Growth prediction model for abdominal aortic aneurysms

Abstract

Background: The most relevant determinant in scheduling monitoring intervals for abdominal aortic aneurysms (AAAs) is maximum diameter. The aim of the study was to develop a statistical model that takes into account specific characteristics of AAA growth distributions such as between-patient variability as well as within-patient variability across time, and allows probabilistic statements to be made regarding expected AAA growth.

Methods: CT angiography (CTA) data from patients monitored at 6-month intervals with maximum AAA diameters at baseline between 30 and 66 mm were used to develop the model. By extending the model of geometric Brownian motion with a log-normal random effect, a stochastic growth model was developed. An additional set of ultrasound-based growth data was used for external validation.

Results: The study data included 363 CTAs from 87 patients, and the external validation set comprised 390 patients. Internal and external cross-validation showed that the stochastic growth model allowed accurate description of the distribution of aneurysm growth. Median relative growth within 1 year was 4.1 (5-95 per cent quantile 0.5-13.3) per cent. Model calculations further resulted in relative 1-year growth of 7.0 (1.0-16.4) per cent for patients with previously observed rapid 1-year growth of 10 per cent, and 2.6 (0.3-8.3) per cent for those with previously observed slow growth of 1 per cent. The probability of exceeding a threshold of 55 mm was calculated to be 1.78 per cent at most when adhering to the current RESCAN guidelines for rescreening intervals. An online calculator based on the fitted model was made available.

Conclusion: The stochastic growth model was found to provide a reliable tool for predicting AAA growth.

Fig. 1

Absolute and relative growth of maximum abdominal aortic aneurysm diameter a Change in maximum abdominal aortic aneurysm (AAA) diameter for individual patients, and median trajectories as estimated from the stochastic growth model for starting values of 30, 40, 50, and 60 mm maximum diameter. b,c Relative growth of maximum AAA diameter and its growth distribution modelled by b stochastic growth model and c linear mixed model. The observed relative growth for each patient is defined as the ratio of the current value of maximum diameter and the value at the initial visit. Median values and selected quantiles are shown for the study sample as estimated from each model.

Fig. 2

Relative growth of maximum abdominal aortic aneurysm diameter in validation data set compared with study data set, and as modelled by stochastic growth model a Validation versus study data sets, and b validation data set. Observed relative growth is shown for each patient in the validation and study data sets, along with median and quantile estimates of the relative growth distribution estimated from the stochastic growth model fit to each data set.

Fig. 3

Updated predictions for growth of maximum abdominal aortic aneurysm diameter based on previous measurements using stochastic growth model a–c Individual growth data are shown for three patients, along with estimates of the median, and 5 and 95 per cent quantiles, of the maximum abdominal aortic aneurysm (AAA) diameter distribution at the next time point, based on the growth model for the overall population and the current value for the patient, and refined estimates of the conditional distribution of maximum AAA diameters taking into account all previous measurements from an individual patient.