast cancer is widely used to determine prognosis, yet survival within each AJCC stage shows wide variation and remains unpredictable. For the third part of this dissertation, biologic markers were hypothesized to be responsible for some of this variation, and the addition of biologic markers to current AJCC staging were examined for possibly provide improved prognostication. The initial cohort included patients treated with surgery as first intervention at MDACC from 1997 to 2006. Cox proportional hazards models were used to create prognostic scoring systems. AJCC pathologic staging parameters and biologic tumor markers were investigated to devise the scoring systems. Surveillance Epidemiology and End Results (SEER) data was used as the external cohort to validate the scoring systems. Binary indicators for pathologic stage (PS), estrogen receptor status (E), and tumor grade (G) were summed to create PS+EG scoring systems devised to predict 5-year patient outcomes. These scoring systems facilitated separation of the study population into more refined subgroups than the current AJCC staging system. The ability of the PS+EG score to stratify outcomes was confirmed in both internal and external validation cohorts. The current study proposes and validates a new staging system by incorporating tumor grade and ER status into current AJCC staging. We recommend that biologic markers be incorporating into revised versions of the AJCC staging system for patients receiving surgery as the first intervention.^ Chapter 1 focuses on developing a Bayesian method to solve misclassified relapse status and application to breast cancer data. Chapter 2 focuses on evaluation of a breast cancer nomogram for predicting risk of IBTR in patients with DCIS after local excision gives the statement of the problem in the clinical research. Chapter 3 focuses on validation of a novel staging system for disease-specific survival in patients with breast cancer treated with surgery as the first intervention. ^

