Technical note: two programs for performing multigroup longitudinal data analyses.
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Biomedical subjects
Publications and source records attributed to S M Willis.
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We consider the problem of growth prediction in the context of Rao's [1] one-sample polynomial growth curve model and provide a PC program, written in GAUSS, to perform the associated computations. Specifically, the problem considered is that of estimating the value of the measurement under consideration for a "new" individual at the Tth time point given measurements on that individual at T-1 previous points in time and the values of the measurement on N "similar" individuals at all T time points. The times of measurement t1, t2, . . ., tT need not be equally spaced, but we assume that each of the N individuals comprising the normative sample were measured at these times. The method and the program are illustrated using the leave-one-out method on a sample of N = 12 male rhesus monkeys whose mandibular ramus height was measured five times at yearly intervals.
A PC-program performing the Potthoff-Roy (PR) multigroup (G-sample) analysis of longtidinal data is described and illustrated. This program and the underlying statistical model are useful in the comparison of several longitudinal samples. Applications include the study of growth, development, adaptation, aging, and treatment effects (in short, any phenomenon in which the passage of time is important) for which serial data are available. Specifically, this method fits polynomials to the average growth curves in the samples, and tests hypotheses concerning the curves themselves and the individual coefficients of the polynomials. The program features the utilization of orthogonal polynomial regression coefficients (OPRCs) and is written in GAUSS, a relatively inexpensive yet comprehensive matrix programming language. It is documented that using OPRCs to comprise the within-individual or time design matrix has several advantages over the more usual choice of the successive-powers-of-t form of this matrix and an example of one important such advantage is provided. GAUSS was employed to make the program readily-accessible (i.e., executable code) to biomedical investigators. The GAUSS compiler is not required to run this program. Information regarding the availability of the program is provided in the Appendix.
For lack of alternatives, longitudinal data are often analyzed with cross-sectional statistical methods, for instance, t-tests, ANOVA and ordinary least-squares regression. Appropriate statistical software has been generally unavailable to investigators using serial records to study growth and development or treatment effects. In an earlier paper (Schneiderman and Kowalski, Am. J. Phys. Anthropol., 67 (1985) 323-333.) we described a suitable method, Rao's polynomial growth curve model (Rao, Biometrika, 46 (1959) 49-58), and provided an SAS computer program for the analysis of a single sample of complete longitudinal data. This method included the computation of an average polynomial growth curve, its 95% confidence band, its coefficients and corresponding confidence intervals. The present paper extends this method to accommodate a sample with observations made at unequal time-intervals. Significant improvements in the accessibility, operation and user-friendliness of the program have been made, facilitated by recent advances in microcomputer technology. This stand-alone GAUSS program (no compiler necessary) runs on PC-compatibles and is available at a nominal cost. In this report we provide an overview of the statistical model, the general structure of the program, and give an example in which a developmental variable (human upper incisor angulation) is analyzed. Ease of installation and use, speed of execution and color graphic displays of growth curves and confidence bands, and most importantly, suitability to longitudinal data, make this method/program a potentially valuable tool for those interested in growth, development, and treatment effects in humans and other species. Some areas in which this method will have immediate applications are orthodontics, maxillofacial surgery and pediatrics.
We describe a case of pancreatic duct-portal vein fistula discovered by endoscopic retrograde cholangiopancreatography, with confirmatory computed tomography and angiographic studies. The fistula was associated with chronic pancreatitis that was complicated by recurrent gram-negative bacteremia and peripheral subcutaneous fat necrosis, although pancreatic pseudocyst was not present. Even though surgical treatment was recommended, medical complications precluded surgery and the patient recovered with supportive therapy only. Follow-up endoscopic retrograde cholangiopancreatography showed spontaneous closure of the fistulous connection.
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