Mathematical and Computer Modelling 50 (2009) 705–712
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Mathematical and Computer Modelling journal homepage: www.elsevier.com/locate/mcm
Identification of surgical practice patterns using evolutionary cluster analysis Manuel Herrera a , Joaquín Izquierdo a,∗ , Idel Montalvo a , Juan García-Armengol b , José V. Roig b a
Centro Multidisciplinar de Modelación de Fluidos, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022, Valencia, Spain
b
Servicio de Cirugía General y Digestiva, Consorcio Hospital General Universitario de Valencia Avda, Tres Cruces 2, 46014, Valencia, Spain
article
info
Article history: Accepted 15 December 2008 Keywords: Particle swarm optimization Evolutionary algorithm Partitional clustering Colorectal surgery Perioperative praxis Multimodal rehabilitation
abstract Modern data analysis and machine learning are strongly dependent on efficient search techniques. However, in general, further exploration into high-dimensional and multimodal spaces is needed, and moreover, many real-world problems exhibit inaccurate, noisy, discrete and complex data. Thus, robust methods of optimization are often required to generate results suitable for these data. Some algorithms that imitate certain natural principles, namely the so-called evolutionary algorithms, have been used in different fields with great success. In this paper, we apply a variant of Particle Swarm Optimization (PSO), recently introduced by the authors, to partitional clustering of a real-world data set to distinguish between perioperative practices and associate them with some unknown relevant facts. Our data were obtained from a survey conducted in Spain based on a pool of colorectal surgeons. The PSO derivative we consider here: (i) is adapted to consider mixed discrete-continuous optimization, with statistical clustering criteria arranged to take these types of mixed measures; (ii) is able to find optimum or near-optimum solutions much more efficiently and with considerably less computational effort because of the richer population diversity it introduces; and (iii) is able to select the right parameter values through self-adaptive dynamic parameter control, thus overcoming the cumbersome aspect common to all metaheuristics. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Computer systems that are able to extract information from large amounts of data (for example, in order to perform Data Mining tasks, like pattern recognition, classification, and diagnosis) as well as systems that are adaptive and show a capacity to learn fundamentally rely on effective and efficient search techniques. Any adaptive system needs some kind of search mechanism in order to explore a feature space describing all possible states of the system. Due to the characteristics of many feature spaces, exploration in high-dimensional and multi-modal spaces is needed. Classical methods of optimization involve the use of gradients or higher-order derivatives of the fitness function. But they are not well suited for many real-world problems, since they are not able to process inaccurate, noisy, discrete and complex data [1,2]. Thus, robust methods of optimization are often required to generate results suitable for these data. Some algorithms that imitate certain natural principles have been used for various applications in many fields, including
∗
Corresponding author. Tel.: +34 963879890; fax: +34 963877981. E-mail address:
[email protected] (J. Izquierdo).
0895-7177/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm.2008.12.026
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evolutionary algorithms like Genetic Algorithms, Ant Colony Optimization, Particle Swarm Optimization, and Harmony Search. One of the evolutionary algorithms that has shown great potential for solving various optimization problems [3–10] is Particle Swarm Optimization (PSO). Swarm intelligence is a relatively new category of stochastic, population-based optimization algorithms. They are closely related to evolutionary algorithms based on procedures that imitate natural evolution. Swarm intelligence algorithms draw inspiration from the collective behavior and emergent intelligence that arise in socially organized populations. In this paper, we apply a derivative of PSO, which was recently introduced by the authors [8–10] to partitional clustering of a real-world data set to distinguish between perioperative practices and associate them with unknown relevant facts. Our data were obtained from a survey conducted among the members of Spanish Coloproctology Associations. The PSO derivative we consider here is adapted to consider mixed discrete-continuous optimization, since the problem we tackle here involves the use of both continuous and discrete variables. Thus, we use statistical clustering criteria arranged to take these types of mixed measure. Also, this formulation is able to find optimum or near-optimum solutions much more efficiently and with considerably less computational effort because of the richer population diversity it introduces. Finally, the cumbersome aspect, which is common to all metaheuristics, of choosing the right parameters values is tackled through self-adaptive dynamic parameter control. Cluster analysis [11] plays an important role in many fields and can be used both for preliminary and descriptive data analysis and unsupervised classification [12] as well as to summarize common features of groups of elements, like identification of centroids or