Int J Biomed Comput, 33 (1993) 249-265 Elsevier Scientific Publishers Ireland Ltd. 249 PC PROGRAM FOR ESTIMATING POLYNOMIAL GROWTH, VELOCITY AND ACCELERATION CURVES WHEN SUBJECTS MAY HAVE MISSING DATA EMET D. SCHNEIDERMAN”, STEPHEN M. WILLIS” and CHARLES J. KOWALSKIb “Department of Oral and Maxillofacial Surgery, Baylor College of Dentistry, 3302 Gaston Ave, Dallas, TX 75246 and hDepartment of Biologic and Materials Sciences and the Center for Statistical Consultation and Research, The University of Michigan, Ann Arbor, MI 48109 (USA) (Received December 23rd, 1992) (Accepted February 8th, 1993) A stand-alone, menu-driven PC program, written in GAVSS386i, for estimating polynomial growth, velocity, and acceleration curves from longitudinal data is described, illustrated and made available to interested readers. Missing data are accommodated: we assume that the study is planned so that individuals will have common times of measurement, but allow some of the sequences to be incomplete. The degrees, D, adequate to tit the growth profiles of the N individuals are determined and the cor- responding polynomial regression coefficients are calculated and can be saved in ASCII tiles which may then be imported into a statistical computing package for further analysis. Examples of the use of the program are provided. Key words: Polynomial growth curves; Longitudinal studies; Missing data; PC program Introduction A number of methods for estimating and comparing the average polynomial growth curves (AGCs) in one or more groups of individuals exist when subjects are measured at identical times, modeled with polynomials of the same degree and when a multivariate normal distribution for the repeated measurements can be assumed. Among the available one-sample methods are those given in Refs. 1-3; the best known of the G-sample procedures is that of Ref. 4. These have been implemented and the procedures are described in Refs. 5-10. Other applications, not concerned solely with AGCs, are considered in Refs. 11-14. These methods and programs are able to provide considerable insight into growth and developmental processes when- ever the conditions mentioned above are satisfied, but practical circumstances often preclude their application. The assumption of common times of measurement is especially troublesome: individuals invariably miss one or more appointments. Ex- cluding such individuals from the analysis wastes information; estimating the miss- ing values so that they may be included is difficult and may introduce additional (strong) assumptions into the analysis which many researchers would rather avoid. Correspondence to: Emet D. Schneiderman, Department of Oral and Maxillofacial Surgery, Baylor College of Dentistry, 3302 Gaston Ave, Dallas, TX 75246, USA. 0020-7101/93/$06.00 0 1993 Elsevier Scientific Publishers Ireland Ltd. Printed and Published in Ireland