In times with increasing health care costs and scarcity in health care budgets, efficiency within hospitals is becoming of the utmost importance. More than 60% of the patients admitted to a hospital are treated in the operating room (OR). Therefore, the OR is one of the major consumers of the total health care budget.1 Accurate OR scheduling is critical for efficiency but remains a challenging problem because of the high inherit variability in OR time.2,3 Variability in OR time causes overutilization and underutilization of the available OR capacity. This inefficient use and overutilization of OR time may lead not only to a waste of resources but also to dissatisfaction and reduced motivation of the surgical staff and increased patient waiting times.4
In the literature, there is a wide availability of methods to estimate OR time ranging from simple estimations based on the sample mean to complex Bayesian prediction models.5 In general, the accuracy of prediction models for continuous outcomes (such as OR time) depends strongly on its capability to model the variability in an outcome.6,7 To increase the accuracy of OR time prediction models, it is, therefore, critical to identify sources of variability in OR time. Subsequently, future prediction models can then be expanded to account for these sources of variability.
There are several research articles that investigated sources of variability in OR time.1,8,10 Not surprising, the type of procedure is the single most important source of variation.1,4,10 The effect of patients characteristics (ie, age, sex, and body mass index) on OR time is rather small in comparison with the type of procedure.1,11 Sources of variability in anesthesia time, and thus total OR time, were identified as well and are mainly because of the anesthetic technique and type of procedure.2,12,13 Several studies showed the importance of surgical team characteristics on OR time.1,9,10,14–18 It is believed that after the type of procedure, the surgeon is the single most important source of variability in OR time.10 The variability in OR time between surgeons can be explained by a difference in work rate9,10; however, it seems that not only a difference in work rate but also that the surgeon’s age and experience with a certain procedure have important effects on OR time.1,9,16 In particular, the age of the youngest and oldest surgeon are important during a certain procedure; they may act as surrogates for the surgeon’s level of experience and the difficulty of a certain procedure.1 Furthermore, the accuracy of the surgeon’s estimate of the OR time may differ between surgeons and may thus lead to an increased variability in OR time.18 All these factors are properties of the individual surgeon or properties of combinations of surgeons. Therefore, it seems plausible that the individual surgeon should account for a fairly large part of the variability in OR time. The effects of these specific surgeon characteristics on OR time are well shown in the literature; however, a clear quantification of the exact amount of variability that can be accounted to the individual surgeons is currently lacking.
The authors of several studies have reported prediction models, using the specific combination of the surgeon and type of procedure and have shown to improve the accuracy of OR time estimation19; however, these models do not take into account the individual characteristics of the patient. As was shown previously, modeling individual case characteristics substantially improved the prediction of OR time.1 Thus, a prediction model based on individual case characteristics and accounting for the variability between surgeons might further improve the prediction of OR time; however, as stated previously, currently, there is no clear quantification available of the surgeon’s variability in OR time, and the exact effects of individual surgeons on the prediction of OR time are unknown. Therefore, the primary aim of this study is to quantify the variability between surgeons in comparison with the type of procedure. Because anesthesia time is an important part of the total OR time,12 our secondary aim was to quantify the variability between anesthesiologists. As illustration, the value of modeling these sources variability for the prediction of OR time will be estimated.
Data and Subjects
To reliably estimate the additional value of modeling the individual surgeons and anesthesiologists during a procedure, we used the same data set as from our previous model based on the individual case characteristics.1 In short, data of the operative sessions were obtained from the Erasmus University Medical Center, Department of General Surgery (Rotterdam, the Netherlands). All operative sessions were registered electronically since January 1993. From this date until June 2005, all consecutive elective operations performed were included in our data set. Data were matched with data from the general electronic hospital information system for details about risk factors of surgical complications (ie, cardiovascular diseases or diabetes). The final database contained 17,412 cases, classified into 253 different types of procedures according to the main procedure during a session. When multiple procedures were performed during a case (ie, breast reconstruction after mastectomy), the operation was coded according to the main procedure. The main procedure was determined from a priority list that was constructed by surgeons of the general surgery department. This method was preferred over statistical determination of the longest procedure,20 because some procedures were never performed in isolation. For accurate determination of the variability between surgeons and anesthesiologists, cases without an anesthesiologist and/or a second surgeon were excluded. The second surgeon is defined as the first registered assistant surgeon during a procedure. After removal, 16,389 cases, classified into 251 different surgical procedures, remained for data analysis.
