Database and coding
Data were derived from the Hospital Episode Statistics (HES) database . All patients over the age of 17 years who underwent elective MIE for esophageal cancer between January 1, 2002, and March 31, 2012, were included in the study. Cancer diagnoses were identified using the relevant International Classification of Disease 10th revision (ICD-10) codes (C15 and D00.1). Procedures were identified using the Office of Population Censuses and Surveys Classification of Surgical Operations and Procedures 4th revision (OPCS) codes. These were G01, G02 and G03 for esophagectomy and were used in combination with Y50.8, Y75, and Y71.4 for laparoscopic and Y49.8 and Y74 for thoracoscopic to identify those patients receiving MIE. Permissions for the comparison of anonymized administrative data were obtained from the National Information Governance Board for Health and Social Care in England.
Outcome measures evaluated included conversion rate from MIE to open esophagectomy, 30-day re-intervention (surgical), 30-day and 90-day mortality.
We retrieved administrative datasets on MIE resections (OES) (N = 1696). To ensure meaningful analyses of the proficiency-gain curves, we selected clinicians who had performed a minimum of 5 cases including at least one adverse event (i.e., conversion, re-intervention or mortality). We also performed a subset analysis of those surgeons who performed a minimum of 20 cases including one adverse event. We analyzed conversion rates, re-intervention, 30-day mortality and 90-day mortality for MIE.
Procedural interval (days)
We assessed the procedural interval by the ratio of the number of days elapsed since the last case and the number of cases carried out so far. For example, if Surgeon A carried out his first, second and third case (i.e., Case 1, 2 and 3) on Day 1, Day 30 and Day 60, respectively. The procedural intervals were, respectively, 0 (= 0/1) for Case 1, 15 days (= 30/2) for Case 2 and 20 days (= 60/3) for Case 3.
Relationship between procedural interval and clinical outcomes
We performed logistic regressions to investigate relationships between procedural interval and the clinical outcomes, adjusting for patient age (< 70 years or ≥ 70 years), sex (male or female) and medical comorbidities as measured by the Charlson comorbidity index score (< 2 or ≥ 2). To understand potential differences from procedural intervals that were small vs. large, we defined low procedural interval cases as those cases carried out within certain time limit from the previous cases, e.g., within 7 days. To determine what these limits are, we carried out change-point modeling whereby multivariate logistic regression models were fitted for each of the outcome variables using patient age, sex and Charlson scores  as independent variables. Procedural interval was captured by a dummy variable that took the value of 1 or 0, which corresponds to whether or not the case gap was below or above the cutoff value. Different relationships between an outcome variable and procedural interval were captured by the interaction between the dummy variable and the patient comorbidities.
We assumed that such cutoffs might take any value between the minimum and maximum procedural interval. We ran the change-point models iteratively, using a gap of 5 between the cutoffs. That is, if the minimum and maximum procedural interval was 0 and 100, we ran the model under assumed cutoffs of 5, 10, 15,…, 100. We then compared the model fit and derived the cutoff from the model that had the smallest deviances.
These cutoffs were used to define low procedural interval cases. We also carried out multivariate logistic regressions to investigate relationships between procedural interval and the clinical outcomes.
Relationship between procedural interval and number of cases required to gain proficiency
We analyzed number of cases required to gain proficiency for each individual surgeon also by employing change-point modeling. One modification was the definition of dummy variable, which took the value of 1 or 0 depending on whether the case volume was above or below certain cutoffs. We assumed that a cutoff could take any value from 1 to the maximum. The number of cases required to gain proficiency was derived from the best-fitted regression model (as above) for each individual surgeon. We then carried out a linear regression to investigate the relationship between the number of cases required to gain proficiency and average procedural interval by surgeon within their respective proficiency gain period.
We used t test for continuous variables and Chi-square test for categorical variables to identify any significant differences between age, sex and Charlson comorbidity index score and case gaps. We performed the analyses in Excel and in open-source software R (version 3.3.0 for Mac OS X, generalized linear mixed models package lme4).