On a test of non-random segregation under linkage for autosomal recessive diseases.

To test the null hypothesis of random segregation of marker haplotypes from an unaffected parent to affected offspring for a one-locus autosomal recessive disease, Majumder proposed a test statistic which was shown to be locally most powerful against the alternative hypothesis of non-random segregation due to linkage between the disease and marker loci. The test procedure relied on a chi-squared approximation to the null distribution of the test statistic. In the present study, we show that the chi-squared approximation is poor for most practical situations and derive the exact null distribution of a function of the test statistic. We illustrate the method using published data on tuberculoid leprosy and HLA. We show that the test procedure is invariant, and extend the method to the case of a two-locus recessive disease.

A time-dependent logistic hazard function for modeling variable age of onset in analysis of familial diseases.

The paper presents an extension of the regressive logistic models proposed by Bonney [Biometrics 42:611-625, 1986], to address the problems of variable age-of-onset and time-dependent covariates in analysis of familial diseases. This goal is achieved by using failure time data analysis methods, and partitioning the time of follow up in K mutually exclusive intervals. The conditional probability of being affected within the kth interval (k = 1...K) given not affected before represents the hazard function in this discrete formulation. A logistic model is used to specify a regression relationship between this hazard function and a set of explanatory variables including genotype, phenotypes of ancestors, and other covariates which can be time dependent. The probability that a given person either becomes affected within the kth interval (i.e., interval k includes age of onset of the person) or remains unaffected by the end of the kth interval (i.e., interval k includes age at examination of the person) are derived from the general results of failure time data analysis and used for the likelihood formulation. This proposed approach can be used in any genetic segregation and linkage analysis in which a penetrance function needs to be defined. Application of the method to familial leprosy data leads to results consistent with our previous analysis performed using the unified mixed model [Abel and Demenais, Am J Hum Genet 42:256-266, 1988], i.e., the presence of a recessive major gene controlling susceptibility to leprosy. Furthermore, a simulation study shows the capability of the new model to detect major gene effects and to provide accurate parameter estimates in a situation of complete ascertainment.

A time-dependent logistic hazard function for modeling variable age of onset in analysis of familial diseases

This paper presents an extension of the regressive logistic model proposed by Bonney [Biometrics 42:611-625, 1986], to address the problems of variable age-of-onset and time-dependent covariates in analysis of familial diseases. The goal is achieved by using failure time data analysis methods, and partitioning the time of follow up in K mutually exclusive intervals. The conditional probability of being affected within the Kth interval (K=1...K) given not affected before represents the hazaard function in this discrete formulation. A logistic model is used to specify a regression relationship between this hazard function and a set of explanatory variables including genotype, phenotype of ancestors and other covariates which can be time independent. The probability that a given person either becomes affected within the Kth interval (ie. interval K includes age of onset of the person) or remains unaffected by the end of the Kth interval (ie. interval K includes age at examination of the person) are derived from the general result of failure time data analysis and used for the likelihood formulation. This proposed approach can be used in any genetic segregation and linkage analysis in which a penetrance function needs to be defined. Application of the method to familial leprosy data leads to results consistent with our previous analysis performed using the unified mixed model [Abel and Demenias, Am J Hum Genet 42:256-266, 1988], ie. the presence of a recessive major gene controlling susceptibility to leprosy. Furthermore, a simulation study shows the capability of the new method to detect major gene effects and to provide accurate parameter estimates in a situation of complete ascertainment. (AU)