The rate of decrease of gallstone diameter appeared to be linear with oral bile acid treatment time, as estimated by inspection of graphic data of individual patient serial oral cholecystograms. A theoretical basis for this model was derived. The hypothesis of diameter decrease proportional to treatment time was tested with data from 223 patients with radiolucent gallbladder stones up to 20 mm in diameter treated with 7-8 or 14-15 mg.kg-1.day-1 of either ursodiol or chenodiol for 1 year, followed up after 3, 6, and 12 months of treatment. Linearity of individual sets of data points was tested by mathematical and statistical methods, including polynomial curve fitting, linear regression analysis, quadratic vs. linear analyses of covariance, and prediction of 12-month stone size by linear extrapolation from diameters at 0 and 6 months. Most patients (greater than 70%) had rates of gallstone diameter decrease that were almost linear with treatment time, independently of different dissolution rates on a given regimen. Additional treatment time needed may be estimated from cholecystograms or ultrasonograms performed before treatment and after several months.