Correcting for non-compliance when determining colonic transit time with radio-opaque markers

Table 1 Examples of scenarios of compliance and non-compliance with radio-opaque marker consumption and their potential correction

Days	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5	Scenario 6	Scenario 7
1	●	●	●	●	●	●	●
2	●	●	●	●	●	●	●
3	●	● (±α h)	○	●	●1	●	●
4	●1	●1	●	●1	●1	○	● (+ 4 h)1
5	●1	●1	●	● (±β h)1	●1	●1	●1
6	●1	●1	●1	●1	○1	●1	●1
n	24	24	24	24	24	24	72
t (h)	24	24	24	24	24	24	72 (-4)
ni (X-ray)	70	52	24	60	69 (+24)	48	65
CTT (h)	70	52	24	60	93	48	61.4

¹The period indicated by the estimated colonic transit time (CTT)-i.e., the markers on the days that are visualized on the X-ray. Scenarios 1 to 6: n is the total number of markers ingested each day, t is the time between marker ingestion in hours, ni is the number of markers observed on X-ray, and CTT is the estimated colonic transit time. Scenario 7: n is the total number of markers ingested during the estimated CTT period, t is the number of days in hours on which the markers are detected minus the number of hours by which consumption is delayed, ni is the number of markers observed on X-ray, and CTT is the estimated colonic transit time. Missed markers are indicated as open circles, consumed markers are indicated as closed circles. α and β are hypothetical deviation times of radio-opaque marker consumption. Values between parenthesis indicate corrections.