baricenters. Central to the goals of cluster analysis is the notion of similarity, in terms of proximity, between the individual objects being clustered; alternatively, dissimilarity is used to explain the difference between individual objects. A clustering method attempts to group objects based on the definition of similarity supplied to it. In the present paper, we will work with clusters in a mixed dissimilarity. For this reason, we will use medoids as representative grouping elements, with an understanding of the medoid as the object of a cluster, whose average dissimilarity to all the objects in the cluster is minimal. By using modern techniques of semi-automatic (machine) learning, this study aims to assess the current practice patterns, approaches and opinions of Spanish colorectal surgeons on perioperative care and multimodal rehabilitation (also known as fast-track surgery or plainly as fast-track) [13,14] and to devise specific, evidence-based specialization skills for different target groups of practitioners. Sometimes surgeons are reluctant to adopt novel recommendations; in addition, there are intangible barriers that preclude evidence-based surgery. Traditional approaches, designed to facilitate safe surgery rather than enhance recovery, remain widely used despite evidence that many components may be unhelpful or even harmful [15]. As a consequence, new methods to sensitize practitioners to the advantages of fast-track approaches and to persuade them to adopt these new recommendations should be addressed by the Health Authorities. In this sense, the results obtained from this study could be of great help to these efforts. The rest of this paper is organized as follows. The next section presents the tool, PSO, including the rules for the manipulation of the swarm population and how parameters are controlled. Also, the main features of the PSO derivative are introduced. Then, the database under consideration is concisely described, and the main objectives in this study are presented. Next, the necessary statistical clustering criteria, including the description of the fitness evaluation, are introduced. Finally, the main results are reported, and conclusions are presented with a number of suggestions for future work. 2. Description of PSO and the used variant A swarm consists of a set of particles moving within the search space, which is D-dimensional, each representing a potential solution of the problem. Each particle has a position vector, Xi = (xi1 , . . . , xiD ), a velocity vector, Vi = (vi1 , . . . , viD ), and the position at which the best fitness was encountered by the particle, Yi = (yi1 , . . . , yiD ). In each cycle of the evolution, the position of the best of the N particles in the swarm, Y ∗ , is identified. Particles evolve in terms of their individual and social behavior by mutually coordinating their movement toward their destinations [16]. 2.1. Manipulation of particles In each generation or cycle, the velocity of each particle changes based on its velocity history, its best encountered position and the best position encountered by any particle: Vi = ωVi + c1 rand() (Yi − Xi ) + c2 rand() (Y ∗ − Xi ).
(1)
On each dimension, particle velocities are clamped between minimum and maximum velocities to control excessive roaming of particles outside the search space: Vmin ≤ Vj ≤ Vmax . Usually Vmin is taken as −Vmax , which is a user-defined parameter.
(2)
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The position of each particle is also updated every generation. This is done by adding the velocity vector to the position vector, X i = X i + Vi .
(3)
The parameters are as follows: ω is a factor of inertia suggested by Shi and Eberhart [16] that controls the impact of the velocity history on the new velocity. Acceleration parameters c1 and c2 are typically two positive constants, called cognitive and social parameters, respectively. rand() generates two independent random numbers between 0 and 1, and it is used to maintain the diversity of the population. 2.2. Manipulation of parameters The role of the inertia, ω, in (1) is considered critical for the PSO algorithm’s convergence behavior. Although at early stages of the algorithm the inertia was constant, it may vary from one cycle to the next. As it facilitates the balancing of global and local searches, it has been suggested to allow ω to decrease linearly with time, usually in a way that at first emphasizes global search and then, with each cycle of the iteration, increasingly prioritizes local search, [17]. A significant improvement in the performance of PSO with decreasing inertia weight over the generations is achieved by using [5]
ω = 0.5 +
1 2 (ln (k) + 1)
,
(4)
where k is the iteration number. In the framework herein described, this parameter is adaptively controlled by using (4). However, the acceleration coefficients and the clamping velocity are neither set to a constant value, as in standard PSO, nor set as a time-varying function, as in adaptive PSO variants [18,19]. Instead, they are incorporated into the optimization problem. Each particle is allowed to self-adaptively set its own parameters by using the same process used by PSO and given by Eqs. (1) and (3). To this end, these three parameters are considered as three new variables that are incorporated into position vectors Xi . In general, if D is the dimension of the problem and P is the number of self-adapting parameters, the new position vector for particle i will be: Xi = (xi1 , . . . , xiD , xiD+1 , . . . , xiD+P ).
