Complex segregation analysis of familial diseases with variable age of onset: Comparison of different methods by a simulation study

Standard methods of segregation analysis, such as originally developed in the unified model (UM) or the regressive logistic model (RLM) do not account for age of onset, and use instead age at examination. To take into account age of onset, models should be formulated using survival analysis concepts, as it was recently proposed with a model based on a logistic hazard function (LHM). A simulation study was conducted to compare the performances of the three methods (UM, RLM, and LHM) in analyzing generated familial data with variable age of onset. When the data were simulated under a polygenic hypothesis, all analysis models were robust with respect to the false conclusion of a major gene, if the tests of transmission probabilities were performed properly. When the data were generated under a major gene hypothesis, two main results were observed: (1) the use of the LHM markedly increased the power to detect a major gene, in particular when a genotype by age interaction was introduced in the model; and (2) in the situation of disease-specific mortality, the use of either UM (whether specific mortality was accounted for or not) or RLM led to both spurious conclusions and bias in parameter estimates. These latter results obtained with the UM and the RLM can be explained by the violation of one constraint of both models observed in a situation of disease-specific mortality, i.e., given all covariates, the probability of being affected and that of not being affected should sum to 1. The use of methods based on survival analysis concepts is recommended in the study of familial diseases with variable age of onset, especially in the case of a correlation between age of onset and age at examination which is induced by disease-specific mortality. ©1995 Wiley-Liss, Inc.     

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.     

Analysis of Swedish male breast cancer family data: A simple way to incorporate a common sibling effect

Based on a population-based cohort study, Olsson et al. [1993] found significant evidence for elevated incidence of breast and ovarian cancers among female first-degree relatives of men with breast cancer. Using an extension of logistic regressive models we investigate whether, after allowing for multifactorial familial correlations, single locus segregation could be the cause of the elevated incidence in these families. The logit for a given sib in the class D logistic regressive model depends on the order in which affected sibs occur in a sibship. That makes the model less appropriate for the situation where a polygenic component or a common sibling environment may be present, as well as being computationally cumbersome. In this paper, we propose to use the proportion of siblings in a sibship who are affected to quantify a sibling correlation. That not only relaxes the interchangeability problem but also makes the model computationally efficient. We then use this modified class D logistic regressive model for our segregation analysis. Using the proportion of siblings in a sibship who are affected as a covariate resulted in a significantly higher likelihoods in all the models we investigated. We found evidence for a dominant Mendelian gene leading to early age of onset of breast and/or ovarian cancer. This could either be a germline mutation of BRCA2 or a mutation in a gene different from BRCA2. Genet. Epidemiol. 15:201–212,1998. © 1998 Wiley-Liss, Inc.     

Regression diagnostics for the Class A regressive model with quantitative phenotypes

Regression diagnostic methods are developed and investigated under the Class A regressive model proposed by Bonney [(1984) Am J Med Genet 18:731–749]. We call a family whose phenotypic distribution does not conform to the same genetic model as the majority of the families an etiotic family. The exact case‐deletion approach for identifying etiotic families, based on examining the changes in each model parameter estimate by excluding one family at a time, is very time‐consuming. We proposed three alternative diagnostic methods: the empirical influence function (EIF), the one‐step approximation, and the approximated one‐step approach. These methods can be computed efficiently and were incorporated into the existing software package S.A.G.E. A thorough Monte‐Carlo investigation of the performance of the diagnostic methods was conducted and generally supports the EIF approach as the recommended alternative. The phenotypic variance is the parameter whose associated regression diagnostic most frequently and correctly identified etiotic families in the models that were examined. An analysis of body mass index data from 402 individuals in 122 Muscatine, Iowa families is used to illustrate the methods. A Class A regressive model with a recessive major locus and equal mother‐offspring and father‐offspring correlations provided the best‐fitting model. The proposed regression diagnostics identified up to 7.4% of the 122 families as etiotic. As a result of this investigation, case‐deletion diagnostic assessment is now a practical component in the analysis of quantitative family data. Genet. Epidemiol. 17:174–187, 1999. © 1999 Wiley‐Liss, Inc.     