TIME SERIES ANALYSIS AS INPUT FOR PREDICTIVE MODELING: PREDICTING CARDIAC ARREST IN A PEDIATRIC INTENSIVE CARE UNIT

The first manuscript, entitled "Time-Series Analysis as Input for Clinical Predictive Modeling: Modeling Cardiac Arrest in a Pediatric ICU" lays out the theoretical background for the project. There are several core concepts presented in this paper. First, traditional multivariate models (where each variable is represented by only one value) provide single point-in-time snapshots of patient status: they are incapable of characterizing deterioration. Since deterioration is consistently identified as a precursor to cardiac arrests, we maintain that the traditional multivariate paradigm is insufficient for predicting arrests. We identify time series analysis as a method capable of characterizing deterioration in an objective, mathematical fashion, and describe how to build a general foundation for predictive modeling using time series analysis results as latent variables. Building a solid foundation for any given modeling task involves addressing a number of issues during the design phase. These include selecting the proper candidate features on which to base the model, and selecting the most appropriate tool to measure them. We also identified several unique design issues that are introduced when time series data elements are added to the set of candidate features. One such issue is in defining the duration and resolution of time series elements required to sufficiently characterize the time series phenomena being considered as candidate features for the predictive model. Once the duration and resolution are established, there must also be explicit mathematical or statistical operations that produce the time series analysis result to be used as a latent candidate feature. In synthesizing the comprehensive framework for building a predictive model based on time series data elements, we identified at least four classes of data that can be used in the model design. The first two classes are shared with traditional multivariate models: multivariate data and clinical latent features. Multivariate data is represented by the standard one value per variable paradigm and is widely employed in a host of clinical models and tools. These are often represented by a number present in a given cell of a table. Clinical latent features derived, rather than directly measured, data elements that more accurately represent a particular clinical phenomenon than any of the directly measured data elements in isolation. The second two classes are unique to the time series data elements. The first of these is the raw data elements. These are represented by multiple values per variable, and constitute the measured observations that are typically available to end users when they review time series data. These are often represented as dots on a graph. The final class of data results from performing time series analysis. This class of data represents the fundamental concept on which our hypothesis is based. The specific statistical or mathematical operations are up to the modeler to determine, but we generally recommend that a variety of analyses be performed in order to maximize the likelihood that a representation of the time series data elements is produced that is able to distinguish between two or more classes of outcomes. The second manuscript, entitled "Building Clinical Prediction Models Using Time Series Data: Modeling Cardiac Arrest in a Pediatric ICU" provides a detailed description, start to finish, of the methods required to prepare the data, build, and validate a predictive model that uses the time series data elements determined in the first paper. One of the fundamental tenets of the second paper is that manual implementations of time series based models are unfeasible due to the relatively large number of data elements and the complexity of preprocessing that must occur before data can be presented to the model. Each of the seventeen steps is analyzed from the perspective of how it may be automated, when necessary. We identify the general objectives and available strategies of each of the steps, and we present our rationale for choosing a specific strategy for each step in the case of predicting cardiac arrest in a pediatric intensive care unit. Another issue brought to light by the second paper is that the individual steps required to use time series data for predictive modeling are more numerous and more complex than those used for modeling with traditional multivariate data. Even after complexities attributable to the design phase (addressed in our first paper) have been accounted for, the management and manipulation of the time series elements (the preprocessing steps in particular) are issues that are not present in a traditional multivariate modeling paradigm. In our methods, we present the issues that arise from the time series data elements: defining a reference time; imputing and reducing time series data in order to conform to a predefined structure that was specified during the design phase; and normalizing variable families rather than individual variable instances. The final manuscript, entitled: "Using Time-Series Analysis to Predict Cardiac Arrest in a Pediatric Intensive Care Unit" presents the results that were obtained by applying the theoretical construct and its associated methods (detailed in the first two papers) to the case of cardiac arrest prediction in a pediatric intensive care unit. Our results showed that utilizing the trend analysis from the time series data elements reduced the number of classification errors by 73%. The area under the Receiver Operating Characteristic curve increased from a baseline of 87% to 98% by including the trend analysis. In addition to the performance measures, we were also able to demonstrate that adding raw time series data elements without their associated trend analyses improved classification accuracy as compared to the baseline multivariate model, but diminished classification accuracy as compared to when just the trend analysis features were added (ie, without adding the raw time series data elements). We believe this phenomenon was largely attributable to overfitting, which is known to increase as the ratio of candidate features to class examples rises. Furthermore, although we employed several feature reduction strategies to counteract the overfitting problem, they failed to improve the performance beyond that which was achieved by exclusion of the raw time series elements. Finally, our data demonstrated that pulse oximetry and systolic blood pressure readings tend to start diminishing about 10-20 minutes before an arrest, whereas heart rates tend to diminish rapidly less than 5 minutes before an arrest.

The performance of human papillomavirus high-risk DNA testing in the screening and diagnostic settings.

OBJECTIVE: We sought to evaluate the performance of the human papillomavirus high-risk DNA test in patients 30 years and older. MATERIALS AND METHODS: Screening (n=835) and diagnosis (n=518) groups were defined based on prior Papanicolaou smear results as part of a clinical trial for cervical cancer detection. We compared the Hybrid Capture II (HCII) test result with the worst histologic report. We used cervical intraepithelial neoplasia (CIN) 2/3 or worse as the reference of disease. We calculated sensitivities, specificities, positive and negative likelihood ratios (LR+ and LR-), receiver operating characteristic (ROC) curves, and areas under the ROC curves for the HCII test. We also considered alternative strategies, including Papanicolaou smear, a combination of Papanicolaou smear and the HCII test, a sequence of Papanicolaou smear followed by the HCII test, and a sequence of the HCII test followed by Papanicolaou smear. RESULTS: For the screening group, the sensitivity was 0.69 and the specificity was 0.93; the area under the ROC curve was 0.81. The LR+ and LR- were 10.24 and 0.34, respectively. For the diagnosis group, the sensitivity was 0.88 and the specificity was 0.78; the area under the ROC curve was 0.83. The LR+ and LR- were 4.06 and 0.14, respectively. Sequential testing showed little or no improvement over the combination testing. CONCLUSIONS: The HCII test in the screening group had a greater LR+ for the detection of CIN 2/3 or worse. HCII testing may be an additional screening tool for cervical cancer in women 30 years and older.

