INDEPENDENT INHERITANCE OF SERUM IMMUNOGLOBULIN E CONCENTRATIONS AND AIRWAY RESPONSIVENESS

	To the Editor :

Writing letters to the editor post factum about papers already published is something I rarely do since, even if my comments are correct, it is "too late" in practice to alter the impact of the paper. On this occasion I felt that I just had to take up my pen to comment upon a statistically invalid device used in the most elegant statistical analysis of the inheritance of serum IgE and airway hyperresponsiveness in the paper by Palmer and colleagues (1). I refer to the expression of airway hyperresponsiveness as the dose-response slope (DRS) of O'Connor and colleagues (2). This measures the response as the difference between the lowest post challenge in FEV₁ and baseline FEV₁ divided by the cumulative dose of agent administeredso far so good. However, if there is no fall in FEV₁ or even a rise after the challenge, as happens in very many normal subjects, the DRS is zero or even negative. In order to avoid taking the logarithm of zero or a negative number for statistical calculations of log-normally distributed bronchial hyperresponsiveness, O'Connor and colleagues (2) add 0.3 to all these "awkward" logarithms. This means that a subject with no fall in FEV₁ after the challenge (zero slope) is given a log value of 0.3, which is equivalent to a provoking dose causing a 20% fall in FEV₁ (PD₂₀) of 10.02 µmol (20/10^0.3). In the present study the authors add 10 to each DRS measurement "in order to allow log_e transformations when the DRS was  0." This is equivalent to assuming a PD₂₀ of 2.0 µmol when there is no response to the challenge. In other words, all nonresponsive subjects are allocated a censored value of the DRS, which is then included along with noncensored true values in the analysis.

In my view this is scientifically unjustified and could easily have led Palmer and colleagues (1) to reach an incorrect conclusion about the inheritance of airway hyperresponsiveness.

Hadassah University Hospital, Jerusalem, Israel

1. Palmer LJ, Burton PR, Faux JA, James AL, Musk AW, Cookson WO. Independent inheritance of serum immunoglobulin E concentrations and airway responsiveness. Am J Respir Crit Care Med 2000; 161: 1836-1843 [Abstract/Free Full Text].

2. O'Connor G, Sparrow D, Taylor D, Segal M, Weiss S. Analysis of dose-response curves to methacholine. Am Rev Respir Dis 1987; 136: 1412-1417 [Medline].

	From the Authors:

Dr. Godfrey raises an interesting point regarding our use of the dose-response slope (DRS) proposed by O'Connor and colleagues (1). He suggests that the addition of a constant of 10.0 to each DRS measurement prior to log_e transformation may have led us to "reach an incorrect conclusion about the inheritance of airway hyperresponsiveness." We would like to make two points in response to these comments.

First, the whole point of the DRS as proposed by O'Connor and coworkers (1) as a measure of airway responsiveness to inhaled agonist was to escape the artificial and somewhat arbitrary dichotomization of response to agonist challenge that is imposed by the PD₂₀. Subjects are allocated a DRS even if the PD₂₀ is not achieved, and thus become available for analysis. The resulting variable shows better correlations with other parameters such as the serum IgE concentration and, as our study has shown, exhibits substantial heritability. The right-censoring inherent in a PD₂₀ is artificial and the resultant censored variable can be difficult to deal with analytically (1, 2). Attempting to frame the DRS in terms of "censoring" and "noncensoring" is illogical in the context of what the DRS was intended to measure. In our subjects, more than 90% had a measurable DRS, whereas only 10% had a measurable PD₂₀; there was therefore nearly an order of magnitude more information inherent in the DRS than in the older measure.

Secondly, there is an important statistical issue that needs emphasizing. Addition of a constant to a variable that is then log_e-transformed is a simple monotonic transformation: it does not alter the ranking of the observations. It is unusual for such a transformation to qualitatively distort inferences, and when it does, it is almost always because too small a constant has been added, resulting in large negative residuals associated with the initially most negative values. This leads to excessive influence of these unusual observations and poor model fit. We have avoided this in two ways: first, we deliberately chose a relatively large constant, and second, we subjected our models to appropriate checks of goodness-of-fit. Consequently, larger constants would have made almost no difference to our conclusions, and smaller constants would only have changed things if the model had fitted badly.

We would, however, strongly agree with Dr. Godfrey that the interpretation of agonist challenges is an important area for ongoing methodological research (3).

Brigham and Women's Hospital and Harvard Medical School, Boston, Massachusetts

Paul Burton

University of Leicester, Leicester, United Kingdom

William Cookson

John Radcliffe Hospital, Oxford, United Kingdom

1. O'Connor G, Sparrow D, Taylor D, Segal M, Weiss S. Analysis of dose-response curves to methacholine: an approach suitable to population studies. Am Rev Respir Dis 1987; 136: 1412-1417 .

2. Chinn S, Burney PG, Britton JR, Tattersfield AE, Higgins BG. Comparison of PD₂₀ with two alternative measures of response to histamine challenge in epidemiological studies. Eur Respir J 1993; 6: 670-679 [Abstract].

3. Scurrah KJ, Palmer LJ, Burton PR. Variance components analysis for pedigree-based censored survival data using generalized linear mixed models (GLMMs) and Gibbs sampling in BUGS. Gene Epidemiol 2000; 19: 127-148 [Medline].