Multipoint linkage analysis of quantitative traits on sex-chromosomes

Variance component models form a powerful and flexible tool for multipoint linkage analysis of quantitative traits. Estimates of genetic similarity are needed for the variance component model to detect linkage and to locate genes, and two methods are commonly used to calculate multipoint identity-by-descent (IBD) estimates for autosomes. Fulker et al. ([1995] Am. J. Hum. Genet. 56: 1229-1233) and Almasy and Blangero ([1998] Am. J. Hum. Genet. 62: 119-121) used multiple regression to estimate the IBD sharing along a chromosome, while the approach of Kruglyak and Lander ([1995] Am. J. Hum. Genet. 57: 439-454) is based on a hidden Markov model. In this paper, we modify the variance component model to accommodate sex-chromosomes, and we extend both multipoint IBD estimation methods to accommodate sex-linked loci. Simulation studies demonstrate the power and precision of the variance component model to detect QTLs located on the sex-chromosome. The two multipoint IBD estimation methods have the same accuracy to identify QTL position, but the hidden Markov model yields a larger average maximum LOD score to detect linkage than the regression model. The extension of the multipoint IBD estimation methods and the variance component model to the X chromosome shows that the variance component model is a powerful and flexible tool for linkage analysis of quantitative traits on both autosomes and sex-chromosomes.     

Modelling sibship environment in the regressive logistic model for familial disease

Recently analytical models for pedigree disease data have been developed that combine genetic and epidemiological modelling techniques. The regressive logistic model [Bonney, Biometrics 42: 611-625; 1986] relies on decomposing the likelihood of a pedigree into the product of conditional probabilities, one for each individual, by imposing a (natural) order on pedigree members. In addition to modelling measured epidemiological variables, vertical transmission, transmission of unmeasured ousiotypes (a special case being genotypes), and some modelling of sibship dependencies have been proposed. In this paper the model is extended to include an unmeasured sibship environment factor using a log-linear model for binary pedigree traits [Hopper et al., Genet Epidemiol 1: 183-188; 1984], which breaks the pedigree into conditionally independent groups. Statistical issues, such as designs for which these factors will be discernible and tests of fit, are discussed.     

A general class of association tests for family-based data using weight functions

Based on the symmetry of transmitted/nontransmitted alleles from heterozygous parents under the null hypothesis of no association, the work proposed here establishes a general statistical framework for constructing association tests with data from nuclear families with multiple affected children. A class of association tests is proposed for both diallelic and multiallelic markers. The proposed test statistics reduce to the transmission disequilibrium test for trios, to T(su) by Martin et al. ([1997] Am. J. Hum. Genet. 61:439-448) for affected sib pairs, and to the pedigree disequilibrium test by Martin et al. ([2000] Am. J. Hum. Genet. 67:146-154); [2001] Am. J. Hum. Genet. 68:1065-1067) when using affected sibships only. The association test used in simulation and for real data (sitosterolemia) is the one which has the best overall power in detecting association. This association test is generally more powerful than the association tests proposed by Martin et al. ([2000] Am. J. Hum. Genet. 67:146-154); [2001] Am. J. Hum. Genet. 68:1065-1067) when using only affected sibships. For the sitosterolemia data set, the association test has its most significant result (P-value=0.0012) for the marker locus on the same bacterial artificial chromosome as the disease locus.     

Modeling the age-of-onset function in segregation analysis: a causal scheme for leprosy

Several methods have been proposed to take into account the variable age of onset of a disease in genetic analysis. A different approach is presented from an etiological point of view. To illustrate the method, we used leprosy, an infectious disease with a variable age of onset depending on both the time of contamination with the bacillus and the latency of the disease; the role of a major gene in the susceptibility to this disease has been recently detected. The age-of-onset function was modeled to account for the two temporal processes: contamination event and incubation period. For genetic analysis, this function was combined with the probability of being susceptible to the disease, which was expressed by the use of regressive models. To test this new approach, ten sets of 500 nuclear families were simulated considering different hypotheses of contamination risks, which were either constant or dependent on contacts with contagious leprosy patients, and varying the extent to which the disease is heritable. Analyses of these data using two versions of the model indicate that the model can detect familial correlations in variable age of onset and discriminate between the different simulated effects.     