(5)
It is clear that the first D variables correspond to the actual position vector of the particle in the search space, while the last P accounts for its personal parameters. Obviously, these new variables do not enter the fitness function, but rather they are manipulated by using the same mixed individual-social learning paradigm used in PSO. Also, Vi and Yi , which give the velocity and thus-far, the best position for particle i, increase their dimension, correspondingly: Vi = (vi1 , . . . , viD , viD+1 , . . . , viD+P )
(6)
Yi = (yi1 , . . . , yiD , yiD+1 , . . . , yiD+P ).
(7)
and
By using Eqs. (1) and (3), each particle is additionally endowed with the ability to adjust its parameters by taking into account both the parameters it had at its best position in the past as well as the parameters of the leader, which facilitated this best-particle’s move to its privileged position. As a consequence, particles use their cognition of individual thinking and social cooperation not only to improve their positions but also to improve the way they improve their position by accommodating themselves to the best-known conditions, namely, their conditions and their leader’s conditions when they achieved the thus-far best position. Before providing a schematic representation of the proposed algorithm, two more observations must be made. First, the discussion so far has considered the standard PSO algorithm, which is applicable to continuous systems and cannot be used for mixed discrete-continuous problems like the one we consider here. To tackle discrete variables, this algorithm takes the integer parts of the flying velocity vector’s discrete components into account; hence, the new discrete component velocities Vi are integers. Consequently, the discrete components of the new position vector will also be integers, since the initial position vectors were generated with integer values. Accordingly, velocity for discrete variables changes as follows: Vi = fix(ωVi + c1 rand() (Yi − Xi ) + c2 rand() (Y ∗ − Xi )),
(8)
where fix(·) implies that we only take the integer part of the result. Second, in [9], PSO was endowed with a re-generation-on-collision formulation, which further improves the performance of standard discrete PSO. The random regeneration of the many birds that tended to collide with the best birds was shown to avoid premature convergence, as it prevented clone populations from dominating the search. The inclusion of this procedure into the discrete PSO produces greatly increased diversity, improved convergence characteristics and yielded higher-quality the final solutions. The modified algorithm can be given by the following pseudo-code, with k as iteration number.
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(1) k = 0 (2) Generate a random population of M particles: {Xi (k)}M i=1 , according to (5) (3) Evaluate the fitness of the particles (only the first D variables enter the fitness function) (4) Record the local best locations {Yi (k)}M i=1 ; according to (7) the values of the corresponding parameters are also recorded (5) Record the global best location, Y ∗ (k), and the list of the m best particles to check collisions (including their corresponding parameters) (6) While (not termination-condition) do (a) Determine the inertia parameter ω(k), according to (4) (b) Begin cycle from 1 to number of particles M Start (1) Calculate new velocity, Vi (k + 1), for particle i according to (1), and take its integer part (for discrete optimization) for the first D variables, according to (8) (2) Update position, Xi (k + 1), of particle i according to (3) (3) Calculate fitness function for particle i and update Yi (4) If particle i has better fitness value than the fitness value of the best particle in history, then set particle i as the new best particle in history (5) If particle i is not currently the best particle but coincides with the best, then re-generate particle i randomly (including its parameters) End (c) k = k + 1 (7) Show the solution given by the best particle In this study, a population size of M = 100 particles has been used. Also, among the different termination conditions that may be stated, if there is no improvement after a pre-fixed number of iterations have been considered, the process is stopped. The performance of the approach herein introduced can be observed from the results reported in Section 5. 3. The database Each member of the Spanish Association of Surgeons (AEC) (Coloproctology section), and the Spanish Association of Coloproctology (AECP) was asked to complete an e-mailed questionnaire between December 2006 and February 2007. The survey comprised 12 questions on demographic and general data, 87 on the use of several perioperative procedures, and 83 on the opinions of surgeons exclusively regarding colorectal elective surgery [20]. We submitted the survey to 413 surgeons; 131 (31.7%) responded. For this study, we selected the questions related to the use of mechanical bowel preparation (MBP), nasogastric tubes (NT), drains (DT) and postoperative oral feeding (OF), because there is currently significant scientific evidence available on them. MBP has proven not useful and even potentially dangerous [21,22]; routine use of NGT tubes and drains also appears useless [23,24], and early oral feeding is associated with a faster recovery [25]. 