Eliminating bias in the estimation of the geometric mean of HI titres

The standard test for anti-haemagglutinin antibody titration is the haemagglutination inhibition (HI) test. The HI titre is defined as the dilution factor of the highest dilution that still completely inhibits haemagglutination. If the highest dilution tested (1:2560) still completely inhibits haemagglutination, an HI titre value of 2560 is assigned. Logarithmically transformed HI titres tend to be normally distributed. But because dilutions less than 1:2560 are not tested, the distribution may be truncated and the assumption of normality may not hold. As a consequence, the geometric mean titre (GMT) will be underestimated. Using data from 10 clinical studies, it is shown here that the GMT may be underestimated by 5–13%.An unbiased estimate of the GMT can be obtained by a statistical method that originates from the analysis of survival data: maximum likelihood estimation for censored observations. The maximum likelihood estimate of the GMT of truncated HI titres can be readily obtained using the statistical software package SAS®.