Model Calibration
Calibration of Colorectal Cancer Incidence
The progression of CRC is driven by a series of exponentially-distributed random variables that determine the time it takes to transition between a given set of disease states that reflect polyp growth and stages of cancer. The figure below outlines the possible transitions along with rates of transitions. All cancers start as a small lesion (<6 mm) and grow into larger sizes according to a particular rate. Once a polyp has been classified as medium (6-9 mm) or large (10 mm or larger), there is a chance that the polyp is considered to be preclinical cancer and thus can transition to the first stage of the preclinical cancer states. There are four stages of pre-clinical and clinical cancer that reflect the four stages used to represent cancer progression according to the American Joint Committee on Cancer. Each of the variables in the figure characterize the rate (corresponding to that of an exponential distribution) at which a transition takes place between two states. The corresponding variables, including descriptions and values are displayed in Table 1 below.
Development of Polyps and Progression to Cancer
Variables
Table 1. Variables Used for Calibration of CRC Incidence
Parameters used to represent the average time to transition in and out of preclinical stages (i.e., pol_p1, p1p2, p2p3, p3p4) are calibrated in order to satisfy specific objective functions that reflect the distribution of cancer cases across stages and patient age groups as well as total cancer incidence according to the NC Central Cancer Registry. Each objective is calculated as follows:
- Cancer stage objective is computed as the root mean square difference between the target data (Table 2) and the corresponding simulated output
- Patient age objective is computed as the root mean square difference between the target data (Table 3) and corresponding simulated output
- Total CRC incidence rate is computed by taking the difference between the total number of cancer incidences per 100,000 people from the target data (obtained by summing all values in Table 2) and the corresponding simulated output
The four calibrated parameters are varied in sequence one at a time: 1) pol_p1, 2) p1p2, 3) p2p3, 4) p3p4. By calibrating each of the parameters in this particular order, the preclinical cancer cases are fixed, which helps to ensure that the number of cancer cases are fully captured from the beginning. During each step of the calibration, the calibrated parameter pertaining to that step is evaluated against the specified objective function, the best performing parameter is used and set constant before beginning the next step in the calibration process.
Target Data
Table 2. North Carolina CRC Cases by Year and Stage