Lagakos S W
Harvard School of Public Health, Boston, Massachusetts.
Stat Med. 1988 Jan-Feb;7(1-2):257-74. doi: 10.1002/sim.4780070126.
We consider three commonly-used statistical tests for assessing the association between an explanatory variable and a measured, binary, or survival-time, response variable, and investigate the loss in efficiency from mismodelling or mismeasuring the explanatory variable. With respect to mismodelling, we examine the consequences of using an incorrect dose metameter in a test for trend, of mismodelling a continuous explanatory variable, and of discretizing a continuous explanatory variable. We also examine the consequences of classification errors for a discrete explanatory variable and of measurement errors for a continuous explanatory variable. For all three statistical tests, the asymptotic relative efficiency (ARE) corresponding to each type of mis-specification equals the square of the correlation between the correct and fitted form of the explanatory variable. This result is evaluated numerically for the different types of mis-specification to provide insight into the selection of tests, the interpretation of results, and the design of studies where the 'correct' explanatory variable cannot be measured exactly.
我们考虑三种常用的统计检验，用于评估一个解释变量与一个测量的、二元的或生存时间的响应变量之间的关联，并研究因对解释变量进行错误建模或错误测量而导致的效率损失。关于错误建模，我们研究在趋势检验中使用错误的剂量指标、对连续解释变量进行错误建模以及对连续解释变量进行离散化的后果。我们还研究离散解释变量的分类错误和连续解释变量的测量误差的后果。对于所有这三种统计检验，对应于每种错误设定类型的渐近相对效率（ARE）等于解释变量的正确形式与拟合形式之间的相关性的平方。针对不同类型的错误设定对该结果进行了数值评估，以深入了解检验的选择、结果的解释以及在无法精确测量“正确”解释变量的研究设计。