Assessing the improved discriminatory power of a new biomarker in prognostic models

Although the area under the receiver operating characteristic (AUC) is the most popular measure of the performance of prediction models, it has limitations, especially when it is used to evaluate the added discrimination of a new biomarker in the model. Pencina et al. (2008) proposed two indices, the net reclassification improvement (NRI) and integrated discrimination improvement (IDI), to supplement the improvement in the AUC (IAUC). Their NRI and IDI are based on binary outcomes in case-control settings, which do not involve time-to-event outcome. However, many disease outcomes are time-dependent and the onset time can be censored. Measuring discrimination potential of a prognostic marker without considering time to event can lead to biased estimates. In this dissertation, we have extended the NRI and IDI to survival analysis settings and derived the corresponding sample estimators and asymptotic tests. Simulation studies were conducted to compare the performance of the time-dependent NRI and IDI with Pencina’s NRI and IDI. For illustration, we have applied the proposed method to a breast cancer study.^ Key words: Prognostic model, Discrimination, Time-dependent NRI and IDI ^

ACCURACY OF THE BRCAPRO RISK ASSESSMENT MODEL IN MALES PRESENTING TO MD ANDERSON FOR BRCA TESTING

ACCURACY OF THE BRCAPRO RISK ASSESSMENT MODEL IN MALES PRESENTING TO MD ANDERSON FOR BRCA TESTING Publication No. _______ Carolyn A. Garby, B.S. Supervisory Professor: Banu Arun, M.D. Hereditary Breast and Ovarian Cancer (HBOC) syndrome is due to mutations in BRCA1 and BRCA2 genes. Women with HBOC have high risks to develop breast and ovarian cancers. Males with HBOC are commonly overlooked because male breast cancer is rare and other male cancer risks such as prostate and pancreatic cancers are relatively low. BRCA genetic testing is indicated for men as it is currently estimated that 4-40% of male breast cancers result from a BRCA1 or BRCA2 mutation (Ottini, 2010) and management recommendations can be made based on genetic test results. Risk assessment models are available to provide the individualized likelihood to have a BRCA mutation. Only one study has been conducted to date to evaluate the accuracy of BRCAPro in males and was based on a cohort of Italian males and utilized an older version of BRCAPro. The objective of this study is to determine if BRCAPro5.1 is a valid risk assessment model for males who present to MD Anderson Cancer Center for BRCA genetic testing. BRCAPro has been previously validated for determining the probability of carrying a BRCA mutation, however has not been further examined particularly in males. The total cohort consisted of 152 males who had undergone BRCA genetic testing. The cohort was stratified by indication for genetic counseling. Indications included having a known familial BRCA mutation, having a personal diagnosis of a BRCA-related cancer, or having a family history suggestive of HBOC. Overall there were 22 (14.47%) BRCA1+ males and 25 (16.45%) BRCA2+ males. Receiver operating characteristic curves were constructed for the cohort overall, for each particular indication, as well as for each cancer subtype. Our findings revealed that the BRCAPro5.1 model had perfect discriminating ability at a threshold of 56.2 for males with breast cancer, however only 2 (4.35%) of 46 were found to have BRCA2 mutations. These results are significantly lower than the high approximation (40%) reported in previous literature. BRCAPro does perform well in certain situations for men. Future investigation of male breast cancer and men at risk for BRCA mutations is necessary to provide a more accurate risk assessment.

External validation study of a clinical prediction rule for ambulation outcomes after traumatic spinal cord injury

The main objective of this study was to determine the external validity of a clinical prediction rule developed by the European Multicenter Study on Human Spinal Cord Injury (EM-SCI) to predict the ambulation outcomes 12 months after traumatic spinal cord injury. Data from the North American Clinical Trials Network (NACTN) data registry with approximately 500 SCI cases were used for this validity study. The predictive accuracy of the EM-SCI prognostic model was evaluated using calibration and discrimination based on 231 NACTN cases. The area under the receiver-operating-characteristics curve (ROC) curve was 0.927 (95% CI 0.894 – 0.959) for the EM-SCI model when applied to NACTN population. This is lower than the AUC of 0.956 (95% CI 0.936 – 0.976) reported for the EM-SCI population, but suggests that the EM-SCI clinical prediction rule distinguished well between those patients in the NACTN population who were able to achieve independent ambulation and those who did not achieve independent ambulation. The calibration curve suggests that higher the prediction score is, the better the probability of walking with the best prediction for AIS D patients. In conclusion, the EM-SCI clinical prediction rule was determined to be generalizable to the adult NACTN SCI population.^

