A technique for summarizing longitudinal data

Abstract

Many studies collect longitudinal data but do not use them efficiently. We propose a technique for reducing a set of longitudinal data into four common summary statistics together with time. These statistics can be used in place of the raw data in further analyses, for example in a regression analysis. Instead of arbitrarily choosing the summary statistics, we derive them mathematically, thus justifying their use. This simplifies the subsequent analyses, and also improves the interpretation of the results. An example from the Framingham Heart Study illustrates the procedure.

Summarizing data through a piecewise linear growth curve model

“…Hathaway et al [2] proposed a statistic that represents how an individual is di erent from other individuals, using the individual's deviation from an overall pattern of all the individuals. Then they partitioned this statistic into several summary statistics and then analyse these summary statistics to determine which pieces from the decomposition relate to the dependent variable of interest.…”

“…One of the major assumptions in the model proposed by Hathaway et al [2] is that it is linear. However, in randomized clinical trials, the data collected are usually at regular intervals and the growth curves need not be linear.…”

“…Sometimes ad hoc summary statistics such as the mean and standard deviation of the series are employed [1]. Hathaway et al [2] provide a mathematical foundation and justiÿcation for the selection of a set of statistics that e ciently summarizes the information in the repeated measures of an independent variable. These statistics, smaller in number than the number of repeated measurements can be used as independent variables in later analyses.…”

“…The longitudinal data when plotted show a non-linear trend. Hence, an attempt has been made (i) to indicate a piecewise linear model and to establish summary statistics on the lines of Hathaway et al [2] (ii) to ÿnd out signiÿcant variations with respect to the regimen, summary statistics, etc. and (iii) to compare the goodness of ÿt of several models.…”

“…Our results are validated through a simulation study using the method of empirical distribution from continuous grouped data; the data are generated by regimen-wise with 50 replications each of a sample of size 100. In Section 2, we describe the clinical trial of leprosy treatment and in Section 3 we brie y describe the model proposed by Hathaway et al [2] and the observations made by Karakostas [4]. Section 4 deals with the summarizing the repeated measurements data using a piecewise linear growth curve model.…”