Regressive logistic and proportional hazards disease models for within-family analyses of measured genotypes,with application to a CYP17 polymorphism and breast cancer

Various statistical methods have been proposed to evaluate associations between measured genetic variants and disease, including some using family designs. For breast cancer and rare variants, we applied a modified segregation analysis method that uses the population cancer incidence and population-based case families in which a mutation is known to be segregating. Here we extend the method to a common polymorphism, and use a regressive logistic approach to model familial aggregation by conditioning each individual on their mother's breast cancer history. We considered three models: 1) class A regressive logistic model; 2) age-of-onset regressive logistic model; and 3) proportional hazards familial model. Maximum likelihood estimates were calculated using the software MENDEL. We applied these methods to data from the Australian Breast Cancer Family Study on the CYP17 5'UTR T-->C MspA1 polymorphism measured for 1,447 case probands, 787 controls, and 213 relatives of case probands found to have the CC genotype. Breast cancer data for first- and second-degree relatives of case probands were used. The three methods gave consistent estimates. The best-fitting model involved a recessive inheritance, with homozygotes being at an increased risk of 47% (95% CI, 28-68%). The cumulative risk of the disease up to age 70 years was estimated to be 10% or 22% for a CYP17 homozygote whose mother was unaffected or affected, respectively. This analytical approach is well-suited to the data that arise from population-based case-control-family studies, in which cases, controls and relatives are studied, and genotype is measured for some but not all subjects.     

Age of onset, age at examination, and other covariates in the analysis of family data

Information on age of onset can easily be incorporated into regressive logistic models by assuming that age of onset follows a logistic distribution. This is analogous to previously proposed models based on the normal distribution. The two distributions, and hence the two types of models, are very similar. In each case the generalized modules power transformation can be used as a basis for more flexibly modeling the age of onset distribution.     

Perils and pitfalls of permutation tests for distinguishing the effects of neighbouring polymorphisms

In a small region several marker loci may be associated with a trait, either because they directly influence the trait or because they are in linkage disequilibrium (LD) with a causal variant. Having established a potentially causal effect at a primary variant, we may ask if any other variants in the region appear to further contribute to the trait, indicating that the additional variant is either causal or is in LD with another causal locus. Methods of approaching this problem using case-parent trio data include the stepwise conditional logistic regression approach described by Cordell and Clayton ([2002] Am. J. Hum. Genet. 70:124-141), and a constrained-permutation method recently proposed by Spijker et al. ([2005] Ann. Hum. Genet. 69:90-101). Through simulation we demonstrate that the procedure described by Spijker et al. [2005], as well as unconditional logistic regression with "affected family-based controls" (AFBACs), can lead to inflated type 1 errors in situations when haplotypes are not inferable for all trios, whereas the conditional logistic regression approach gives correct significance levels. We propose an alternative to the permutation method of Spijker et al. [2005], which does not rely on haplotyping, and results in correct type 1 errors and potentially high power when assumptions of random mating, Hardy-Weinberg Equilibrium, and multiplicative effects of disease alleles are satisfied.     

A note on genetic variance components in mixed models

Burton et al. ([1999] Genet. Epidemiol. 17:118-140) proposed a series of generalized linear mixed models for pedigree data that account for residual correlation between related individuals. These models may be fitted using Markov chain Monte Carlo methods, but the posterior mean for small variance components can exhibit marked positive bias. Burton et al. ([1999] Genet. Epidemiol. 17:118-140) suggested that this problem could be overcome by allowing the variance components to take negative values. We examine this idea in depth, and show that it can be interpreted as a computational device for locating the posterior mode without necessarily implying that the original random effects structure is incorrect. We illustrate the application of this technique to mixed models for familial data.     

Combined haplotype relative risk (CHRR): a general and simple genetic association test that combines trios and unrelated case-controls

In some genetic association studies, samples contain both parental and unrelated controls. Under such scenarios, instead of analyzing only trios using family-based association tests or only unrelated subjects using a case-control study design, Nagelkerke et al. ([2004] Eur. J. Hum. Genet. 12:964-970) and Epstein et al. ([2005] Am. J. Hum. Genet. 76:592-608) proposed methods that implemented a likelihood ratio test to combine the two different types of data. In this article, we put forward a more powerful and simplified strategy to combine trios with unrelated subjects based on the haplotype relative risk (HRR) (Falk and Rubinstein [1987] Ann. Hum. Genet. 51:227-233). The HRR compares parental marker alleles transmitted to an affected offspring to those not transmitted as a test for association, a strategy that is similar to a case-control study that compares allele frequencies in diseased cases to those of unrelated controls. We prove that affected offspring can be pooled with diseased cases and that parental controls can be treated as unrelated controls when the trios and unrelated subjects are randomly sampled from the same population. Therefore, unrelated subjects can be incorporated into the HRR intuitively and effortlessly. For trios without complete parental genotypes, we adopted the strategy proposed by (Guo et al. [2005a] BMC Genet. 6:S90; [2005b] Hum. Hered. 59: 125-135), which is more feasible than the one proposed by Weinberg ([1999] Am. J. Hum. Genet. 64:1186-1193). In addition, simulation results suggest that the combined haplotype relative risk is more powerful than Epstein et al.'s method regardless of the disease prevalence in a homogeneous population.     

