A Procedure for Comparing Groups of Time-Dependent Measurements

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Abstract
A three stop procedure is proposed for the comparison of groups, where for each individual a process is investigated on the basis of repeated measurements (e.g. 3 up to about 15 time points).1. A natural cubic spline function is fitted to the time-dependent measurements of each individual. A cubic spline is a function which is composed of piecewise polynomials, continuous up to and including second derivatives; it has a minimal »curvature«, so that a »smooth« curve is generated.2. For each individual the value of a problem-oriented parameter is estimated from the spline function.3. The values of the problem-oriented parameter are evaluated with standard, not necessarily longitudinal methods for estimating and hypothesis testing.The proposed procedure requires neither an equal number of measurements for each individual, nor the same time points of measurement for all individuals, nor equal length of the time intervals. Splines can be fitted to very different patterns of curves. They can be used for a more exact calculation of parameters adequate to the problem concerned. The procedure necessitates the use of a computer; programs are available and do not demand excessive arithmetic precision and computing time.

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