4. Statistical measures and fitness evaluation 4.1. Introduction Clustering is the grouping of similar objects [11]. An object can be described by a set of measurements or by its relation to other objects. The goals of cluster analysis are varied and include wide-ranging activities, such as looking for ‘‘natural’’ groups and hypothesis generation. Central to the goals of all cluster analysis is the notion of similarity, in terms of proximity, between the individual objects being clustered; alternatively, dissimilarity is used to explain the difference between clustered objects. A clustering method attempts to group the objects based on the definition of similarity or dissimilarity supplied to it. 4.2. Dissimilarities The dissimilarity between two objects measures how different they are [12]. It has to be noted here that, although the usual metrics can be used, they do not necessarily have to verify the triangle inequality. The computation of the dissimilarity between two objects depends on the type of the original variables. Many data sets contain variables of different types. The next method solves the computation of the dissimilarity in a general form, considering that the data set contains p variables: p P
d(i, j) =
∂ij(f ) d(ijf )
f =1 p P f =1
(f )
∂ij
∈ [0, 1],
(9)
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(f )
709
(f )
with ∂ij = 0 if xif or xjf is missing or if xif = xjf = 0 and f is an asymmetric binary variable. Otherwise, ∂ij contribution of variable f , which depends on its type: (f )
= 1. d(ijf ) is the
(f )
1. If f is binary or nominal, dij = 0 if xif = xjf and dij = 1 otherwise. (f )
2. If f is interval-scaled, dij =
|xif −xjf | . maxh (xhf )−minh (xhf )
3. For ordinal and ratio-scaled variables, ranks rif and zif =
rif −1 Mf − 1
are computed, and then zif is treated as interval-scaled.
4.3. Clustering algorithms The goal of cluster analysis is to partition the observations into groups so that the pair-wise dissimilarities between objects assigned to the same cluster tend to be smaller than those in different clusters. Clustering algorithms can be classified in two categories: partitioning and hierarchical algorithms. Most partitional clustering algorithms assume an a priori number of clusters, c, and a partition of the data set into c clusters. To get the correct partition, an objective function must be formulated that evaluates the partition with respect to the data set. Hierarchical clustering algorithms transform a proximity data set into a tree-like structure. One drawback of these algorithms is their high computational cost; in addition, it is unclear as to where to prune the generated tree. In real-life problems, very large data sets containing variables of several types are typically found. This requires a clustering algorithm to be scalable and capable of handling different attribute types. Classical methods cannot address such data: for example, PAM (Partitioning Around Medoids) algorithm [26] can handle various attribute types but is not efficient with large data sets. k-means algorithms [27,28] can handle large data sets but deal only with data sets formed from intervalscaled variables. 4.4. Statistical clustering criteria Several clustering criteria have been proposed, some of which are based on the fundamental matrix equation: T = W + B, where W and B are the within-cluster and between-cluster variations, respectively. T , then, is the total scatter matrix. For univariate data, the above expression reduces to the usual ANOVA decomposition. From this point of view, the ideal form of T is a matrix built with a small W and a large B, so that the distances within the clusters are small when compared with distances between cluster medoids. An intuitive procedure for choosing clusters is to minimize the ‘‘size’’ of W and/or maximize B. The statistical criteria used to measure the adequacy of the partition and to define the optimization problem in order to solve the clustering paradigm via heuristics focus on W and B. Friedman and Rubin [29] proposed minimizing the W trace. Another possibility is to minimize det (W ) or maximize trace(BW −1 ). More recently, McGregor et al. [30] have also developed new methodologies for validation results based on W . Barbará et al. [31] have worked with entropy-based measures for categorical data clustering. Here, we use the fitness function: n P
Cost (M , D) =
d(Oi , rep(M , Oi ))
i=1
n
,
(10)