The total OR time was defined as the elapsed time between the patients’ arrival at the OR and departure from the OR. The recorded data contained the following: (1) procedure characteristics (expected duration, number of separate procedures, and laparoscopic or open surgery), (2) operating team characteristics (surgeon, second surgeon, anesthesiologist, total of the ages as a measure of the combined experience, age of the youngest and oldest surgeon, and number of surgeons and anesthesiologists), and (3) patient characteristics (age, sex, the number of admissions before the operation, length of current admission, body mass index, and cardiovascular risk factors [diabetes, hypercholesterolemia, hypertension, heart failure, cerebrovascular accident, chronic obstructive pulmonary disease, and renal and cardiac diseases]). Log transforming the OR time was necessary because of right skewness.1,10,20 A more detailed description of multiple imputation of missing data and the corrections that were necessary to make the data suitable for prediction modeling can be found in our previous article.1
The primary aim was to estimate how much of the total amount of variability in log OR time can be accounted for by the type of procedure, surgeon, and anesthesiologist. First, the total amount of variability (or variance) in log OR time was estimated. Subsequently, for the type of procedure, surgeon, or anesthesiologist, their unique part of this total variance was determined. The random effects part of linear mixed models (LMMs) was used to estimate these variance components, because LMM allow inclusion of infrequent procedures, surgeons, or anesthesiologists, even those that only occurred once.1,5
It was hypothesized that for certain procedures, the difference between surgeons (or anesthesiologists) could be bigger than for other procedures. Thus, for highly technical procedures, surgeons may perform less similar than for relatively easy routine procedures. This means that variability between surgeons and anesthesiologists depends on the type of procedure. Furthermore, the difference between first surgeons could depend on the second surgeon (and vice versa). In example, the OR time for a certain procedure performed by 2 senior surgeons is probably different from the OR time when there is 1 senior and 1 junior surgeon. Therefore, interaction terms were constructed for the type of procedure with the first surgeon, second surgeon, and anesthesiologist and for the first surgeon with the second surgeon. To illustrate the construction of the final multivariate random effect LMM with only an intercept, the equation was given by the following:
In this model, Yij represents the predicted log OR time, β0 the intercept and μ0 … the various random effects. εij is the residual variance and is the part that the model cannot explain. The total variance in this model is the sum of all random effect variances plus the residual variance. Dividing the variance attributed to a certain random effect (ie, the variance of μ0 procedure) by the total variance will give the percentage of the total variance that can be accounted for by the random effect (known as intraclass correlation coefficient [ICC]21). Thus, the ICC represents how much of the total variability in log OR time can be accounted for by the surgeons, anesthesiologists, and types of procedures.
The second aim of the analysis was to illustrate the improvement of a prediction model incorporating the aforementioned random effects. All models were corrected for predictive factors as fixed effects (surgeon’s estimate and the operation, team, and patient characteristics). The total variance was calculated in a base model with only a random intercept for the type of procedure. The random effects terms subsequently were added to the model to evaluate how much the unexplained variance could be reduced. The ratio explained/unexplained variance was given by the adjusted R2. In example, when the adjusted R2 was 70%, this indicated that 70% of the variance in OR time could be explained by the model and 30% was left unexplained. To quantify the improvement of a new model compared with the base model, the gain in adjusted R2 was calculated as (R2model − R2base)/(1 − R2base). Model fit was further evaluated by Akaike information criterion (AIC) and likelihood ratio tests. For each random effect, the absolute reduction in over and idle time (in minutes) was estimated. The 95% confidence intervals (CIs) around these estimates were bootstrapped by drawing 2000 random samples. Predictions in log OR time were multiplied by a smearing factor to reduce back-transformation bias.22 After the random effects parts were fitted, the fixed effect part of the model was stepwise reduced based on the AIC to obtain the most parsimonious model. For the final model, the ICCs for the type of procedure, surgeons, and anesthesiologist were recalculated. We evaluated the stability of the variance estimates and their 95% CIs by refitting the model several times and determining ζ for each random effect.23 LMMs were fitted using the lmer function in the R package lme4 (version 1.1–11).31
The final database contained 251 different types of procedures, 215 first surgeons, 243 second surgeons, and 168 anesthesiologists. Figure 1 shows the median OR time for all types of procedures, surgeons, and anesthesiologists univariately. The type of procedure has the widest interquartile range and showed the highest variability in median OR time. Table 1 summarizes the ICCs obtained from univariate models (incorporating only 1 random effect) with and without correction for the predictive factors. In accordance with Figure 1, the type of procedure caused the largest variability in log OR time and accounted for 33.1% (CI, 27.0–41.0) of the total variability in log OR time in a corrected model. The overall effect of differences between the first surgeons on variability in OR time was small (ICC, 3.9%; CI, 2.8–5.5). When the type of procedure was considered, however, differences between first surgeons accounted for 31.4% (CI, 28.5%–34.5%) of the total variability in log OR time in a univariate corrected model.