Gamma regression improves Haseman-Elston and variance components linkage analysis for sib-pairs

Existing standard methods of linkage analysis for quantitative phenotypes rest on the assumptions of either ordinary least squares (Haseman and Elston [1972] Behav. Genet. 2:3-19; Sham and Purcell [2001] Am. J. Hum. Genet. 68:1527-1532) or phenotypic normality (Almasy and Blangero [1998] Am. J. Hum. Genet. 68:1198-1199; Kruglyak and Lander [1995] Am. J. Hum. Genet. 57:439-454). The limitations of both these methods lie in the specification of the error distribution in the respective regression analyses. In ordinary least squares regression, the residual distribution is misspecified as being independent of the mean level. Using variance components and assuming phenotypic normality, the dependency on the mean level is correctly specified, but the remaining residual coefficient of variation is constrained a priori. Here it is shown that these limitations can be addressed (for a sample of unselected sib-pairs) using a generalized linear model based on the gamma distribution, which can be readily implemented in any standard statistical software package. The generalized linear model approach can emulate variance components when phenotypic multivariate normality is assumed (Almasy and Blangero [1998] Am. J. Hum Genet. 68: 1198-1211) and is therefore more powerful than ordinary least squares, but has the added advantage of being robust to deviations from multivariate normality and provides (often overlooked) model-fit diagnostics for linkage analysis.     

Robust ascertainment-adjusted parameter estimation

Nonrandom ascertainment is commonly used in genetic studies of rare diseases, since this design is often more convenient than the random-sampling design. When there is an underlying latent heterogeneity, Epstein et al. ([2002] Am. J. Hum. Genet. 70:886-895) showed that it is possible to get unbiased or consistent estimation of population parameters under ascertainment adjustment, but Glidden and Liang ([2002] Genet. Epidemiol. 23:201-208) showed in a simulation study that the resulting estimates are highly sensitive to misspecification of the latent components. To overcome this difficulty, we consider a heavy-tailed model for latent variables that allows a robust estimation of the parameters. We describe a hierarchical-likelihood approach that avoids the integration used in the standard marginal likelihood approach. We revisit and extend the previous simulation, and show that the resulting estimator is efficient and robust against misspecification of the distribution of latent variables.     

Analytic strategies to detect linkage to a common disorder with genetically determined age of onset: Diabetes mellitus in Pima Indians

Segregation analysis suggests that the high prevalence of non-insulin-dependent diabetes mellitus in Pima Indians may be partially due to a single locus with a major effect on age of onset. A simulation study was conducted to evaluate the power of various age-adjustment strategies in linkage analysis to detect this putative gene in 1,862 sib-pairs from 264 potentially informative nuclear families. Simulations were performed at a recombination fraction (θ) of 0.05 for values of polymorphism information content (PIC) ranging from 0.38 to 1.00. Under the codominant age-of-onset model supported by segregation analysis, power to detect linkage (at P < 0.0001) at PIC = 1.00 was 75% for the Haseman-Elston (HE) sib-pair test and 63% for the affected sib-pair test (ASP) with no age adjustment. Substantial improvements in power were possible for the HE test by defining the trait as a survival analysis "residual" (power = 91%) and for the ASP test by use of an age-of-onset threshold above which individuals are not included in the analysis (power = 90%, for age of onset < 45 yrs). The parametric method of linkage analysis was most powerful, as long as both the analysis model and the simulation model involved a genetic effect on age of onset, regardless of whether dominance at the trait locus was misspecified. Methods of age adjustment based on the probability of eventually becoming affected only improved power when the genetic effect was on susceptibility rather than age of onset. The method of age adjustment in linkage analysis may depend on whether one anticipates a genetic effect primarily on age of onset or on ultimate susceptibility. Genet. Epidemiol. 15:299–315, 1998. © 1998 Wiley-Liss, Inc. This article is a US Government work and, as such, is in the public domain in the United States of America.     