where D is the data set to be clustered, n the number of objects in D, M is a set of selected medoids, d(Oi , Oj ) is the dissimilarity (9) between objects Oi and Oj , and rep(M , Oi ) returns the medoid in M which is closest to Oi . 5. Results The database was analyzed using both PAM and PSO. PAM, which was computationally much more expensive than PSO, was performed to contrast the results yielded by PSO. This algorithm was run ten times with almost identical results and showed no relevant differences with respect to those obtained with PAM. A population size of 100 particles was used. Maximum velocity, Eq. (2), was established as 50% of variable range, and Minimum velocity = −(Maximum velocity). The termination condition was such that the process stopped if after 60 iterations, no improvement in the solution had been obtained. Results were obtained in a mean value of around 200 iterations. Cluster analysis was performed considering different possibilities, namely, 2, 3 and 4 clusters. The analysis for 2 clusters, which we present here, was conclusive. When trying to identify more than 2 clusters, the algorithm detected the same two clusters plus other clusters made out of registers with relatively large amounts of missing data. To reiterate, the results obtained in this study using the two aforementioned algorithms clearly identify two clusters of surgeons within the surveyed pool. The first one includes 20% of those questioned and the second one the remaining 80%. Fig. 1 shows the silhouette plot [32,33] of the partition obtained with PAM. According to the obtained results, experience and accreditation in colorectal surgery is correlated with more accurate perioperative protocols. This fact is clearly identified in this study, as most of the members of cluster #1 had received the
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Fig. 1. Silhouette plot of the partition.
Table 1 Representative answers to main questions. Fields
Board
NoBoard
Use of MBP Use of MBP in right colon Use of MBP in left colon Use of MBP in rectum Use of DT Use of DT in colon surgery Use of DT in rectum surgery Use of NT Open surgery feed tolerance Laparoscopic surgery feed tolerance Fast-track (use)
No No No Yes Selectively Low Mid-high Never Day 0 or 1 Day 0 or 1 Yes
Yes Yes Yes Yes Routine High High Selectively When peristalsis When peristalsis No
European Board in Coloproctology, while none of the members in cluster #2 had. We use this fact to refer to cluster #1 as Board and cluster #2 as NoBoard. The Board’s surgeons have developed higher specific activity, with 80% having colorectal surgery activity as opposed to 60% for the NoBoard members. Regarding laparoscopic versus open surgery, activity figures are 35% and 22%, respectively. Nevertheless, experience is not a conclusive feature. More professionals should have access to suitable knowledge and thus be able to adopt a number of measures, even as they struggle to change what has historically been routine medical practice. This fact can be appreciated after examining the fields related to Certification and Professional status. Even though no difference can be observed between the average values in these fields for both clusters, a close examination reveals that the members of NoBoard either have a plain college degree (which could be associated with a lack of specific training), or in contrast, they are professionals with long experience in the field but no updated knowledge. On the contrary, people from the Board have more recent and advanced education, suggesting more up-to-date qualifications. Four main activities have been considered in the survey: mechanical bowel preparation (MBP), use of nasogastric tubes (NT), use of drains (DT) and late feeding after surgery. The necessary use of these surgical activities has been treated as immutable dogma, even though their use, from a non-physiological perspective, may aggravate surgical operations. However, in a sense opposed to tradition, they also characterize aspects of novel and more efficient fast-track protocols. Table 1 shows the representative answers to the main questions regarding these activities. Use of MBP. Regarding MBP, members of the Board definitely disregard this practice, while those of the NoBoard continue to use it. Only in the case of MBP for rectum operations do both groups agree on the convenience of using MBP (see Table 1). More specific questions reveal respondents’ opinions on MBP. Members of the Board do not view MBP as reducing infection
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and dehiscence; rather, they see it as increasing electrolytic alterations. Opinions from the NoBoard are just the opposite. Also, the Board members consider MBP to be useless, while those in the NoBoard deem MBP somehow useful. Use of DT. The Board’s surgeons use drains ‘never or perhaps selectively,’ while those in the NoBoard use them routinely. Surgeons in the Board use a low number of drains during colon surgery; the number of drains is higher for the NoBoard. For rectum surgery, the figures reflect the same relative trends between clusters, but both clusters use a larger number of drains (see Table 1). Regarding the effect of the use of drains, points of view also differ from one cluster to the other: The NoBoard’s members think that drains reduce fluid collection and haematomas and favor anastomosis leaks and dehiscences, while the Board’s members disagree. Finally, in the Board, drains are considered