Comparing observed average numbers of affected sibs with those expected under geometric ascertainment bias in an extended range in both simplex and multiple sibships.

Detection bias in recessive ascertainment is generally considered to be confined in a narrow range between unbiased truncate ascertainment and single ascertainment, where methods of segregation analysis are established. While there are arguments for an extended range of analysis, a deflated detection progression below the unbiased level is still being considered as theoretical ground or ignored as sporadics. I show here a method of gauging the ascertainment levels of surveyed data in a geometric continuum. The method is valid for recessive segregation at any ascertainment level and in simplex or multiplex sibships of whatever degree of truncation. Four previously published surveys are used to show conformation with real data and the existence of detection trends spanning the range from the unsuspected very depressed bias level to the inflated level above single ascertainment.     

Empirical, free of genetic model, estimation of recurrence risks in multifactorial diseases: conditional probability approach]

Conditional probability approach in estimation of recurrence risks in sibships of different parental phenotypic matings with the different set of affected and normal siblings is considered. The formulae are presented for calculation of recurrence risks in cases of equal and different susceptibility of two sexes under different ways of sampling of family data: direct selection of offsprings through the parents; indirect selection of offsprings through affected siblings--the probands, under different ascertainment probability--from pi = 1.0 ("exhaustive selection") up to pi----0 ("single selection"); for the case of different susceptibility of the two sexes a possibility of the differences in the ascertainment probabilities of men (pi m) and of women (pi w) is allowed, unlike "independent ascertainment model", which requires the constancy of pi. The case of multiple incompatible subforms is considered for estimation of the recurrence risks of the specified subforms. The methods of the risks estimation proposed are free of genetic models being universal both for classical mendelian traits (with the constant risks) and for multifactorial ones (with variable risks).     

Schizophrenia: the systematic construction of genetic models.

Methods are described for the systematic construction of genetic models of schizophrenia with one, two, and four loci. All models are constrained to fit the following three parameters: (1) frequency of schizophrenia in the general population = 0.9%; (2) frequency of schizophrenia in the sibs of schizophrenics = 8%; and (3) frequency of "schizophrenic spectrum" in the sibs of schizophrenics = 15%. In addition, a fourth parameter, the frequency of the allele predisposing to schizophrenia, is freely variable. The problems of correcting for ascertainment bias, and of comparing and testing these genetic models, are discussed.     

Excess of twins among affected sibling pairs with autism: implications for the etiology of autism

It is widely accepted that genes play a role in the etiology of autism. Evidence for this derives, in part, from twin data. However, despite converging evidence from gene-mapping studies, aspects of the genetic contribution remain obscure. In a sample of families selected because each had exactly two affected sibs, we observed a remarkably high proportion of affected twin pairs, both MZ and DZ. Of 166 affected sib pairs, 30 (12 MZ, 17 DZ, and 1 of unknown zygosity) were twin pairs. Deviation from expected values was statistically significant (P<10(-6) for all twins); in a similarly ascertained sample of individuals with type I diabetes, there was no deviation from expected values. We demonstrate that to ascribe the excess of twins with autism solely to ascertainment bias would require very large ascertainment factors; for example, affected twin pairs would need to be, on average, approximately 10 times more likely to be ascertained than affected non-twin sib pairs (or 7 times more likely if "stoppage" plays a role). Either risk factors (related to twinning or to fetal development) or other factors (genetic or nongenetic) in the parents may contribute to autism.     

A cooperative binomial ascertainment model.

It has been shown that the classical binomial form of ascertainment, assuming a constant probability pi that any affected individual may become a proband for his pedigree, cannot describe a rather wide range of ascertainment procedures that might arise in practice. Some more general heuristic ascertainment formulas might then be preferred, and in this paper we consider the probabilistic basis for these formulas. We retain the binomial assumption of the classical scheme but allow the ascertainment probability to depend on the number of potential probands per pedigree. This probability can be expressed by an increasing or a decreasing function of that number. Various illustrations are given and situations where the "cooperative" binomial scheme should be valuable are discussed.     

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.     

Simulation studies of segregation analysis: application to two-locus models

We tested the power of a segregation analysis method (first proposed by Elandt-Johnson) to distinguish between single-locus and two-locus models, with and without environmentally caused reduced penetrance. We also looked at the effect of ascertainment probability on the analysis and at the proband-conditioned ascertainment correction proposed by Cannings and Thompson. We found that: (1) the segregation analysis has sufficient power to distinguish between the fully-penetrant double-recessive (RR) model and the fully-penetrant single-locus dominant and recessive models; (2) the method can also distinguish fairly well between the dominant-recessive (DR) and RR models, even when one does not take into account the population prevalence; (3) the method has much less power to distinguish between the fully-penetrant RR model and the single-locus models with reduced penetrance; (4) when environmental penetrance is taken account of in the analysis, the power of the method to distinguish between the one- and two-locus models improved substantially; (5) the estimates of ascertainment probability, pi, were robust, regardless of the model under which the data were generated; and (6) the Cannings-Thompson approach to ascertainment correction worked well only when the pi used to generate the data was less than .1.     

The Discovery of Single-Nucleotide Polymorphisms—and Inferences about Human Demographic History

A method of historical inference that accounts for ascertainment bias is developed and applied to single-nucleotide polymorphism (SNP) data in humans. The data consist of 84 short fragments of the genome that were selected, from three recent SNP surveys, to contain at least two polymorphisms in their respective ascertainment samples and that were then fully resequenced in 47 globally distributed individuals. Ascertainment bias is the deviation, from what would be observed in a random sample, caused either by discovery of polymorphisms in small samples or by locus selection based on levels or patterns of polymorphism. The three SNP surveys from which the present data were derived differ both in their protocols for ascertainment and in the size of the samples used for discovery. We implemented a Monte Carlo maximum-likelihood method to fit a subdivided-population model that includes a possible change in effective size at some time in the past. Incorrectly assuming that ascertainment bias does not exist causes errors in inference, affecting both estimates of migration rates and historical changes in size. Migration rates are overestimated when ascertainment bias is ignored. However, the direction of error in inferences about changes in effective population size (whether the population is inferred to be shrinking or growing) depends on whether either the numbers of SNPs per fragment or the SNP-allele frequencies are analyzed. We use the abbreviation "SDL," for "SNP-discovered locus," in recognition of the genomic-discovery context of SNPs. When ascertainment bias is modeled fully, both the number of SNPs per SDL and their allele frequencies support a scenario of growth in effective size in the context of a subdivided population. If subdivision is ignored, however, the hypothesis of constant effective population size cannot be rejected. An important conclusion of this work is that, in demographic or other studies, SNP data are useful only to the extent that their ascertainment can be modeled.     

Between-generation differences in ascertainment and penetrance: relevance to genetic hypotheses in fragile X

Between-generation differences in ascertainment were examined in 54 extended fragile X pedigrees, where all available members were clinically, psychometrically, and cytogenetically investigated. In 24 families a diagnosis was verified by molecular characterization using the pfxa3 fragile X-specific probe. We found considerable differences between generations in relative proportions of affected fragile X subjects versus non-penetrant carriers. We also found deviation in the segregation ratio in unbiased samples of relatives in pedigrees. We claim that these irregularites are influenced by different rates of ascertainment, depending on the clinical expression of the condition (penetrance) and the fertility of fragile X individuals in a pedigree, as well as by the thoroughness of clinical investigation in individual families. Penetrance and fertilty were estimated in fragile X females assessed by psychometric tests, and they were compared with earlier estimates based on a subjective judgement of their intellectual status. We suggest that the standard correction for ascertainment bias, such as has been applied in segregation analysis of this condition, is not sufficient to adjust for all types of bias.     

Detection probability in aerial surveys of feral horses

Observation bias pervades data collected during aerial surveys of large animals, and although some sources can be mitigated with informed planning, others must be addressed using valid sampling techniques that carefully model detection probability. Nonetheless, aerial surveys are frequently employed to count large mammals without applying such methods to account for heterogeneity in visibility of animal groups on the landscape. This often leaves managers and interest groups at odds over decisions that are not adequately informed. I analyzed detection of feral horse (Equus caballus) groups by dual independent observers from 24 fixed-wing and 16 helicopter flights using mixed-effect logistic regression models to investigate potential sources of observation bias. I accounted for observer skill, population location, and aircraft type in the model structure and analyzed the effects of group size, sun effect (position related to observer), vegetation type, topography, cloud cover, percent snow cover, and observer fatigue on detection of horse groups. The most important model-averaged effects for both fixed-wing and helicopter surveys included group size (fixed-wing: odds ratio = 0.891, 95% CI = 0.850–0.935; helicopter: odds ratio = 0.640, 95% CI = 0.587–0.698) and sun effect (fixed-wing: odds ratio = 0.632, 95% CI = 0.350–1.141; helicopter: odds ratio = 0.194, 95% CI = 0.080–0.470). Observer fatigue was also an important effect in the best model for helicopter surveys, with detection probability declining after 3 hr of survey time (odds ratio = 0.278, 95% CI = 0.144–0.537). Biases arising from sun effect and observer fatigue can be mitigated by pre-flight survey design. Other sources of bias, such as those arising from group size, topography, and vegetation can only be addressed by employing valid sampling techniques such as double sampling, mark–resight (batch-marked animals), mark–recapture (uniquely marked and identifiable animals), sightability bias correction models, and line transect distance sampling; however, some of these techniques may still only partially correct for negative observation biases. © 2011 The Wildlife Society.     

An evaluation of the gradsect biological survey method

Biological surveys are necessary to gather species distribution data for the identification of priority conservation areas. The rationale of the gradsect method is that sampling (transects) oriented along the steepest environmental gradient should detect the maximum number of species in an area. The efficiency of the gradsect survey method was evaluated by comparing it to random, systematic and habitat-specific survey methods, during faunal field surveys (target groups: birds and dung beetles). Three gradsects were positioned within the study area to follow the major physiographical characteristics, incorporate all environmental strata (land facets) and yet be as logistically convenient as possible. The efficiency of survey methods was expressed as the number of species recorded per sampling unit effort and illustrated using bootstrap estimations to plot species accumulation curves. The gradsect method proved to be as efficient as the habitat-specific survey method and consiste ntly more efficient than the systematic and random surveys for both taxa sampled. The present study therefore illustrates that the gradsect survey method provides a cost-effective and swift representative sample of regional fauna. Moreover, the results indicate that land-form sequences, specifically land facets, are useful surrogates when sampling environmental diversity where distinct environmental gradients such as altitude and rainfall are absent.     

Improving species occupancy estimation when sampling violates the closure assumption

Site occupancy models that account for imperfect detection of species are increasingly utilized in ecological research and wildlife monitoring. Occupancy models require replicate surveys to estimate detection probability over a time period where the occupancy status at sampled sites is assumed closed. Unlike mark–recapture models, few studies have examined how violations of closure can bias occupancy estimates. Our study design allowed us to differentiate among two processes that violate the closure assumption during a sampling season: 1) repeated destructive sampling events that result in either short‐ or long‐term site avoidance by the target species and 2) sampling occurring over a time period during which non‐random movements of the target species result in variable occupancy status. We used dynamic occupancy models to quantify the potential bias in occupancy estimation associated with these processes for a terrestrial salamander system. Our results provide strong evidence of a systematic decrease in salamander occupancy within a field season. Chronic disturbance due to repeated searches of natural cover objects accelerated natural declines in species occurrence on the forest surface as summer progressed. We also observed a strong but temporary disturbance effect on salamander detection probability associated with repeated sampling within a 24‐h. period. We generalized our findings by conducting a simulation to evaluate how violations of closure can bias occupancy estimates when local extinction occurs within a sampling season. Our simulation study revealed general sensitivity of estimates from single‐season occupancy models to violations of closure, with the strength and direction of bias varying between scenarios. Bias was minimal when extinction proba bility or the number of sample occasions was relatively low. Our research highlights the importance of addressing closure in occupancy studies and we provide multiple solutions, using both design‐ and model‐based frameworks, for minimizing bias associated with non‐random changes in occupancy and repeated sampling disturbances.     

The relative efficiency of penetrance estimators for sib pairs

Here we present analytical studies to evaluate the relative efficiency of commonly used penetrance estimators using linkage designs. We investigated three different methods of estimating penetrance using sib pairs: Maximum likehood estimation (MLE) with trait information alone, MLE with both trait and marker information and the MOD score approach. Modeling sib pairs with unknown phase, we evaluated the asymptotic relative efficiency between estimators under either random sampling or single ascertainment for an autosomal dominant or recessive disease. We then provide plots of the asymptotic relative efficiency, enabling researchers to easily determine regions where the MOD score or segregation alone performs with comparable efficiency relative to joint segregation and linkage.     

On models for binomial data with random numbers of trials

A binomial outcome is a count s of the number of successes out of the total number of independent trials n=s+f, where f is a count of the failures. The n are random variables not fixed by design in many studies. Joint modeling of (s, f) can provide additional insight into the science and into the probability pi of success that cannot be directly incorporated by the logistic regression model. Observations where n= 0 are excluded from the binomial analysis yet may be important to understanding how pi is influenced by covariates. Correlation between s and f may exist and be of direct interest. We propose Bayesian multivariate Poisson models for the bivariate response (s, f), correlated through random effects. We extend our models to the analysis of longitudinal and multivariate longitudinal binomial outcomes. Our methodology was motivated by two disparate examples, one from teratology and one from an HIV tertiary intervention study.     

Evaluating SNP ascertainment bias and its impact on population assignment in Atlantic cod, Gadus morhua

The increasing use of single nucleotide polymorphisms (SNPs) in studies of nonmodel organisms accentuates the need to evaluate the influence of ascertainment bias on accurate ecological or evolutionary inference. Using a panel of 1641 expressed sequence tag-derived SNPs developed for northwest Atlantic cod (Gadus morhua), we examined the influence of ascertainment bias and its potential impact on assignment of individuals to populations ranging widely in origin. We hypothesized that reductions in assignment success would be associated with lower diversity in geographical regions outside the location of ascertainment. Individuals were genotyped from 13 locations spanning much of the contemporary range of Atlantic cod. Diversity, measured as average sample heterozygosity and number of polymorphic loci, declined (c. 30%) from the western (H(e) = 0.36) to eastern (H(e) = 0.25) Atlantic, consistent with a signal of ascertainment bias. Assignment success was examined separately for pools of loci representing differing degrees of reductions in diversity. SNPs displaying the largest declines in diversity produced the most accurate assignment in the ascertainment region (c. 83%) and the lowest levels of correct assignment outside the ascertainment region (c. 31%). Interestingly, several isolated locations showed no effect of assignment bias and consistently displayed 100% correct assignment. Contrary to expectations, estimates of accurate assignment range-wide using all loci displayed remarkable similarity despite reductions in diversity. Our results support the use of large SNP panels in assignment studies of high geneflow marine species. However, our evidence of significant reductions in assignment success using some pools of loci suggests that ascertainment bias may influence assignment results and should be evaluated in large-scale assignment studies.     

Sporadic cases in Duchenne muscular dystrophy

Summary A new estimation of the proportion of sporadic cases in Duchenne muscular dystrophy was attempted by means of segregation analysis in a sample of 988 sibships collected on a world-wide scale by different authors. Maximum likelihood estimates of ascertainment probability (), segregation frequency (p), and frequency of sporadic cases (x) were calculated by Morton's equations under different hypotheses. The best fit was found for p=0.454±0.024 and x=0.235±0.034. The possibility that the proportion of sporadic cases might be lower than the expected 1/3 is suggested.     

