Assessment of learning curves in complex surgical interventions: a consecutive case-series study

Background: Surgical interventions are complex, which complicates their rigorous assessment through randomised clinical trials. An important component of complexity relates to surgeon experience and the rate at which the required level of skill is achieved, known as the learning curve. There is considerable evidence that operator performance for surgical innovations will change with increasing experience. Such learning effects complicate evaluations; the start of the trial might be delayed, resulting in loss of surgeon equipoise or, if an assessment is undertaken before performance has stabilised, the true impact of the intervention may be distorted. Methods: Formal estimation of learning parameters is necessary to characterise the learning curve, model its evolution and adjust for its presence during assessment. Current methods are either descriptive or model the learning curve through three main features: the initial skill level, the learning rate and the final skill level achieved. We introduce a fourth characterising feature, the duration of the learning period, which provides an estimate of the point at which learning has stabilised. We propose a two-phase model to estimate formally all four learning curve features. Results: We demonstrate that the two-phase model can be used to estimate the end of the learning period by incorporating a parameter for estimating the duration of learning. This is achieved by breaking down the model into a phase describing the learning period and one describing cases after the final skill level is reached, with the break point representing the length of learning. We illustrate the method using cardiac surgery data. Conclusions: This modelling extension is useful as it provides a measure of the potential cost of learning an intervention and enables statisticians to accommodate cases undertaken during the learning phase and assess the intervention after the optimal skill level is reached. The limitations of the method and implications for the optimal timing of a definitive randomised controlled trial are also discussed

Change Point Analysis based on Empirical Characteristic Functions

62G20, 62E20, 60F17, Empirical characteristic function, Change point analysis,