The Variance Calculation Following Multiple Imputation: Illustration with Cholera Mortality Data Collected by John Snow

• Activity Number: 251
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): James A. Hanley*+ and Juli Atherton
• Companies: McGill University and McGill University
• Keywords: missing data ; epidemiology ; case-control study ; historical data ; estimated denominators ; variance component

Abstract

Multiple imputation (MI) is increasingly used. To appreciate the basis for the variance formula, we study situations where there is an established formula, such as Woolf's variance of the log of an odds ratio. This ratio is used to estimate a rate ratio when the relative sizes of the denominators of the compared rates are estimated (via a 'denominator' series) rather than known. In the 'grand experiment' of 1854, John Snow exploited the intimate intermixing of the water supply of two water companies over an extensive part of London. We compare the MI and Woolf formulae, using the water supply data in Snow's (numerator) series of 300 cholera deaths, and in a similarly-sized denominator (control) series. Snow used the already-known numbers of customers served by these two companies; we simulate a situation where he had to estimate the relative denominator sizes from a sample survey