A computer programme to calculate risk in X linked disorders using multiple marker loci

Modelling Germline Mosaicism and Different New Mutation Rates Simultaneously for Appropriate Risk Calculations in Families with Duchenne Muscular Dystrophy

For several genetic diseases two biological phenomena have been recognised as important: germline mosaicism; and different new mutation rates in males and females depending on mutation type. Both principles have been investigated separately and their influence on risk estimation in families has been exemplified in the literature. The aim of this paper is to present a general model that includes mosaicism and different new mutation rates. Mosaicism is introduced by defining additional alleles at the disease locus in combination with adapted segregation rules. Taking Duchenne muscular dystrophy as an example, we derive the conditions which have to be fulfilled for a population in mutation selection equilibrium. Our approach describes the model at the population level and not in individual subjects. This has the advantage of being able to use well known algorithms for the calculation of likelihoods in pedigrees, and to include additional diagnostic information such as marker genotypes and carrier deletion test results. We demonstrate the impact of the new model on a typical pedigree. In families where the patient is not available, the distinction between point mutations and deletions is important, since often molecular diagnostic tests for females can only screen for deletions. Negative deletion test results can now be included in the risk calculations.

Hazard and probabilities of unknown genotypes

The likelihood of a genotype of an unsampled individual depends upon genetic data from relatives. When these relatives may be carriers of a mutation as in X-linked disease, the likelihood of a genotype is altered by the consequences of the possible genotypes on offspring. The probabilities of the possible genotypes are easily derived from the probabilities conditional on the genotype obtained from a computer program aimed at risk calculation. This procedure of genotype reconstruction brings to light a potential hazard in the interpretation of computer data: a compound risk may be better represented as the harmonic mean of a set of conditional probabilities than the simple average of these probabilities.

A simple method for calculating risks before DNA analysis

Calculation of carrier risk of an X linked disease may be performed on a small computer after DNA analysis, but a method for rapid hand estimation of the risk is still useful for a quick check of the results and weighing the relative importance of each element of information, such as the determination of a haplotype. Each risk estimation is a function of a prior risk and the product of likelihood ratios and these terms are derived themselves from parameters such as fitness or the relative mutation rate in male and female gametes. Even if it is often difficult to have strong experimental estimation of these variables, the existence of a normal father or grandfather must be considered whenever male fitness is not null. The likelihood ratio for a woman for not being a carrier, when her father is not affected and her mother has herself a likelihood R for not having the mutated gene, may be expressed as the ratio 2R/(CmR + 1), with Cm being a function of male fitness and relative mutation rate. Cm represents the odds ratio for the mother of a carrier not to be a carrier, given that the father of the known carrier is not affected. This formula can be used recurrently and reduces to 2R/(R + 1) in lethal X linked disease. When likelihood ratios are expressed as an algebraic function, maximum values are easily determined, hence fixing the limits of DNA analysis.

Making the most of multiple measurements in estimating carrier probability in Duchenne muscular dystrophy: the Bayesian incorporation of repeated measurements using logistic discrimination

In carrier detection studies, females-at-risk are usually tested several times if the results are ambiguous, whereas subjects in the control and obligate carrier reference groups may not be tested as often. The question is how to incorporate the multiple measurements most effectively with information in the family pedigree into combined carrier risks. Sets of measurements on individuals are not independent, but are related with the correlation coefficient 0 less than rho less than 1. We have developed a procedure for incorporating repeated measurements on individuals and their a priori chance of having the disease into logistic models. This procedure utilizes the set of measurements and an estimate of rho. We describe application of this procedure to carrier detection in Duchenne muscular dystrophy (DMD) using serum creatine kinase (CK) measurements as the biochemical indicator of carrier status. Estimates of rho for controls and obligate DMD carriers did not differ significantly from 0.5. Repeated testing with use of rho = 0.5 significantly decreased the median logistic carrier probability for controls and increased it for carriers. In some cases four to six rather than the three CK tests conventionally used in genetic counseling were necessary to obtain a stable logistic carrier probability for a subject.

The population genetics of Duchenne: natural and artificial selection in Duchenne muscular dystrophy

The dynamics of X linkage was derived by Haldane in 1935. It is clear that the majority of mutations to an X linked lethal are new and that methods of control based on relatives of known cases can have limited impact on future incidence. The ability to define and track neighbouring loci allows some carriers who are daughters of carriers to be detected, and possible carriers to be excluded, with high reliability. Fetal diagnosis may also be made in the same way, but not without a substantial casualty rate. The precision of such diagnosis by proxy is limited both by the estimate of the recombination fraction and its variance, and can rarely exceed 1/s where the recombinational data are based on s informative meioses. Bracketing loci provide greater security from failure to diagnose cases but may involve substantial casualty rates. The estimation of both failure rates and casualty rates is discussed.

A multipoint linkage analysis program for X-linked disorders, with the example of Duchenne muscular dystrophy and seven DNA probes

The analysis of linkage data with multiple markers is a complex problem, only soluble with the help of computer programs. A package of programs is presented which allows the analysis of X-linked data with reasonable speed. Published data relating Duchenne muscular dystrophy and seven X-specific DNA probes are analysed. The results presented are the maximum likelihoods of the eight possible orders and the interlocus distances of the most likely order. Also calculated are the mean and standard deviation of risk for selected cases with information derived from both single probes and pair of probes bridging the disease locus.