Pairwise relatedness testing in the context of inbreeding: expectation and variance of the likelihood ratio.

In this paper we investigate various effects of inbreeding on the likelihood ratio (LR) in forensic kinship testing. The basic setup of such testing involves formulating two competing hypotheses, in the form of pedigrees, describing the relationship between the individuals. The likelihood of each hypothesis is computed given the available genetic data, and a conclusion is reached if the ratio of these exceeds some pre-determined threshold. An important aspect of this approach is that the hypotheses are usually not exhaustive: The true relationship may differ from both of the stated pedigrees. It is well known that this may introduce bias in the test results. Previous work has established formulas for the expected value and variance of the LR, given the two competing hypotheses and the true relationship. However, the proposed method only handles cases without inbreeding. In this paper we extend these results to all possible pairwise relationships. The key ingredient is formulating the hypotheses in terms of Jacquard coefficients instead of the more restricted Cotterman coefficients. While the latter describe the relatedness between outbred individuals, the more general Jacquard coefficients allow any level of inbreeding. Our approach also enables scrutiny of another frequently overlooked source of LR bias, namely background inbreeding. This ubiquitous phenomenon is usually ignored in forensic kinship computations, due to lack of adequate methods and software. By leveraging recent work on pedigrees with inbred founders, we show how background inbreeding can be modeled as a continuous variable, providing easy-to-interpret results in specific cases. For example, we show that if true siblings are subjected to a test for parent-offspring, moderate levels of background inbreeding are expected to inflate the LR by more than 50%.

Advancing estimation of chronological age by utilizing available evidence based on two radiographical methods.

This paper describes a strategy for estimating chronological age of individuals based on age indicators of X-ray of the hand and the third molar tooth. The great majority of studies in the field provide group-wise data of different formats, which makes them difficult to compare and utilize in a model. In this paper, we have provided a framework to utilize different types of data formats to build a common model for estimating chronological age. We used transition analysis to describe the relationship between the age indicators and chronological age. Further, likelihood ratio weight of evidence and posterior distribution of chronological age were used to model the distribution of chronological age given the observed age indicators. Being able to utilize such a large amount of data, with different data formats, from different studies, as presented in this paper improves previous age estimation methods.

The failing measurement of attitudes: How semantic determinants of individual survey responses come to replace measures of attitude strength.

The traditional understanding of data from Likert scales is that the quantifications involved result from measures of attitude strength. Applying a recently proposed semantic theory of survey response, we claim that survey responses tap two different sources: a mixture of attitudes plus the semantic structure of the survey. Exploring the degree to which individual responses are influenced by semantics, we hypothesized that in many cases, information about attitude strength is actually filtered out as noise in the commonly used correlation matrix. We developed a procedure to separate the semantic influence from attitude strength in individual response patterns, and compared these results to, respectively, the observed sample correlation matrices and the semantic similarity structures arising from text analysis algorithms. This was done with four datasets, comprising a total of 7,787 subjects and 27,461,502 observed item pair responses. As we argued, attitude strength seemed to account for much information about the individual respondents. However, this information did not seem to carry over into the observed sample correlation matrices, which instead converged around the semantic structures offered by the survey items. This is potentially disturbing for the traditional understanding of what survey data represent. We argue that this approach contributes to a better understanding of the cognitive processes involved in survey responses. In turn, this could help us make better use of the data that such methods provide.

Characterization of degradation and heterozygote balance by simulation of the forensic DNA analysis process.

Simulation experiments were used to show the impact of varying extraction efficiency, aliquot proportion, and PCR efficiency on the heterozygote balance of a range of diploid and haploid cells. Reducing either parameters introduces variance. It is well-known that the variance in heterozygote balance increases as the amount of DNA is reduced. Surprisingly the distribution is in fact diamond shaped - the variance start to decrease at very low amounts of DNA. Simulations suggest that pristine diluted DNA is an acceptable approximation in validations to infer heterozygote balance. However, the difference in distribution of the variance between diploid and haploid cell types may, under some circumstances, need to be considered in statistical models. Finally, we exemplify how simulations can be used to predict the outcome of PCR for degraded samples. Visualizing the predicted DNA profile as an electropherogram can help to identify the best approach for sample processing.