useless, while they are deemed useful or very useful for the NoBoard’s members. Use of NT. Again, surgeons in the Board cluster almost never (representatively-speaking) use NT; in contrast, those in the NoBoard tend to use it selectively (see Table 1). Once more, specific opinions about NT’s effects are different. For the NoBoard members, NTs reduce vomits and ileum while increasing pulmonary infections. Members of the Board recognize that NT produces pulmonary infections but do not attribute a reduction in vomits and ileum to NT. Overall, in the Board, NT is definitely disregarded, while in the NoBoard, NT is broadly accepted. Feeding schedule. The survey also questioned surgeons regarding the feeding schedule. Surgeons in the Board start a patient’s oral intake at day 0 or 1 both after open surgery with anastomosis as well as after laparoscopic colon resection. In contrast, those in the NoBoard wait until peristalsis after both open and laparoscopic surgeries (see Table 1). Also surgeons in the Board cluster do not relate early feeding with an increase of leaks and dehiscence. The opinion of those in the other cluster is just the opposite. Both clusters, however, think that early feeding reduces postoperative ileus. Again, those in the Board believe that early feeding is very useful, while the others are more prone to think it is useless. Fast-track protocols. Finally, we consider the use of fast-track protocols. Surgeons in the Board use fast-track protocols, while those in the NoBoard show clear skepticism or lack of knowledge about this relatively new technique (see Table 1). Also, regarding specific questions, members in the Board clearly state that fast-track allows shorter stays, reduces postoperative complications, increases patient’s comfort and does not increase risks; most answers from the NoBoard reveal insufficient knowledge or even incorrect knowledge, such as understanding fast-track to increase risks. As a consequence, surgeons in the Board consider a fast track protocol very useful, while those in the NoBoard are reluctant to believe it is useful. 6. Conclusions Data mining analysis helped to characterize perioperative practices within a pool of Spanish colorectal surgeons and associate them with certain non-evident relevant facts. Cluster analysis was carried out by minimizing dissimilarities using a variant of the PSO algorithm. Richer results could be obtained by incorporating other new fields in the database. In that case, it would be necessary to use a larger population size; fortunately, using a larger population would not entail any added conceptual difficulty. The PSO algorithm was compared to partitional clustering performed by PAM, an algorithm that works with various attribute types. There were no significant differences regarding the results obtained using PAM as opposed to PSO; however, in terms of efficiency, PSO efficiency was superior. Thus, these results show PSO’s ability in cluster-building. Relatively largesized databases would enhance PSO superiority in terms of efficiency relative to PAM (particularly with regard to time of execution and best optimization solution). In addition, PSO avoids any need to adapt to new types of data, as would be the case with PAM. Evidence-based medicine is a very important tool for improving the quality and efficiency of healthcare. However, ensuring the practical impact of clinical evidence that is available appears harder to realize than expected. This study shows that recent evidence-based changes in the perioperative management of colorectal patients need to be better understood and applied in clinical practice in order to offer patients a more effective, safer, faster and more comfortable recovery. Spanish surgeons, like most in the world, maintain classical habits. However, in order to optimize patient care, there are tendencies to comply with new scientific results concerning the optimization of perioperative care, such as so-called fast-track surgery and multimodal rehabilitation. These new techniques have profound, positive effects on postoperative recovery and outcome. Results can be used to alert practitioners to the advantages of novel techniques such as fast-track and to persuade them to adopt these new procedures. Also, Health Authorities can use these results to devise strategic plans for continued professional development as well as to launch programs for specific training. This could eventually improve the quality of health service by increasing the efficiency of the system, saving costs and improving outcomes. Acknowledgements This work has been performed with support from the Grants BES-2005-9708 and MAEC-AECI 0000202066, awarded to the first and third authors, respectively, by the Ministerio de Educación y Ciencia and the Ministerio de Asuntos Exteriores y Cooperación of Spain. Also, we thank the Spanish Association of Surgeons (AEC) (Coloproctology section) and the Spanish Association of Coloproctology (AECP) for allowing us to carry out our survey among their associates.
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