Leigh J P, Ward M M, Fries J F
Department of Economics, San Jose State University, CA 95192-0114.
Stat Med. 1993 Jun 15;12(11):1005-18. doi: 10.1002/sim.4780121102.
This study proposes an econometric technique to reduce attrition bias in panel data. In the simplest case, one estimates two regressions. The first is a probit regression based on sociodemographic and clinical characteristics measured at baseline. The probit regression estimates the probability that subjects stay or leave over the duration of the study. We insert the predicted probabilities from the probit regression into an inverse Mills ratio (IMR) or hazard rate to form an instrumental variable. We use this instrumental variable subsequently as an additional covariate in a second regression model that attempts to explain fluctuations in the dependent variable. The second regression, which is linear, includes only subjects who remained in the study. In alternative models, instrumental variables are created using predicted values from least squares and logit regressions estimating the probability that subjects stay or leave. The use of the instrumental variables reduces the effects of attrition bias in the linear regression model. We applied the technique to a panel of patients with rheumatoid arthritis (RA) enrolled in 1981 and followed through 1990. We attempted to predict values for a measure of functional disability recorded in 1990 with use of covariates measured in 1981. The dependent variable was an index of disability in 1990 and the independent variables (covariates) included the disability index from 1981, the years of duration of RA, gender, marital status, education, and age in 1981. The correction technique suggested that ignoring attrition bias would underestimate the strength of associations between being female and the subsequent disability index, and overestimate the strength of associations between being married spouse present, age, and the initial disability index on the one hand and the subsequent disability index on the other.
本研究提出了一种计量经济学技术，以减少面板数据中的损耗偏差。在最简单的情况下，估计两个回归模型。第一个是基于基线时测量的社会人口统计学和临床特征的概率单位回归。概率单位回归估计了受试者在研究期间留下或离开的概率。我们将概率单位回归的预测概率插入到逆米尔斯比率（IMR）或风险率中，以形成一个工具变量。随后，我们在第二个回归模型中使用这个工具变量作为一个额外的协变量，该模型试图解释因变量的波动。第二个回归模型是线性的，只包括留在研究中的受试者。在替代模型中，使用最小二乘法和逻辑回归的预测值创建工具变量，估计受试者留下或离开的概率。工具变量的使用减少了线性回归模型中损耗偏差的影响。我们将该技术应用于一组1981年登记并随访至1990年的类风湿性关节炎（RA）患者。我们试图使用1981年测量的协变量来预测1990年记录的功能残疾测量值。因变量是1990年的残疾指数，自变量（协变量）包括1981年的残疾指数、RA病程、性别、婚姻状况、教育程度和1981年的年龄。校正技术表明，忽略损耗偏差会低估女性与随后残疾指数之间关联的强度，高估已婚配偶在场、年龄以及初始残疾指数与随后残疾指数之间关联的强度。
