How to interpret the learning curve?

The Global Assessment (GAS) scores recorded by the trainers from the training sessions represent the level of independence for a trainee to perform a procedure or certain tasks of a procedure. The higher the score, the less support from the assisting trainer was required.

This data allows analysis of learning curves of individual or multiple delegates. A learning curve in this context describes the increase of skill (=independence) to perform a straightforward laparoscopic colorectal resection. The main components of a learning curve are:

  • The “plateau” (asymptote) of the learning curve describes the level of desired performance
  • The length of the learning curve (how long does it take to reach the plateau)
  • The learning rate (at what rate are skills acquired?)

A score of 5 represents independent performance (without any substantial guidance by the trainer). This means that the delegates are able to perform a certain task on their own or with non-expert assistance.

If the raw scores were simply plotted on a graph, the learning curve would look “messy”, i.e. the scores would go up and down due to variation in the data (see Figure 1). It would be difficult to assess at what point a sufficient level of independence has been reached. Therefore, a trend curve analysis (CUSUM) is used to depict the data.


Figure 1. Raw score of a delegate. It is difficult to see when this delegate reaches independence. After 9 procedures? 14? 21?

CUSUM (cumulative sum) is a trend chart that tells us at what point a certain performance level has been consistently reached. With the method used, the curve shows a downward trend as long as a score of 5 has not been reached. Once the curve becomes “flat” (i.e. parallel to the x bar) it can be assumed that a consistent level of independence has been achieved (see Figure 2).


Figure 2. Same delegate as in Figure 1, this time showing the CUSUM score. The curve becomes “flat” at the 20th procedure, which represents the plateau of this delegate’s learning curve.

The steepness of the curve tells us something about the learning rate; the steeper the curve, the slower the rate and vice versa.

This analysis allows comparison of different delegates and also to compare individuals with the average learning curve.

Figure 3 demonstrates a worked example for three different trainees. The smooth line represents the average learning curve of all delegates within the programme. The average length of the learning curve in this example is approximately 15 procedures (note all examples shown in this document are hypothetical data and do not represent real results of lapco delegates).  Trainee 1 learns at a low rate (steep curve) and reaches the plateau at 20 procedures. Trainee 3 is a fast learner (flat curve) and reaches the plateau after 5 procedures. Trainee 2 also learns at a high rate, nevertheless, it takes him about the same time to reach the plateau as Trainee 1.


Figure 3. See text for details.

These learning curves are only an approximation of your performance in terms of independency compared to the average. There are potential sources of bias:

  • Some trainers may give different scores,
  • Some delegates already have experience in laparoscopic colorectal surgery when they enter the programme
  • Some delegates “share” cases with other trainees, so it may take more procedures to reach the plateau

Hence, this analysis is not judging you (“good” and “bad” trainee), but it should give you an impression where you stand and which areas of the procedure you may focus to improve.

Any comments or questions on the Learning Curve? 
Please contact Danilo Miskovic MD FRCS, Imperial College, London: