STATISTICS IN MEDICINE Statist. Med. 2004; 23:411–429 (DOI: 10.1002/sim.1601) Estimating linear regression models in the presence of a censored independent variable Peter C. Austin 1; 2; ∗; † and Jerey S. Hoch 3 1 Institute for Clinical Evaluative Sciences; Toronto; Ont.; Canada 2 Department of Public Health Sciences; University of Toronto; Toronto; Ont.; Canada 3 Department of Epidemiology and Biostatistics; University of Western Ontario; London; Ont.; Canada SUMMARY The current study examined the impact of a censored independent variable, after adjusting for a second independent variable, when estimating regression coecients using ‘na ve’ ordinary least squares (OLS), ‘partial’ OLS and full-likelihood models. We used Monte Carlo simulations to determine the bias associated with all three regression methods. We demonstrated that substantial bias was introduced in the estimation of the regression coecient associated with the variable subject to a ceiling eect when na ve OLS regression was used. Furthermore, minor bias was transmitted to the estimation of the regression coecient associated with the second independent variable. High correlation between the two independent variables improved estimation of the censored variable’s coecient at the expense of estimation of the other coecient. The use of ‘partial’ OLS and maximum-likelihood estimation were shown to result in, at most, negligible bias in estimation. Furthermore, we demonstrated that the full- likelihood method was robust under misspecication of the joint distribution of the independent random variables. Lastly, we provided an empirical example using National Population Health Survey (NPHS) data to demonstrate the practical implications of our main ndings and the simple methods available to circumvent the bias identied in the Monte Carlo simulations. Our results suggest that researchers need to be aware of the bias associated with the use of na ve ordinary least-squares estimation when estimating regression models in which at least one independent variable is subject to a ceiling eect. Copyright ? 2004 John Wiley & Sons, Ltd. KEY WORDS: linear regression; ceiling eect; censored independent variable; regression models; censoring INTRODUCTION Applied researchers frequently analyse limited dependent variables. Floor or ceiling eects commonly aect variables like expenditures [1–3], hours worked [4] and number of arrests ∗ Correspondence to: Peter C. Austin, Institute for Clinical Evaluative Sciences, G1 06, 2075 Bayview Avenue, Toronto, Ont., Canada M4N 3M5. † E-mail: peter.austin@ices.on.ca Contract=grant sponsor: Natural Sciences and Engineering Research Council Contract=grant sponsor: Ontario Ministry of Health and Long-Term Care Received September 2002 Copyright ? 2004 John Wiley & Sons, Ltd. Accepted May 2003