IJE Advance Access originally published online on August 8, 2005
International Journal of Epidemiology 2005 34(5):1167-1168; doi:10.1093/ije/dyi161
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Published by Oxford University Press on behalf of the International Epidemiological Association
Letter to the Editor |
Genetic biases in using ‘Mendelian randomization’ to compare transplantation with chemotherapy
School of Applied Statistics, The University of Reading, PO Box 240, Reading RG6 6FN, UK. E-mail: r.n.curnow{at}reading.ac.uk
Sirs—The recent paper by Wheatley and Gray1 pointed out that Mendelian randomization may not entirely remove biases in the comparison of stem cell transplantation (SCT) with chemotherapy. These biases arise from the probable delays in SCT treatment and because of prognostic factors that may be correlated with the number of siblings in the family.
There may also be biases because patients with an HLAcompatible sibling will have HLA genotypes in differing proportions to those without a compatible sibling. This will only be important if the relative effectiveness of the treatments is related directly to the patient's HLA genotype or to any genotypes at other loci that are associated with the HLA genotypes.
Consider a single locus with n alleles, A1, A2, ..., An, that have frequencies in the population pi, i = 1, 2, ..., n, and assume that the there is random mating in the parental generation; that a match with a sibling means a complete genotypic match at the locus and that the patient who is a candidate for a transplant has only one sibling available for testing as a donor. Table 1 shows the parental matings that may produce siblings that are identical at the locus, either both homozygous, A1A1, or both heterozygous, A1Ax. In Table 1 X, Y, and Z represent all possible distinct alleles that are not A1. The probability of each parental mating is obtained by multiplying the product of the frequencies of the four alleles involved by a coefficient obtained by multiplying factors of 2 for each heterozygous parent as in the Hardy–Weinberg formula and further by a factor of 2 if the parents differ in genotype. The latter allows for the two genotypes being either male/female or female/male. Also shown for each parental mating are the probabilities of the matched pairs of siblings, A1A1 or A1Ax. By summing the product of the probabilities of the parental mating type and the probabilities of the matching pairs over all possible pairs of distinct alleles Ax and Ay, the probability of a matching pair of homozygous A1A1 siblings is
 | (1) |
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The probability of a matching pair of heterozygous siblings, for example A1A2, is
 | (2) |
and 2p1p2. Summing (1) and (2) over the n alleles and n(n – 1)/2 pairs of alleles gives, respectively, the probability of a homozygous and a heterozygous match.
Matching of siblings is by phenotype not genotype with some alleles at each of the three HLA loci, A, B, and DR, merged into broad antigenic equivalents. The chromosome sections with the merged alleles will be referred to as haplotypes. Providing there are no recombinations within the HLA locus, haplotypes can be treated for our purposes as alleles at a single locus with one exception. Two siblings can be phenotypically identical although not sharing identical haplotypes. As an example, among the 15 haplotypes commonest in Caucasian American populations (Mori et al.2) there is one set of four haplotypes that can in two pairs achieve the same phenotype. The pairs are A1B8DR3/A2B57DR7 and A1B57DR7/A2B8DR3. The parental haplotypes must have been A1B8DR3/A1B57DR7 and A2B8DR3/A2B57DR7 with probability 8p1p2p3p4 where p1, p2, p3 and p4 are the frequencies of the four haplotypes. Patients with matching siblings will, therefore, be equally A1B8DR3/A2B57DR7 and A1B57DR7/A2B8DR3 each with probability p1p2p3p4 = 0.000000032. The corresponding probabilities of a child with a matching sibling through identical haplotypes are 0.000196 and 0.000044. Clearly the matches with non-identical haplotypes can safely be ignored.
The National Marrow Donor Program Donor Register (www.ashi-hla.org/resourcesfiles/resources-frequencies.html) provides estimates of the ABDR haplotype frequencies for three North American populations. Using the data on the Caucasian American population in which 9642 haplotypes were estimated to have non-zero frequencies, only 184 had estimated frequencies >0.1%. The three highest estimated frequencies were 0.0518, 0.0263, and 0.0215 (Mori et al.2).
Table 2 shows that the probability of a matched sibling pair in this population is 0.2531. With the large number of haplotypes and the small frequencies associated with each, most parental pairs of identical siblings will be heterozygous with different haplotypes in the two parents. All such parental pairs would give a probability of 0.25 of a matched sibling pair and phenotypic frequencies the same as in a random population. The additional probability of 0.0033 arises from other types of parental pairs. The frequencies of the three commonest haplotypes and the six corresponding phenotypes shown in Table 2 demonstrate that this small set of additional parental pairs results in very small differences between the frequencies in the general population and in patients with a matching sibling. Clearly the genetic bias is very small and can safely be ignored particularly remembering that, to be important, the difference in phenotype has to affect differentially the consequences of the two treatments. Corresponding results for the African American and Asian American populations were even closer to 0.25, 0.2508 and 0.2516, respectively.
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The differences will be doubled if the patient has a sibling who does not match, but the difference will still be negligible. The effect on the comparison when the patient has more than one sibling with varying numbers of them matching their phenotype is more difficult to quantify but again unlikely to be important.
Clearly, the number of possible HLA haplotypes at the A, B, and DR loci and their low frequencies results in the majority of parents of siblings with identical HLA phenotypes being heterozygous and sharing no haplotypes in common. This means that differences in the distribution of phenotypes of siblings with and without an HLA identical sibling are very small. They should be ignored and concentration should be continued on the non-genetic biases that may occur between the types of patient being used to compare SCT with chemotherapy.
Acknowledgments
I am grateful to Dr Linda Shelper of UK Transplant for providing access to the data used in this paper.
References
1 Wheatley K, Gray R. Commentary: Mendelian randomization—an update on its use to evaluate allogenic stem cell transplantation in leukaemia. Int J Epidemiol 2004;33:15–17.
2 Mori M, Beatty PG, Graves M, Boucher KM, Milford EL. HLA gene and haplotype frequencies in the North American population: The National Marrow Donor Program Donor Registry. Transplantation 1997;64:1017–27.[ISI][Medline]
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