Overadjustment: a Misunderstood Phenomenon

Abstract

Overadjustment: a Misunderstood PhenomenonAbstract Number:1983 Ben Armstrong* Ben Armstrong* London School of Hygiene and Tropical Medicine, United Kingdom, E-mail Address: [email protected] Search for more papers by this author AbstractThere is a common view that adjusting ‘too aggressively’ for covariates will bias exposure effects towards the null. We review what is known on this through an illustration in which wind speed is adjusted for in a time series study of air pollution (AP) effects on health. We assume that windspeed is strongly associated with AP but is not with mortality other than possibly through its impact on AP. Linear model algebra and simulations show that adjusting in regression for windspeed leads to imprecision but no bias in the AP coefficient provided the AP is measured without classical measurement error. With such error the attenuation bias present without adjustment is exacerbated by the adjustment. For example, in simulations true coefficient b= 0.2 and estimation without adjusting windspeed gives SE=0.06. If adjusted for windspeed, correlated at r=0.5 with AP, the means of simulated b’s remains 0.20, but SE is raised to 0.10. Adding classical error in AP with SD=40% that of true AP gives bias (mean b =0.17) WITHOUT windspeed adjustment, but bias increases to b=0.14 in adjusting windspeed. This result – loss of precision but not bias other than through measurement error – holds for adjusting for any covariate associated with the exposure of interest but not independently with the outcome. It holds in particular for including in a time series regression model unnecessarily large number of degrees of freedom in a time or temperature spline. Adjusting for covariates on the causal pathway between exposure and outcome does bias the exposure coefficient towards the null, other than in special cases of ‘mediation’ analysis aimed at estimating the association by other causal routes. In conclusion, unless a covariate lies causally between exposure and outcome, the ‘overadjustment’ caused by adjusting for it if it is not related to the outcome causes imprecision but not bias, though it does exacerbate bias if there is classical exposure measurement error.