Table 2 shows the model in which the various random effects subsequently were added to the base model. The base model consisted of the type of procedure as random effect and all predictive factors. The base model was identical to our previous work, but exclusion of data with only 1 surgeon led to an altered adjusted R2 of 79.5 instead of the 79.8 reported previously.1 The final R2 relatively increased with 17.6% (CI, 15.1%–20.0%) when we incorporated all significant random effects. In other words, incorporating random effects for surgeons and anesthesiologists can explain 17.6% of the previously unexplained variance. Both interaction terms for the first and second surgeons with the type of procedure were significant additions (P < .001). This finding indicates that the differences between first and second surgeons depend on the type of procedure. Thus, for some procedures, the surgeons will perform more similar than for other procedures. Furthermore, the difference between first surgeons depends also on the second surgeon (P < .001). Table 3 shows the effect on the accuracy of a prediction model in over and idle time. When the final significant interaction was added to the model (procedure × surgeon II, P < .001), this led to an average reduction of over and idle time of 1.9 (CI, 1.8–2.0) minutes and 3.1 (CI, 3.0–3.3) minutes per case, respectively.
After inclusion of all significant random effects from Table 2, the fixed part of the model with the predictive factors was stepwise reduced based on the AIC. The excluded predictive factors are given in Table 4. Interestingly, most of the excluded factors were related to either characteristics of the surgeon or anesthesiologist (ie, age of the oldest and the youngest surgeon during a procedure) or related to the kind of procedure the surgeon performs (ie, length of current admission).
The random effects part of the final model is summarized in Table 5. Overall, differences between first surgeons can account for only 2.9% (2.0–4.2) of the variability in log OR time. Differences between anesthesiologists can account only for 0.1% (0.0–0.3) of the variability in log OR time. When the type of procedure is considered, differences between first surgeons can account for 5.5% (4.3–6.8) of the variability in log OR time. Figure 2 shows that there is no severe deviation from normality for the random effects, indicating reliable estimations and stability of the model. The final model, which incorporates the individual surgeons and anesthesiologists, had an adjusted R2 of 83.1% (relative increase of 17.6%) and led to an average reduction of overtime and idle time of 1.8 (CI, 1.7%–2.0, 10.5% reduction) minutes and 3.0 (CI, 2.8%–3.2, 17.0% reduction) minutes, respectively. Although this is a significant reduction (P < .001) in over and idle time, the differences are likely too marginal to have practical consequences for OR scheduling.
In this study, we identified and quantified the amount of variability in log OR time that can be accounted to differences between individual surgeons and anesthesiologists. To elaborate on our previous article,1 we evaluated whether individual case characteristics, in this case the individual surgeons and anesthesiologists, can improve the precision of OR prediction. Several studies showed the importance of surgical team characteristics on OR time.1,9,10,14–18 Reported factors are often properties of the individual surgeon (ie, work rate, age, or experience1,9,10,16) or properties of combinations of surgeons (ie, team familiarity and the number of surgeons1,17). Therefore, we hypothesized that modeling the individual surgeons should account for a fairly large part of the total variability in OR time. Surprisingly, differences between first surgeons could only account for 2.9% (CI, 2.1%–4.2%) of the total variability in log OR time. Differences between anesthesiologists had a negligible effect on OR time and accounted for merely 0.1% (CI, 0.0%–0.3%). This finding confirms an earlier report that the anesthesiologist has little impact on OR time.10 The type of procedure accounted for the largest part in variability in OR time (31.6%; CI, 25.6%–39.4%). Although the surgeons and anesthesiologists can account for a unique part of the total variability in OR time (relative increase in adjusted R2 of 17.6%), the mean effect on the precision of a prediction model was minimal. Probably the reduction in overutilized OR time by our increase in precision is negligible and has no practical consequences for OR planning.5,24 Furthermore, decision making would not be affected because a small reduction in overtime rarely changes the decision whether a case is performed or cancelled.25
The final model contained significant random interaction terms for the first surgeon and second surgeon with the type of procedure. This indicates that the differences between first and second surgeons depend on the type of procedure. Thus, for some procedures, the surgeons will perform more similar than for other procedures. Several explanations can be given. First, Strum et al mentioned that surgeons consistently work in different places: the work rate effect.10 Differences between surgeons increase proportionately with longer procedures. Thus, for procedures with short median OR time, surgeons will be more similar than for longer procedures in terms of median OR time. Second, several studies have shown that the experience of the surgeon or the surgical team influences the duration of the OR time.17,26,27 These studies illustrate that increased experience (expressed as performance frequency of a procedure) decreases the duration of procedures. Therefore, surgeons with less experience with a certain type of procedure are likely to show more variability in their OR time. At last, these data originate from a university medical center at which oncologic procedures were performed by specific surgeons. For oncologic procedures, the discrepancy between procedure times can be high because of incorrect preoperative tumor staging or conversion of the planned procedures. For example, during laparoscopic tumor resections, conversion rates to open procedures can be as high as 20%.28 Incorrect preoperative staging may reveal inoperable oncology during surgery. In that case, the predicted duration will be much longer than the actual time, and this leads to an increased variability in OR time.