Comparison of Bispectral Index (BIS) and Patient State Index (PSI) as objective measures of sedation and analgesia in critically ill/injured patients

Critically ill and injured patients require pain relief and sedation to reduce the body's stress response and to facilitate painful diagnostic and therapeutic procedures. Presently, the level of sedation and analgesia is guided by the use of clinical scores which can be unreliable. There is therefore, a need for an objective measure of sedation and analgesia. The Bispectral Index (BIS) and Patient State Index (PSI) were recently introduced into clinical practice as objective measures of the depth of analgesia and sedation. ^ Aim. To compare the different measures of sedation and analgesia (BIS and PSI) to the standard and commonly used modified Ramsay Score (MRS) and determine if the monitors can be used interchangeably. ^ Methods. MRS, BIS and PSI values were obtained in 50 postoperative cardiac surgery patients requiring analgesia and sedation from June to December 2004. The MRS, BIS and PSI values were assessed hourly for up to 6-h by a single observer. ^ The relationship between BIS and PSI values were explored using scatter plots and correlation between MRS, BIS and PSI was determined using Spearman's correlation coefficient. Intra-class correlation (ICC) was used to determine the inter-rater reliability of MRS, BIS and PSI. Kappa statistics was used to further evaluate the agreement between BIS and PSI at light, moderate and deep levels of sedation. ^ Results. There was a positive correlation between BIS and PSI values (Rho = 0.731, p<0.001). Intra-class correlation between BIS and PSI was 0.58, MRS and BIS 0.43 and MRS and PSI 0.27. Using Kappa statistics, agreement between MRS and BIS was 0.35 (95% CI: 0.27–0.43) and for MRS and PSI was 0.21 (95% CI: 0.15–0.28). The kappa statistic for BIS and PSI was 0.45 (95% CI: 0.37–0.52). Receiver operating characteristics (ROC) curves constructed to detect undersedation indicated an area under the curve (AUC) of 0.91 (95% CI = 0.87 to 0.94) for the BIS and 0.84 (95% CI = 0.79 to 0.88) for the PSI. For detection of oversedation, AUC for the BIS was 0.89 (95% CI = 0.84 to 0.92) and 0.80 (95% CI = 0.75 to 0.85) for the PSI. ^ Conclusions. There is a statistically significant positive correlation between the BIS and PSI but poor correlation and poor test agreement between the MRS and BIS as well as MRS and PSI. Both the BIS and PSI demonstrated a high level of prediction for undersedation and oversedation; however, the BIS and PSI can not be considered interchangeable monitors of sedation. ^

Performance of HbA1c for classifying diabetes and diagnostic threshold for diabetes among the Mexican American border community