A parametric approach to kinship hypothesis testing using identity-by-descent parameters.

There is a large number of applications where family relationships need to be determined from DNA data. In forensic science, competing ideas are in general verbally formulated as the two hypotheses of a test. For the most common paternity case, the null hypothesis states that the alleged father is the true father against the alternative hypothesis that the father is an unrelated man. A likelihood ratio is calculated to summarize the evidence. We propose an alternative framework whereby a model and the hypotheses are formulated in terms of parameters representing identity-by-descent probabilities. There are several advantages to this approach. Firstly, the alternative hypothesis can be completely general. Specifically, the alternative does not need to specify an unrelated man. Secondly, the parametric formulation corresponds to the approach used in most other applications of statistical hypothesis testing and so there is a large theory of classical statistics that can be applied. Theoretical properties of the test statistic under the null hypothesis are studied. An extension to trios of individuals has been carried out. The methods are exemplified using simulations and a real dataset of 27 Spanish Romani individuals.

The likelihood ratio as a random variable for linked markers in kinship analysis.

The likelihood ratio is the fundamental quantity that summarizes the evidence in forensic cases. Therefore, it is important to understand the theoretical properties of this statistic. This paper is the last in a series of three, and the first to study linked markers. We show that for all non-inbred pairwise kinship comparisons, the expected likelihood ratio in favor of a type of relatedness depends on the allele frequencies only via the number of alleles, also for linked markers, and also if the true relationship is another one than is tested for by the likelihood ratio. Exact expressions for the expectation and variance are derived for all these cases. Furthermore, we show that the expected likelihood ratio is a non-increasing function if the recombination rate increases between 0 and 0.5 when the actual relationship is the one investigated by the LR. Besides being of theoretical interest, exact expressions such as obtained here can be used for software validation as they allow to verify the correctness up to arbitrary precision. The paper also presents results and advice of practical importance. For example, we argue that the logarithm of the likelihood ratio behaves in a fundamentally different way than the likelihood ratio itself in terms of expectation and variance, in agreement with its interpretation as weight of evidence. Equipped with the results presented and freely available software, one may check calculations and software and also do power calculations.

Exclusion probabilities and likelihood ratios with applications to mixtures.

The statistical evidence obtained from mixed DNA profiles can be summarised in several ways in forensic casework including the likelihood ratio (LR) and the Random Man Not Excluded (RMNE) probability. The literature has seen a discussion of the advantages and disadvantages of likelihood ratios and exclusion probabilities, and part of our aim is to bring some clarification to this debate. In a previous paper, we proved that there is a general mathematical relationship between these statistics: RMNE can be expressed as a certain average of the LR, implying that the expected value of the LR, when applied to an actual contributor to the mixture, is at least equal to the inverse of the RMNE. While the mentioned paper presented applications for kinship problems, the current paper demonstrates the relevance for mixture cases, and for this purpose, we prove some new general properties. We also demonstrate how to use the distribution of the likelihood ratio for donors of a mixture, to obtain estimates for exceedance probabilities of the LR for non-donors, of which the RMNE is a special case corresponding to L R>0. In order to derive these results, we need to view the likelihood ratio as a random variable. In this paper, we describe how such a randomization can be achieved. The RMNE is usually invoked only for mixtures without dropout. In mixtures, artefacts like dropout and drop-in are commonly encountered and we address this situation too, illustrating our results with a basic but widely implemented model, a so-called binary model. The precise definitions, modelling and interpretation of the required concepts of dropout and drop-in are not entirely obvious, and we attempt to clarify them here in a general likelihood framework for a binary model.

Relationship inference based on DNA mixtures.

