A Mixed Effects Model for Gastric Ulcer Data
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Drug Infomtion Journal, Vol. 3 1, pp. 1249-1 254, I 997
Copyright 0 1997 Drug lnfomation Association Inc.
R i n d in the USA. All rights reserved.
A MIXED EFFECTS MODEL FOR GASTRIC ULCER DATA DONGHUIZHANG,PHD Biometrician. Biometrics Research Department, Merck Research Laboratories, Rahway, New Jersey
The concern of this work is the statistical evaluation of healing rate of gastric ulcers. To measure healing progress, the distance of linear advance of a specific ulcer margin toward center is recommended as an appropriate parameter: The sequence of linear advances is approximately linear over time; thus, the slope of this linear profile provides a good indication of the healing rate of the specific ulcer area. To estimate the mean slope in a treatment group, the mixed effects model technique is employed. A treatment effects comparison is made by both the F-test and the likelihood ratio test for a common slope across treatments. Also discussed are the advantages of using the linear advance as an endpoint and the mixed effects model technique as an analysis tool. A numerical example is presented as an illustration. Key Words: Gastric ulcer; Linear advance of ulcer margin; Mixed effects model; F-test; Likelihood ratio test
INTRODUCTION THE TRADITIONAL ENDPOINT for measuring healing of duodenal or gastric ulcer is complete ulcer healing. The healing rate is typically reported as the percentage of complete healing; and the traditional methodology for assessing treatment effects is the Mantel Haenszel technique to compare the ratio of complete healing across treatment groups at various time points (1). There are some drawbacks of using complete healing as an endpoint: it depends on severity and size of an ulcer; it may fail to reach any conclusions for short period studies, or it may result in lengthy studies. Another typical endpoint is the percent
Presented at the DIA “First International Taipei Symposium,” August 29-30, 1996, Taipei, Taiwan. Reprint address: Donghui Zhang, PhD, Biometrician, Biometrics Research Department, Merck Research Laboratories, PO Box 2000, RY70-38. Rahway. NJ 07065-0900.
or absolute reduction in specific ulcer area which is captured by computer at each scheduled endoscopic examination. The sequence of ulcer areas follows a nonlinear pattern, typically an exponential curve, over the study period. The initial healing rate, estimated as the slope of the linear approximation of the nonlinear curve during the initial time period, is usually used as a variable for certain analyses, for example, treatment effect on early healing (2). Since the rate of healing in terms of change in ulcer area varies with time, it is inconvenient to define the overall healing rate based on the rate of change in the area for the indication of overall treatment effects. The nonlinearity issue may be handled by fitting the nonlinear curve directly and then using the fitted parameters of the nonlinear function as the analysis variables. For instance, if the pattern of change in area (A) over time (r) can be described
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