This study has several limitations. First, the influence of surgeons and anesthesiologists was determined by analyzing the total OR time. The OR time started when the patient entered the OR and ended when the patient was leaving the OR. This may distort the precision of the analysis because anesthesia time only consumes 7% to 25% of the total OR time.4,12 Because of this disproportionate division of OR time, the effect of the anesthesiologist on OR time is, therefore, already lower than the surgeon. Because both the effect of the surgeon and anesthesiologist are small, however, it is unlikely that the division in surgical and anesthetic time would cause large alterations in our results.
The second limitation of this study is the strict separation between first and second surgeon. For some procedures, the second surgeon of a case could be the first surgeon in another case and vice versa. Thus, it is not always clear whether the first surgeon primarily determined the length of a procedure. Therefore, the variance components we determined separately for first and second surgeons are likely to be related to each other. We partially corrected this by including a random interaction term for the first and second surgeon. Because this term accounted only for 0.8% of the total variability in OR time, it is unlikely that a strict separation generates very different results. A solution to this problem would be to analyze the first and second surgeon as a team; however, that would have prevented us to determine the difference between individual surgeons. Moreover, by analyzing individual surgeons and not teams of surgeons, the model could be used for planning of minor, single surgeon, procedures such as blepharoplasties or excisions of small skin defects. Third, the within-surgeon variability was not evaluated during this study. Random slopes for the predictive factors incorporate differences between surgeons and may have a significant influence on OR time. It is likely that the variability within a surgeon can vary and may depend on many other factors such as surgical experience, education, and age.
On the basis of our results and the aforementioned limitations, we have several recommendations for future research. As our primary aim was to make an inventory and quantify the effects of individual surgeons and anesthesiologists on OR time, future studies should externally validate its value for prediction models of OR time. We showed that the mean precision of a prediction model could be improved, albeit minimally; however, because this concerns the mean reduction in overtime and idle time at the center of the distribution, it is likely that larger gains were achieved in the tails of the distribution. If modeling surgeons and anesthesiologists leads to large reductions in the 90% upper prediction bounds, this could affect daily decision making and planning.5,24 It is important for future studies to investigate the effect of surgeons and anesthesiologists by a separate analysis of anesthesia-controlled time and surgeon-controlled time, with separate variance components for each surgeon individually, independent if he or she is the first or second surgeon. Further gains can be achieved by incorporating random slopes for known predictive factors (ie, surgeon’s estimate, patient, and procedure characteristics) and inclusion of not evaluated case characteristics such as American Society of Anesthesiologists score, anesthetic method, or use of operating microscope.10,16 Finally, it might be interesting to evaluate the effect of surgical nurses, because they are part of the surgical team as well and may affect OR time.6,29,30
In conclusion, this work quantified the amount of variability in OR time caused by differences between individual surgeons and anesthesiologists. In comparison with the type of procedure, differences between surgeons account for a small part of OR time variability. The impact of differences between anesthesiologists on OR time is negligible. A prediction model incorporating the individual surgeons and anesthesiologist has an increased precision, but improvements are likely too marginal to have practical consequences for OR scheduling.
Name: Ruben P. A. van Eijk, MD.
Contribution: This author helped design and conduct the study, perform the data analysis, and write the manuscript.
Name: Elizabeth van Veen-Berkx, MSc.
Contribution: This author helped prepare, edit, and review the manuscript.
Name: Geert Kazemier, MD, PhD.
Contribution: This author helped provide the data and edit and review the manuscript.
Name: Marinus J. C. Eijkemans, PhD.
Contribution: This author helped design the study, analyze the statistical data, and prepare the manuscript.
This manuscript was handled by: Franklin Dexter, MD, PhD.
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