Svärdsudd K, Blomqvist N
Scand J Soc Med. 1978;6(2):85-95. doi: 10.1177/140349487800600207.
The relation between change and initial value is of great interest in longitudinal studies. With variables containing random errors (short-term intra-individual variations and measurement errors) the directly computed relation is however, biased by the regression towards the mean phenomenon. Earlier proposed solutions of the problem are unsatisfactory. In this paper the regression towards the mean phenomenon is described and a new method is proposed by which the error caused by the regression towards the mean is avoided. The method is applied to a set of longitudinal blood pressure data. It is shown that the observed, biased relation in this case is significantly negative, while the correct relation obtained with this method is significantly positive. Since random errors are present in most biological variables, similar erroneous conclusions may easily be drawn also in other cases if the regression towards the mean phenomenon is not corrected for. In this analysis, random errors constitute 65--80% of the observed blood pressure change. To reduce this dominance, recommendations about study design for future studies of change/initial value relationships are given.
在纵向研究中，变化与初始值之间的关系备受关注。然而，对于包含随机误差（个体内短期变化和测量误差）的变量，直接计算得出的关系会受到均值回归现象的影响而产生偏差。早期提出的该问题解决方案并不令人满意。本文描述了均值回归现象，并提出了一种新方法，通过该方法可避免均值回归所导致的误差。该方法应用于一组纵向血压数据。结果表明，在此情况下观察到的有偏差关系显著为负，而用此方法获得的正确关系显著为正。由于大多数生物学变量中都存在随机误差，如果不校正均值回归现象，在其他情况下也很容易得出类似的错误结论。在该分析中，随机误差占观察到的血压变化的65%至80%。为减少这种主导作用，给出了关于未来变化/初始值关系研究的研究设计建议。
