Curve fitting for repeated measurements made at irregular time-points.

In longitudinal studies of human populations, it is often not feasible to measure all subjects at the same time-points. This precludes the use of classical methods of curve fitting for repeated measurements. When the total interval of follow-up is short for all subjects in the study, an intraclass correlation matrix is assumed for the measurements on each subject. An estimation procedure based on iteratively reweighted least squares is described. The model is then generalized to incorporate covariables, with little modification in the estimation procedure. The proposed method is applied to data from a longitudinal study of bone mass in postmenopausal women.

[1]  Calyampudi R. Rao,et al.  Linear Statistical Inference and Its Applications. , 1975 .

[2]  Calyampudi R. Rao,et al.  The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves. , 1965, Biometrika.

[3]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[4]  D. M. Allen,et al.  Analysis of growth and dose response curves. , 1969, Biometrics.

[5]  S. Walker,et al.  A randomization test for comparison of groups of growth curves with different polynomial design matrices. , 1977, Biometrics.

[6]  Frederick E. Smith,et al.  Matrix Algebra for the Biological Sciences , 1966 .

[7]  R. Potthoff,et al.  A generalized multivariate analysis of variance model useful especially for growth curve problems , 1964 .

[8]  Tom Fearn,et al.  A Bayesian approach to growth curves , 1975 .

[9]  C. G. Khatri,et al.  A note on a manova model applied to problems in growth curve , 1966 .

[10]  Barr Rosenberg,et al.  Linear regression with randomly dispersed parameters , 1973 .

[11]  C. Johnston,et al.  The loss of bone mineral with aging and its relationship to risk of fracture. , 1975, The Journal of clinical investigation.

[12]  D. Lindley,et al.  Bayes Estimates for the Linear Model , 1972 .

[13]  P. Sprent Models in regression and related topics , 1971 .

[14]  D. Kleinbaum A generalization of the growth curve model which allows missing data , 1973 .

[15]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .