Ascertainment bias in rate ratio estimation from case-sibling control studies of variable age-at-onset diseases

Motivated by a Finnish case-control study of early onset diabetes in which diabetic children are matched to sibling controls, we investigate ascertainment bias of the usual rate ratio estimator from case-control data under simplex complete ascertainment of families during a fixed interval of time. Analytic results indicate that the assumptions necessary for valid estimation are that the disease is rare and the factors under study are exchangeable--essentially that the covariate distribution does not depend on calendar time or birth order. Further, we found that the rare disease assumption could be dropped by restricting to cases that were diagnosed during the enrollment period of the study or including all cases but eliminating the proband as a control for non-enrollment-period cases. An important consequence of this work is that standard family-based case-control studies are subject to ascertainment bias if exchangeability of the covariates under investigation does not hold.     

The relationship between the sibling recurrence-risk ratio and genotype relative risk

The recurrence-risk ratio of disease in siblings, lambdaS, is a standard parameter used in genetic analysis to estimate the statistical power for detection of a disease locus. However, the relationship between the underlying risk conferred by a disease-susceptibility allele and lambdaS has not been well described. The former is generally quantified as a genotype relative risk, gamma, and measures the ratio of disease risks between those with and those without the susceptibility genotype(s). We demonstrate that lambdaS varies significantly more with respect to gamma and the disease-allele frequency for two-locus multiplicative models than for other two-locus and for single-locus models. For the single- and two-locus dominant-inheritance models that we studied, when a disease-susceptibility allele had a frequency >/=.2, lambdaS had an upper limit of <10. In general, lambdaS values >10 are possible only under recessive inheritance, dominant inheritance with relatively rare (<5%) disease-susceptibility alleles, or when two or more disease loci have alleles acting either epistatically or multiplicatively. We introduce the idea of a restricted sib recurrence-risk ratio (lambda*S) estimated by restriction of sibships to those ascertained through a proband who already has a putative high-risk allele. A lambda*S larger than the lambdaS value estimated from randomly selected probands can serve as an indirect way of testing whether the posited susceptibility allele increases disease risk. Our results demonstrate that a lambdaS of 2-3 may portend successful mapping for a variety of genetic models but that, for some two-locus models, a lambdaS as high as 10 does not guarantee underlying genes easily mapped by linkage.     

A note on a conditional-likelihood approach for family-based association studies of candidate genes

The family-based association study design is a variation of the case-control study design, where unaffected family members instead of unrelated subjects are sampled as controls. This variation is useful in assessing the effects of candidate genes on disease, because it avoids false associations caused by admixture of populations. A complication of this design is that because of an inherited genotypic correlation among family members, the genotypic distributions between cases and relative controls may be distorted by the ascertainment criteria of families, which could involve not only cases and relative controls, but also other relatives. Analyzing such data naively may lead to biased estimates of relative risk. In this note, we will discuss the consistency of a conditional-likelihood approach. We show analytically that maximum conditional-likelihood estimators are consistent for the true relative risks, if genotypes for family members are exchangeable under the sampling process, for example, sibling clusters. Besides being straightforward conceptually and computationally, this approach is robust to ascertainment bias and naturally accommodates genetic heterogeneity across families.     

Bias correction for segregation ratio estimation in human genetics

Segregation ratio estimation has long been important in human genetics. A simple truncated binomial model is considered that assumes complete ascertainment and a deterministic genotype-phenotype relationship. A simple but intuitively appealing estimator of the segregation ratio, previously proposed, is shown to have a negative bias. It is also shown that the bias of this estimator can be largely reduced via a randomization device, resulting in a new estimator that has the same large-sample behavior but with a negligible bias (decaying at a geometric rate). Numerical results are given to show the small-sample performance of this new estimator. An extension to incomplete ascertainment is also considered.     

Quantifying ascertainment bias and species-specific length differences in human and chimpanzee microsatellites using genome sequences

Surveys of variability of homologous microsatellite loci among species reveal an ascertainment bias for microsatellite length where microsatellite loci isolated in one species tend to be longer than homologous loci in related species. Here, we take advantage of the availability of aligned human and chimpanzee genome sequences to compare length difference of homologous microsatellites for loci identified in humans to length difference for loci identified in chimpanzees. We are able to quantify ascertainment bias for a range of motifs and microsatellite lengths. Because ascertainment bias should not exist if a microsatellite selected in one species is as likely to be longer as it is to be shorter than its homologue, we propose that the nature of ascertainment bias can provide evidence for understanding how microsatellites evolve. We show that bias is greater for longer microsatellites but also that many long microsatellites have short homologues. These results are consistent with the notion that growth of long microsatellites is constrained by an upper length boundary that, when reached, sometimes results in large deletions. By evaluating ascertainment bias separately for interrupted and uninterrupted repeats we also show that long microsatellites tend to become interrupted, thereby contributing a second component of ascertainment bias. Having accounted for ascertainment bias, in agreement with results published elsewhere, we find that microsatellites in humans are longer on average than those in chimpanzees. This length difference is similar among repeat motifs but surprisingly comprises two roughly equal components, one associated with the repeats themselves and one with the flanking sequences. The differences we find can only be explained if microsatellites are both evolving directionally under a biased mutation process and are doing so at different rates in different closely related species.     

A likelihood ratio test for completed sampling in population size estimation studies

We propose a likelihood ratio test to assess that sampling has been completed in closed population size estimation studies. More precisely, we assess if the expected number of subjects that have never been sampled is below a user-specified threshold. The likelihood ratio test statistic has a nonstandard distribution under the null hypothesis. Critical values can be easily approximated and tabulated, and they do not depend on model specification. We illustrate in a simulation study and three real data examples, one of which involves ascertainment bias of amyotrophic lateral sclerosis in Gulf War veterans.     

Statistical properties of maximum likelihood estimators for genetic parameters of HLA-linked diseases.

This paper considers questions of standard error and questions of bias in the maximum likelihood estimation of parameters associated with an HLA-linked disease. It is shown that a considerable reduction in standard error is possible using data on population prevalence and parental disease status, if available. Comparison is made with standard errors arising in the shared haplotypes method. The biases considered relate to misspecification of the ascertainment scheme, to incorrect assumptions about parameter values, to the possibility that affected parents have lower fitness than unaffected parents, and to the possibility of within family correlation of penetrance values due to effects of a common environment.     

A resolution of the ascertainment sampling problem. II. Generalizations and numerical results

The ascertainment problem arises when families are sampled by a nonrandom process and some assumption about this sampling process must be made in order to estimate genetic parameters. Under classical ascertainment assumptions, estimation of genetic parameters cannot be separated from estimation of the parameters of the ascertainment process, so that any misspecification of the ascertainment process causes biases in estimation of the genetic parameters. Ewens and Shute proposed a resolution to this problem, involving conditioning the likelihood of the sample on the part of the data which is "relevant to ascertainment." The usefulness of this approach can only be assessed by examining the properties (in particular, bias and standard error) of the estimates which arise by using it for a wide range of parameter values and family size distributions and then comparing these biases and standard errors with those arising under classical ascertainment procedures. These comparisons are carried out in the present paper, and we also compare the proposed method with procedures which condition on, or ignore, parts of the data.     

Likelihood Formulation of Parent-of-Origin Effects on Segregation Analysis, Including Ascertainment

We developed a likelihood-based method for testing for parent-of-origin effect in complex diseases. The likelihood formulations model parent-of-origin effect and allow for incorporation of ascertainment, as well as differential male and female ascertainment probabilities. The results based on simulated data indicated that the estimates of parental effect (either maternal or paternal) were biased when ascertainment was ignored or when the wrong ascertainment model was used. The exception was single ascertainment, in which we proved that ignoring ascertainment does not bias the estimation of parental effect, in a simple parent-of-origin model. These results underscore the importance of considering ascertainment models when testing for parent-of-origin effect in complex diseases.     

Factors Influencing Ascertainment Bias of Microsatellite Allele Sizes: Impact on Estimates of Mutation Rates

Microsatellite loci play an important role as markers for identification, disease gene mapping, and evolutionary studies. Mutation rate, which is of fundamental importance, can be obtained from interspecies comparisons, which, however, are subject to ascertainment bias. This bias arises, for example, when a locus is selected on the basis of its large allele size in one species (cognate species 1), in which it is first discovered. This bias is reflected in average allele length in any noncognate species 2 being smaller than that in species 1. This phenomenon was observed in various pairs of species, including comparisons of allele sizes in human and chimpanzee. Various mechanisms were proposed to explain observed differences in mean allele lengths between two species. Here, we examine the framework of a single-step asymmetric and unrestricted stepwise mutation model with genetic drift. Analysis is based on coalescent theory. Analytical results are confirmed by simulations using the simuPOP software. The mechanism of ascertainment bias in this model is a tighter correlation of allele sizes within a cognate species 1 than of allele sizes in two different species 1 and 2. We present computations of the expected average allele size difference, given the mutation rate, population sizes of species 1 and 2, time of separation of species 1 and 2, and the age of the allele. We show that when the past demographic histories of the cognate and noncognate taxa are different, the rate and directionality of mutations affect the allele sizes in the two taxa differently from the simple effect of ascertainment bias. This effect may exaggerate or reverse the effect of difference in mutation rates. We reanalyze literature data, which indicate that despite the bias, the microsatellite mutation rate estimate in the ancestral population is consistently greater than that in either human or chimpanzee and the mutation rate estimate in human exceeds or equals that in chimpanzee with the rate of allele length expansion in human being greater than that in chimpanzee. We also demonstrate that population bottlenecks and expansions in the recent human history have little impact on our conclusions.     

Disease mapping and spatial regression with count data

In this paper, we provide critical reviews of methods suggested for the analysis of aggregate count data in the context of disease mapping and spatial regression. We introduce a new method for picking prior distributions, and propose a number of refinements of previously used models. We also consider ecological bias, mutual standardization, and choice of both spatial model and prior specification. We analyze male lip cancer incidence data collected in Scotland over the period 1975-1980, and outline a number of problems with previous analyses of these data. In disease mapping studies, hierarchical models can provide robust estimation of area-level risk parameters, though care is required in the choice of covariate model, and it is important to assess the sensitivity of estimates to the spatial model chosen, and to the prior specifications on the variance parameters. Spatial ecological regression is a far more hazardous enterprise for two reasons. First, there is always the possibility of ecological bias, and this can only be alleviated by the inclusion of individual-level data. For the Scottish data, we show that the previously used mean model has limited interpretation from an individual perspective. Second, when residual spatial dependence is modeled, and if the exposure has spatial structure, then estimates of exposure association parameters will change when compared with those obtained from the independence across space model, and the data alone cannot choose the form and extent of spatial correlation that is appropriate.     

A method for estimating penetrance from families sampled for linkage analysis

When a gene variant is discovered to segregate with a disease, it may be of interest to estimate the risk (or the age-specific risk) of the disease to carriers of the variant. The families that contributed to the discovery of the variant would typically contain multiple carriers, and so, especially if the variant is rare, might prove a valuable source of study subjects for estimation of the risk. These families, by virtue of having brought the gene in question to the attention of researchers, however, may not be representative of the relationship between carrier status and the risk of the disease in the population. Using these families for risk estimation could bias the observed association between the variant and the risk. The purpose here is to present an approach to adjusting for the potential bias while using the families from linkage analysis to estimate the risk.     

Correcting for variable age of onset in the estimation of familial relative risk when there is a secular trend in incidence of disease

We discuss the effects that a secular trend in incidence would have on estimation of familial relative risk (ratio of observed to expected cumulative incidence among relatives of index cases). For example, when age-specific incidence rates of a condition have increased during the lifetimes of relatives among whom relative risk is to be estimated, familial relative risk will be biased downward if cross-sectional, age-specific incidence data are used to estimate expected cumulative incidence among relatives. The stronger the trend and the older the ages of unaffected relatives, the greater the bias will be. Incorporating different age-specific incidence curves for different birth cohorts into the analysis is an approach we suggest for correcting the bias.     

The effects of conditioning on probands to correct for multiple ascertainment.

Cannings and Thompson suggested conditioning on the phenotypes of the probands to correct for ascertainment in the analysis of pedigree data. The method assumes single ascertainment and can be expected to yield asymptotically biased parameter estimates except in this specific case. However, because the method is easy to apply, we investigated the degree of bias in the more typical situation of multiple ascertainment, in the hope that the bias might be small and that the method could be applied more generally. To explore the utility of conditioning on probands to correct for multiple ascertainment, we calculated the asymptotic value of the segregation ratio for two versions of the simple Mendelian segregation model on sibship data. For both versions, we found that this asymptotic value decreased approximately linearly as the ascertainment probability increased. When ascertainment was complete, the segregation-ratio estimates were zero, not just asymptotically but for finite sample size as well. In some cases, conditioning on probands actually resulted in greater parameter bias than no ascertainment correction at all. These results hold for a variety of sibship-size distributions, several modes of inheritance, and a wide range of population prevalences of affected individuals.     

On the bias of recombination fractions, Kosambi's and Haldane's distances based on frequencies of gametes

The estimation of recombination frequencies is a crucial step in genetic mapping. For the construction of linkage maps, nonadditive recombination fractions must be transformed into additive map distances. Two of the most commonly used transformations are Kosambi's and Haldane's mapping functions. This paper reports on the calculation of the bias associated with estimation of recombination fractions, Kosambi's distances, and Haldane's distances. I calculated absolute and relative biases numerically for a wide range of recombination fractions and sample sizes. I assumed that the ratio of recombinant gametes to the total number of gametes can be adequately represented by a binomial function. I found that the bias in recombination fraction estimates is negative, i.e., the estimator is an underestimate. However, significant values were only obtained when recombination fractions were large and sample sizes were small. The relevant estimates of recombination fractions were, therefore, nearly unbiased. Haldane's and Kosambi's distances were found to be strongly biased, with positive bias for the most interesting values of recombination fractions and sample sizes. The bias of Kosambi's distance was considerably smaller than the bias of Haldane's distance.     

Selection bias in genetic-epidemiological studies of cleft lip and palate.

The possible impact of selection bias in genetic and epidemiological studies of cleft lip and palate was studied, using three nationwide ascertainment sources and an autopsy study in a 10% sample of the Danish population. A total of 670 cases were identified. Two national record systems, when used together, were found suitable for ascertaining facial cleft in live births. More than 95% ascertainment was obtained by means of surgical files for cleft lip (with or without cleft palate) without associated malformations/syndromes. However, surgical files could be a poor source for studying isolated cleft palate (CP) (only a 60% and biased ascertainment), and they cannot be used to study the prevalence of associated malformations or syndromes in facial cleft cases. The male:female ratio was 0.88 in surgically treated cases of CP and was 1.5 in nonoperated CP cases, making the overall sex ratio for CP 1.1 (95% confidence limits 0.86-1.4) The sex ratio for CP without associated malformation was 1.1 (95% confidence limits 0.84-1.6). One of the major test criteria in CP multifactorial threshold models (higher CP liability among male CP relatives) must be reconsidered, if other investigations confirm that a CP sex-ratio reversal to male predominance occurs when high ascertainment is achieved.     

The transmission/disequilibrium test and parental-genotype reconstruction for X-chromosomal markers

Family-based association methods have recently been introduced that allow testing for linkage in the presence of linkage disequilibrium between a marker and a disease even if there is only incomplete parental-marker information. No such tests are currently available for X-linked markers. This report fills this methodological gap by presenting the X-linked sibling transmission/disequilibrium test (XS-TDT) and the X-linked reconstruction-combination transmission/disequilibrium test (XRC-TDT). As do their autosomal counterparts (S-TDT and RC-TDT), these tests make no assumption about the mode of inheritance of the disease and the ascertainment of the sample. They protect against spurious association due to population stratification. The two tests were compared by simulations, which show that (1) the X-linked RC-TDT is, in general, considerably more powerful than the X-linked S-TDT and (2) the lack of parental-genotype information can be offset by the typing of a sufficient number of sibling controls. A freely available SAS implementation of these tests allows the calculation of exact P values.     

The effect of proband designation on segregation analysis

In many family studies, it is often difficult to know exactly how the families were ascertained. Even if known, the circumstances under which the families came to the attention of the study may violate the assumptions of classical ascertainment bias correction. The purpose of this work was to investigate the effect on segregation analysis of violations of the assumptions of the classical ascertainment model. We simulated family data generated under a simple recessive model of inheritance. We then ascertained families under different "scenarios." These scenarios were designed to simulate actual conditions under which families come to the attention of-and then interact with-a clinic or genetic study. We show that how one designates probands, which one must do under the classical ascertainment model, can influence parameter estimation and hypothesis testing. We demonstrate that, in some cases, there may be no "correct" way to designate probands. Further, we show that interactions within the family, the conditions under which the genetic study must function, and even social influences can have a profound effect on segregation analysis. We also propose a method for dealing with the ascertainment problem that is applicable to almost any study situation.     

Evaluating genetic heterogeneity in complex disorders

OBJECTIVES: The Admixture test is routinely used in linkage analysis to take account of genetic heterogeneity, and yields an estimate of the proportion of families (alpha) segregating the linked disease gene. In complex disorders, the assumptions of the Admixture test are violated. We therefore explore how the estimate of alpha relates to the true proportion of linked families with a complex disorder in a population or dataset. METHODS: We simulated a two-locus heterogeneity model and varied genetic parameters, ascertainment scheme and phenocopy frequency. RESULTS: In this model, alpha is almost always overestimated, by as little as 5% to as much as 60%. The bias is largely attributable to (1). intrafamilial heterogeneity arising from ascertainment of families with many affected members or from analysis of dense pedigrees; (2). low informativeness, which occurs in the presence of reduced penetrance; and (3). differences in the evidence for linkage in linked and unlinked families. This bias is also affected by the analysis phenocopy frequency, but only if the linked locus is dominant and the unlinked locus is recessive. CONCLUSIONS: We conclude that, in complex diseases, the Admixture test has greater value in detecting linkage than in estimating the proportion of linked families in a dataset.     

Genetic association analysis using sibship data: a multilevel model approach

Family based association study (FBAS) has the advantages of controlling for population stratification and testing for linkage and association simultaneously. We propose a retrospective multilevel model (rMLM) approach to analyze sibship data by using genotypic information as the dependent variable. Simulated data sets were generated using the simulation of linkage and association (SIMLA) program. We compared rMLM to sib transmission/disequilibrium test (S-TDT), sibling disequilibrium test (SDT), conditional logistic regression (CLR) and generalized estimation equations (GEE) on the measures of power, type I error, estimation bias and standard error. The results indicated that rMLM was a valid test of association in the presence of linkage using sibship data. The advantages of rMLM became more evident when the data contained concordant sibships. Compared to GEE, rMLM had less underestimated odds ratio (OR). Our results support the application of rMLM to detect gene-disease associations using sibship data. However, the risk of increasing type I error rate should be cautioned when there is association without linkage between the disease locus and the genotyped marker.