Fig 1.
Study design to assess the stability, predictive accuracy, and statistical power of computational approaches for modeling abdominal aortic aneurysms.
The original dataset was preprocessed and filtered as indicated. For risk factor assessment, only two measurements were needed for each patient. After combining close-together measurements, 540 patients had at least two measurements. For the growth estimate stability comparison, a minimum of three measurements were needed for each patient. After combining close-together measurements, 362 patients had at least three measurements. Lastly, for forecasting future diameter, each patient’s final measurement was used as the “target” datapoint to predict, and therefore censored from the models’ training data. To ensure that the forecasting period represented a substantial gap in time, measurements less than two years prior to the target point were also censored. After censoring these datapoints, close-together measurements were merged, resulting in 251 patients with two or more measurements in the training dataset. The dataset summaries in the dashed boxes reflect the quantity of the raw data, i.e. before averaging close-together points and censoring endpoints.
Fig 2.
Impact of AAA diameter at detection on estimated AAA growth rate.
The linear models showed a clear relationship between size at detection and growth rate, in which AAAs discovered at larger sizes were estimated to be faster growing. In the exponential models, however, a larger size at detection did not necessarily imply a higher growth rate. (n = number of patients).
Table 1.
Median AAA growth rate according to each model and relationship between growth rate and initial diameter.
Fig 3.
Impact of the removal of the earliest (left-censored) or latest (right-censored) aortic diameter measurements on estimation of aneurysm growth rates. We evaluated the magnitude and direction of changes in growth rate estimates from each model. A wider-spread histogram was seen in the unpooled models, meaning more patients had large changes in their growth rate estimate, indicating that the model was unstable and sensitive to noise. The two mixed models showed a narrower distribution, indicating stability and noise tolerance. A similar distribution of changes from left-censoring the data (orange) and right-censoring the data (blue) was seen in the exponential models, indicating that the direction of change was unrelated to the direction of censor. In the linear models, the left-censored distribution was shifted right, meaning the model tended to assign higher growth rates after losing the earliest datapoint, and vice versa. This asymmetry suggested that the linear models were more vulnerable to bias from the observation window, such as assigning higher growth rates to aortic aneurysms detected at large sizes, and assigning lower growth rates to aortic aneurysms not yet followed to a large size.
Table 2.
Differences between projected and actual AAA diameters.
Table 3.
Clinical variables that were significantly associated (p < 0.1) with average growth rate by all four models.
Average growth rate is shown in mm/year for each clinical category.
Table 4.
Clinical variables that were not significantly associated (p < 0.1) with average growth rate by all four models.
Average growth rate in mm/year is shown for each clinical category.
Table 5.
Clinical variables that were significantly associated (p < 0.1) with average growth rate by the exponential mixed model only.
Average growth rate in mm/year is shown for each clinical category.