Segregation analysis with uncertain ascertainment: application to Fanconi anemia.

A Bayesian solution for making inferences about segregation parameters with no information about the ascertainment is presented. Inferences about the segregation probability and the probability of being sporadic are made through the posterior marginal distribution of these parameters after integrating out the ascertainment probability, the nuisance parameter. The method was tested with real and simulated data and performed well. Original Fanconi anemia data, for which no information about the ascertainment was available, were then analyzed, with results that confirmed a monogenic autosomal recessive mode of inheritance.     

Inherent intractability of the ascertainment problem for pedigree data: a general likelihood framework.

The problem of ascertainment in segregation analysis arises when families are selected for study through ascertainment of affected individuals. In this case, ascertainment must be corrected for in data analysis. However, methods for ascertainment correction are not available for many common sampling schemes, e.g., sequential sampling of extended pedigrees (except in the case of "single" selection). Concerns about whether ascertainment correction is even required for large pedigrees, about whether and how multiple probands in the same pedigree can be taken into account properly, and about how to apply sequential sampling strategies have occupied many investigators in recent years. We address these concerns by reconsidering a central issue, namely, how to handle pedigree structure (including size). We introduce a new distinction, between sampling in such a way that observed pedigree structure does not depend on which pedigree members are probands (proband-independent [PI] sampling) and sampling in such a way that observed pedigree structure does depend on who are the probands (proband-dependent [PD] sampling). This distinction corresponds roughly (but not exactly) to the distinction between fixed-structure and sequential sampling. We show that conditioning on observed pedigree structure in ascertained data sets obtained under PD sampling is not in general correct (with the exception of "single" selection), while PI sampling of pedigree structures larger than simple sibships is generally not possible. Yet, in practice one has little choice but to condition on observed pedigree structure. We conclude that the problem of genetic modeling in ascertained data sets is, in most situations, literally intractable. We recommend that future efforts focus on the development of robust approximate approaches to the problem.     

General models for segregation analysis.

Theoretical details are given of various oligogenic models for segregation analysis that are available as a general segregation analysis ("GENSEG") package, programmed in FORTRAN iv. The models allow for up to two autosomal loci and one X-linked locus, normally distributed or dichotomous phenotypes, variable age of onset, and various ascertainment functions (including one that allows the probability of becoming a proband to be dependent on the age of onset). Current programs are limited to the analysis of 2-generational data, using the joint likelihood of the sibship and parental phenotypes, unless it can be assumed that the pedigrees being analyzed are a random sample from the population; half-sibships and twins, however, are explicitly allowed.     

Mapping dominant markers using F2 matings

The development of efficient methods for amplifying random DNA sequences by the polymerase chain reaction has created the basis for mapping virtually unlimited numbers of mixed-phase dominant DNA markers in one population. Although dominant markers can be efficiently mapped using many different kinds of matings, recombination frequencies and locus orders are often mis-estimated from repulsion F₂ matings. The major problem with these matings, apart from excessive sampling errors of recombination frequency () estimates, is the bias of the maximum-likelihood estimator (MLE) of ( _ML). when the observed frequency of double-recessive phenotypes is 0 and the observed frequency of double-dominant phenotypes is less than 2/3 — the bias for those samples is — . We used simulation to estimate the mean bias of _ML. Mean bias is a function of n and and decreases as n increases. Valid maps of dominant markers can be built by using sub-sets of markers linked in coupling, thereby creating male and feamle coupling maps, as long as the maps are fairly dense (about 5 cM) — the sampling errors of increase as increases for coupling linkages and are equal to those for backcross matings when =0. The use of F₂ matings for mapping dominant markers is not necessarily proscribed because they yield twice as many useful markers as a backcross population, albeit in two maps, for the same number of DNA extractions and PCR assays; however, dominant markers can be more effeciently exploited by using doubled-haploid, recombinant-inbred, or other inbred populations.