Objective. In 2009, the International Expert Committee recommended the use of HbA1c test for diagnosis of diabetes. Although it has been recommended for the diagnosis of diabetes, its precise test performance among Mexican Americans is uncertain. A strong “gold standard” would rely on repeated blood glucose measurement on different days, which is the recommended method for diagnosing diabetes in clinical practice. Our objective was to assess test performance of HbA1c in detecting diabetes and pre-diabetes against repeated fasting blood glucose measurement for the Mexican American population living in United States-Mexico border. Moreover, we wanted to find out a specific and precise threshold value of HbA1c for Diabetes Mellitus (DM) and pre-diabetes for this high-risk population which might assist in better diagnosis and better management of patient diabetes. ^ Research design and methods. We used CCHC dataset for our study. In 2004, the Cameron County Hispanic Cohort (CCHC), now numbering 2,574, was established drawn from randomly selected households on the basis of 2000 Census tract data. The CCHC study randomly selected a subset of people (aged 18-64 years) in CCHC cohort households to determine the influence of SES on diabetes and obesity. Among the participants in Cohort-2000, 67.15% are female; all are Hispanic. ^ Individuals were defined as having diabetes mellitus (Fasting plasma glucose [FPG] ≥ 126 mg/dL or pre-diabetes (100 ≤ FPG < 126 mg/dL). HbA1c test performance was evaluated using receiver operator characteristic (ROC) curves. Moreover, change-point models were used to determine HbA1c thresholds compatible with FPG thresholds for diabetes and pre-diabetes. ^ Results. When assessing Fasting Plasma Glucose (FPG) is used to detect diabetes, the sensitivity and specificity of HbA1c≥ 6.5% was 75% and 87% respectively (area under the curve 0.895). Additionally, when assessing FPG to detect pre-diabetes, the sensitivity and specificity of HbA1c≥ 6.0% (ADA recommended threshold) was 18% and 90% respectively. The sensitivity and specificity of HbA1c≥ 5.7% (International Expert Committee recommended threshold) for detecting pre-diabetes was 31% and 78% respectively. ROC analyses suggest HbA1c as a sound predictor of diabetes mellitus (area under the curve 0.895) but a poorer predictor for pre-diabetes (area under the curve 0.632). ^ Conclusions. Our data support the current recommendations for use of HbA1c in the diagnosis of diabetes for the Mexican American population as it has shown reasonable sensitivity, specificity and accuracy against repeated FPG measures. However, use of HbA1c may be premature for detecting pre-diabetes in this specific population because of the poor sensitivity with FPG. It might be the case that HbA1c is differentiating the cases more effectively who are at risk of developing diabetes. Following these pre-diabetic individuals for a longer-term for the detection of incident diabetes may lead to more confirmatory result.^

Learning curve for robotic-assisted laparoscopic colorectal surgery.

BACKGROUND: Robotic-assisted laparoscopic surgery (RALS) is evolving as an important surgical approach in the field of colorectal surgery. We aimed to evaluate the learning curve for RALS procedures involving resections of the rectum and rectosigmoid. METHODS: A series of 50 consecutive RALS procedures were performed between August 2008 and September 2009. Data were entered into a retrospective database and later abstracted for analysis. The surgical procedures included abdominoperineal resection (APR), anterior rectosigmoidectomy (AR), low anterior resection (LAR), and rectopexy (RP). Demographic data and intraoperative parameters including docking time (DT), surgeon console time (SCT), and total operative time (OT) were analyzed. The learning curve was evaluated using the cumulative sum (CUSUM) method. RESULTS: The procedures performed for 50 patients (54% male) included 25 AR (50%), 15 LAR (30%), 6 APR (12%), and 4 RP (8%). The mean age of the patients was 54.4 years, the mean BMI was 27.8 kg/m(2), and the median American Society of Anesthesiologists (ASA) classification was 2. The series had a mean DT of 14 min, a mean SCT of 115.1 min, and a mean OT of 246.1 min. The DT and SCT accounted for 6.3% and 46.8% of the OT, respectively. The SCT learning curve was analyzed. The CUSUM(SCT) learning curve was best modeled as a parabola, with equation CUSUM(SCT) in minutes equal to 0.73 × case number(2) - 31.54 × case number - 107.72 (R = 0.93). The learning curve consisted of three unique phases: phase 1 (the initial 15 cases), phase 2 (the middle 10 cases), and phase 3 (the subsequent cases). Phase 1 represented the initial learning curve, which spanned 15 cases. The phase 2 plateau represented increased competence with the robotic technology. Phase 3 was achieved after 25 cases and represented the mastery phase in which more challenging cases were managed. CONCLUSIONS: The three phases identified with CUSUM analysis of surgeon console time represented characteristic stages of the learning curve for robotic colorectal procedures. The data suggest that the learning phase was achieved after 15 to 25 cases.