Familial analysis of bipolar affective disorder using logistic models

Data on bipolar affective disorder in 187 pedigrees from the Collaborative Depression Study were analyzed using logistic models that have been extended to incorporate age of onset information. Logistic regression analysis and segregation analysis revealed evidence for complex familial effects on this disorder.     

Complex segregation analysis of families ascertained through Gilles de la Tourette syndrome

Although family and twin studies suggest that genetic factors are involved in the etiology of Tourette syndrome and other related tic disorders, further evidence is needed to demonstrate that the familial transmission is consistent with known genetic factors. We performed a complex segregation analysis that allowed for a variable age of onset of Gilles de la Tourette, other tic disorders and obsessive compulsive phenotype information on 108 extended families, each ascertained through one Tourette proband by using regressive models that are able to incorporate additional explanatory variables and major gene effects. A special version of the S.A.G.E. program, REGTLhunt, was used to explore the likelihood surface of all examined models. Results indicated that the pattern of Tourette and other related tic disorders in our data sample is not consistent with Mendelian inheritance even after modelling explanatory variables such as obsessive compulsive symptomatology.     

Interactions between genetic and reproductive factors in breast cancer risk in a population-based sample of African-American families

Incidence of breast cancer (BC) varies among ethnic groups, with higher rates in white than in African-American women. Until now, most epidemiological and genetic studies have been carried out in white women. To investigate whether interactions between genetic and reproductive risk factors may explain part of the ethnic disparity in BC incidence, a genetic epidemiology study was conducted, between 1989 and 1994, at the Howard University Cancer Center (Washington, DC), which led to the recruitment of 245 African-American families. Segregation analysis of BC was performed by use of the class D regressive logistic model that allows for censored data to account for a variable age of onset of disease, as implemented in the REGRESS program. Segregation analysis of BC was consistent with a putative dominant gene effect (P < 0.000001) and residual sister-dependence (P < 0.0001). This putative gene was found to interact significantly with age at menarche (P = 0.048), and an interaction with a history of spontaneous abortions was suggested (P = 0.08). A late age at menarche increased BC risk in gene carriers but had a protective effect in non-gene carriers. A history of spontaneous abortions had a protective effect in gene carriers and increased BC risk in non-gene carriers. Our findings agree partially with a similar analysis of French families showing a significant gene x parity interaction and a suggestive gene x age at menarche interaction. Investigating gene x risk factor interactions in different populations may have important implications for further biological investigations and for BC risk assessment.     

Impact of parental relationships in maximum lod score affected sib-pair method

Many studies are done in small isolated populations and populations where marriages between relatives are encouraged. In this paper, we point out some problems with applying the maximum lod score (MLS) method (Risch, [1990] Am. J. Hum. Genet. 46:242-253) in these populations where relationships exist between the two parents of the affected sib-pairs. Characterizing the parental relationships by the kinship coefficient between the parents (f), the maternal inbreeding coefficient (alpha(m), and the paternal inbreeding coefficient (alpha(p)), we explored the relationship between the identity by descent (IBD) vector expected under the null hypothesis of no linkage and these quantities. We find that the expected IBD vector is no longer (0.25, 0.5, 0.25) when f, alpha(m), and alpha(p) differ from zero. In addition, the expected IBD vector does not always follow the triangle constraints recommended by Holmans ([1993] Am. J. Hum. Genet. 52:362-374). So the classically used MLS statistic needs to be adapted to the presence of parental relationships. We modified the software GENEHUNTER (Kruglyak et al. [1996] Am. J. Hum. Genet. 58: 1347-1363) to do so. Indeed, the current version of the software does not compute the likelihood properly under the null hypothesis. We studied the adapted statistic by simulating data on three different family structures: (1) parents are double first cousins (f=0.125, alpha(m)=alpha(p)=0), (2) each parent is the offspring of first cousins (f=0, alpha(m)=alpha(p)=0.0625), and (3) parents are related as in the pedigree from Goddard et al. ([1996] Am. J. Hum. Genet. 58:1286-1302) (f=0.109, alpha(m)=alpha(p)=0.0625). The appropriate threshold needs to be derived for each case in order to get the correct type I error. And using the classical statistic in the presence of both parental kinship and parental inbreeding almost always leads to false conclusions.