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Cost-effective analysis of candidate genes using htSNPs: a staged approach

Genes & Immunity volume 5, pages 301–305 (2004)Cite this article

Abstract

We have previously shown that the selection of haplotype tag single nucleotide polymorphisms (htSNPs) and their statistical analysis in a multi-locus transmission/disequilibrium test (TDT) results in a more cost-effective genotyping strategy in disease association studies of genes by minimising redundancy due to linkage disequilibrium between SNPs. Further savings can be achieved by the use of a two-stage genotyping strategy. This approach is illustrated here in conjunction with the multi-locus TDT in determining whether common alleles of the immune regulatory genes RANK and its ligand TRANCE (RANKL) are associated with type 1 diabetes (T1D). A saving of approximately 75% of potential genotyping reactions could be made with minimal loss of power. There was little evidence from our analysis for association between the TRANCE and RANK genes and T1D in the populations tested.

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Acknowledgements

The Wellcome Trust and the Juvenile Diabetes Research Foundation International have funded this work. We thank Vin Everett, Geoff Dolman and Neil Walker for data management and the DNA team for sample preparation. Diabetes UK and the Human Biological Data Interchange are acknowledged for multiplex family collections. We also thank the Norwegian Study Group for Childhood Diabetes, Dag Undlien and Kjersti Ronningen for the collection and provision of Norwegian samples.

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Author notes

  1. C E Lowe and J D Cooper: These authors contributed equally to this work

Authors and Affiliations

  1. Juvenile Diabetes Research Foundation/Wellcome Trust Diabetes and Inflammation Laboratory, Cambridge Institute for Medical Research, University of Cambridge, Wellcome Trust/MRC Building, Cambridge, UK

    C E Lowe, J D Cooper, J M Chapman, B J Barratt, R C J Twells, E A Green, J A Todd & D G Clayton

  2. Department of Medical Genetics, Queen's University Belfast, Belfast City Hospital, Belfast, UK

    D A Savage

  3. Clinic of Diabetes, Institute of Diabetes, Nutrition and Metabolic Diseases ‘N Paulescu’, Bucharest, Romania

    C Guja & C Ionescu-Tîrgovişte

  4. Diabetes and Genetic Epidemiology Unit, National Public Health Institute, University of Helsinki, Helsinki, Finland

    E Tuomilehto-Wolf & J Tuomilehto

  5. Department of Public Health, University of Helsinki, Helsinki, Finland

    J Tuomilehto

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  1. C E Lowe
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  2. J D Cooper
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  3. J M Chapman
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  4. B J Barratt
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  5. R C J Twells
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  6. E A Green
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  7. D A Savage
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  8. C Guja
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  13. D G Clayton
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Corresponding author

Correspondence to D G Clayton.

Appendix A. Adjusting χ2 tests for stopping for futility in multi-stage association studies

Appendix A. Adjusting χ2 tests for stopping for futility in multi-stage association studies

We consider a study in which the test is carried out in a series of n stages, stopping for futility at each stage if the results, thus far, do not achieve a given nominal significance level. For a conventional frequentist interpretation, the nominal significance level at the end of the study should be corrected for the intermediate analyses.

χ2 tests are generated by quadratic forms T=uTV−1u, where u is (asymptotically) multivariate normal with variance V. The test statistic T is then distributed as a non-central χ2 distribution with df v, the rank of V and non-centrality parameter η=μTV−1μ where μ=E(u). If the test is carried out in a series of n stages, involving proportions p1,…,pn of the total available sample, the score vector decomposes into independent contributions u=u1+u2+···+un, where

Writing u[k], p[k] for the partial sums

the test statistic carried out after stage k is

The distribution of Tk, conditional upon the history of previous results, u1,,…,uk−1 is that of pkχ2/p[k], where χ2 is a non-central χ2 variate with v df and non-centrality parameter

We stop after stage k if Tk fails to exceed a critical value ck. The probability of exceeding this critical value conditional upon reaching stage k is

This integral is intractable but may be approximated by simulation.

An accurate and efficient Monte Carlo method for calculating the overall probability of rejection is to simulate sequences of score vectors subject to the stopping rule described. The length of such sequences will vary from one to n. The probability of exceeding the test criterion after stage 2 conditional upon reaching stage 2 may then be calculated by averaging Pr(T2>c2∣u1) over all simulated values of u1. Similarly, the probability of exceeding the test criterion after stage 3 conditional upon reaching stage 3 may be calculated by averaging Pr(T3>c3∣u1, u2) over all simulated pairs of values (u1, u2). In this manner, the complete sequence of conditional probabilities can be estimated. When generating the sequences of score vectors, without loss of generality, we may take the v elements of ui to be independent variates. The overall probability of rejecting the null hypothesis is given by the cumulative product

These calculations are implemented in the R language by the program Nstage.

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Lowe, C., Cooper, J., Chapman, J. et al. Cost-effective analysis of candidate genes using htSNPs: a staged approach. Genes Immun 5, 301–305 (2004). https://doi.org/10.1038/sj.gene.6364064

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