Key Points
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Statistical gene mapping allows the approximate localization of disease susceptibility genes on the human gene map in the absence of any functional knowledge of such genes.
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After a brief introduction to conventional mapping methods, we focus on the mapping of complex heritable traits, such as diabetes and schizophrenia, and outline the known statistical methods that specifically address the multi-locus nature of complex traits.
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These methods require sophisticated statistical approaches to allow for the consideration of multiple genetic marker loci and their combined effects on disease, while at the same time keeping the overall rate of false-positive results at an acceptably low level.
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The development of statistical multi-locus methods for gene mapping has only recently begun on a larger scale; statistical properties, such as power under different scenarios, still need to be explored. In addition, little is known about the actions and interactions of genes that underlie complex traits, although such genes are likely to exist.
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Extreme cases of complex traits might only be due to interactions between genes such that each single gene does not exert an effect by itself. It is shown that even here statistical approaches can come up with useful results, but the required computational effort might be higher than the capacity that is available at present.
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Many of these methods have been incorporated in computer programs that represent delicate and sensitive tools for the hands of specialists. If used without the proper background knowledge, they can lead to misinterpretation of data.
Abstract
Statistical analysis methods for gene mapping originated in counting recombinant and non-recombinant offspring, but have now progressed to sophisticated approaches for the mapping of complex trait genes. Here, we outline new statistical methods that capture the simultaneous effects of multiple gene loci and thereby achieve a more global view of gene action and interaction than is possible by traditional gene-by-gene analysis. We aim to show that the work of statisticians goes far beyond the running of computer programs.
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This work was supported by grants from the National Institute of Mental Health.
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Glossary
- RECOMBINATION FRACTION
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The proportion of offspring that receives a recombinant haplotype from a parent, or the probability that recombination occurs between two loci.
- BACKCROSS
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Originally, backcross referred to the mating of an offspring with one of its parents, in which the offspring is heterozygous, with the parent being homozygous for one of the alleles in the offspring's genotype. Nowadays, backcross simply refers to a mating between individuals with those two genotypes.
- LIKELIHOOD ANALYSES
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A statistical method that calculates the probability of the observed data under varying hypotheses, to estimate model parameters that best explain the observed data and determine the relative strengths of alternative hypotheses.
- LOD SCORE
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The logarithm of the likelihood ratio (odds) for genetic linkage versus no linkage at a given value of the recombination fraction.
- LOGISTIC REGRESSION MODEL
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A statistical model for the dependency of a binomial (two-class) phenotype on a number of risk factors. The probability, p, for one of the two phenotype states is expressed in the form of its logit, log(p/(1 – p)), which is assumed to be predicted by the linear combination (weighted sum) of the risk factors.
- STEPWISE REGRESSION
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The step-by-step build-up of a regression model, which represents a dependent variable as a weighted sum (linear combination) of independent (risk) variables.
- TEST STATISTIC
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A statistic is any function of a random sample — in particular, of the observations in an experiment. A test statistic is a statistic that is used in a statistical test to discriminate between two competing hypotheses, the so-called null and alternative hypotheses.
- SIGNIFICANCE LEVEL
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The proportion of false-positive test results out of all false results — that is, results that are obtained when the effect investigated is known to be absent (see also false discovery rate).
- ANGIOPLASTY
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A medical procedure that is used to widen coronary arteries with a thin balloon because these blood vessels have become clogged.
- CORONARY ARTERY RESTENOSIS
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The re-occurrence of a narrowing or blockage of an artery at the site where angioplasty had previously been performed.
- HARDY–WEINBERG EQUILIBRIUM
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A state in which the proportions of genotypes present depends only on the frequencies of alleles in the genotypes.
- RESTENOSIS
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A re-narrowing or blockage of an artery at a site where angioplasty was previously done.
- RECURSIVE PARTITIONING
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A process for identifying complex relationships in large sets by dividing them into a hierarchy of smaller and more homogeneous subgroups on the basis of the most statistically significant indicators.
- CLUSTER ANALYSIS
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A mathematical algorithm that organizes a set of items according to their similarity. For example, genes can be clustered according to their similarity in pattern of expression.
- MARGINAL PENETRANCE
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In epistatic interactions between two loci asscoiated with disease, each with three genotypes, the nine genotype pairs might each be associated with a certain penetrance — that is, the probability that the genotype pair leads to disease. From these penetrances and the genotype frequencies, (marginal) penetrances might be computed — that is, penetrances that are associated with the genotypes at one of the two loci.
- BONFERRONI CORRECTION
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When n statistical tests are carried out, each has the potential (probability, p, the significance level) to return a false-positive result. If tests are independent of each other, the so-called experiment-wise probability that one or more tests show a false-positive result is approximately np. So, to achieve an experiment-wise false-positive rate of p, each individual test must only be allowed a false-positive error rate of p/n, which is referred to as the Bonferroni correction.
- FALSE DISCOVERY RATE
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(FDR). The proportion of false-positive test results out of all positive (significant) tests (note that the FDR is conceptually different to the significance level).
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Hoh, J., Ott, J. Mathematical multi-locus approaches to localizing complex human trait genes. Nat Rev Genet 4, 701–709 (2003). https://doi.org/10.1038/nrg1155
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DOI: https://doi.org/10.1038/nrg1155
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