{'fraction_non_alphanumeric': 0.01639344262295082, 'fraction_numerical': 0.013909587680079483, 'mean_word_length': 5.3734177215189876, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Reducing attrition bias with an instrumental variable in a regression model: results from a panel of rheumatoid arthritis patients.

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.