Today, there exists a number of tools for solving kinship cases. But what happens when information comes from a mixture? DNA mixtures are in general rarely seen in kinship cases, but in a case presented to the Norwegian Institute of Public Health, sample DNA was obtained after a rape case that resulted in an unwanted pregnancy and abortion. The only available DNA from the fetus came in form of a mixture with the mother, and it was of interest to find the father of the fetus. The mother (the victim), however, refused to give her reference data and so commonly used methods for paternity testing were no longer applicable. As this case illustrates, kinship cases involving mixtures and missing reference profiles do occur and make the use of existing methods rather inconvenient. We here present statistical methods that may handle general relationship inference based on DNA mixtures. The basic idea is that likelihood calculations for mixtures can be decomposed into a series of kinship problems. This formulation of the problem facilitates the use of kinship software. We present the freely available R package relMix which extends on the R version of Familias. Complicating factors like mutations, silent alleles, and θ-correction are then easily handled for quite general family relationships, and are included in the statistical methods we develop in this paper. The methods and their implementations are exemplified on the data from the rape case.

Mixtures with relatives and linked markers.

Mixture DNA profiles commonly appear in forensic genetics, and a large number of statistical methods and software are available for such cases. However, most of the literature concerns mixtures where the contributors are assumed unrelated and the genetic markers are unlinked. In this paper, we consider mixtures of linked markers and related contributors. If no relationships are involved, linkage can be ignored. While unlinked markers can be treated independently, linkage introduces dependencies. The use of linked markers presents statistical and computational challenges, but may also lead to a considerable increase in power since the number of markers available is much larger if we do not require the markers to be unlinked. In addition, some cases that cannot be solved with an unlimited number of unlinked autosomal markers can be solved with linked markers. We focus on two special cases of linked markers: pairs of linked autosomal markers and X-chromosomal markers. A framework is presented for calculation of likelihood ratios for mixtures with general relationships and with linkage between any number of markers. Finally, we explore the effect of linkage disequilibrium, also called allelic association, on the likelihood ratio.

Lipoprotein subfractions by nuclear magnetic resonance are associated with tumor characteristics in breast cancer.

BACKGROUND: High-Density Lipoprotein (HDL)-cholesterol, has been associated with breast cancer development, but the association is under debate, and whether lipoprotein subfractions is associated with breast tumor characteristics remains unclear. METHODS: Among 56 women with newly diagnosed invasive breast cancer stage I/II, aged 35-75 years, pre-surgery overnight fasting serum concentrations of lipids were assessed, and body mass index (BMI) was measured. All breast tumors were immunohistochemically examined in the surgical specimen. Serum metabolomics of lipoprotein subfractions and their contents of cholesterol, free cholesterol, phospholipids, apolipoprotein-A1 and apolipoprotein-A2, were assessed using nuclear magnetic resonance. Principal component analysis, partial least square analysis, and uni- and multivariable linear regression models were used to study whether lipoprotein subfractions were associated with breast cancer tumor characteristics. RESULTS: The breast cancer patients had following means: age at diagnosis: 55.1 years; BMI: 25.1 kg/m(2); total-Cholesterol: 5.74 mmol/L; HDL-Cholesterol: 1.78 mmol/L; Low-Density Lipoprotein (LDL)-Cholesterol: 3.45 mmol/L; triglycerides: 1.18 mmol/L. The mean tumor size was 16.4 mm, and the mean Ki67 hotspot index was 26.5%. Most (93%) of the patients had estrogen receptor (ER) positive tumors (≥ 1% ER+), and 82% had progesterone receptor (PgR) positive tumors (≥ 10% PgR+). Several HDL subfraction contents were strongly associated with PgR expression: Apolipoprotein-A1 (ß 0.46, CI 0.22-0.69, p < 0.001), HDL cholesterol (ß 0.95, CI 0.51-1.39, p < 0.001), HDL free cholesterol (ß 2.88, CI 1.28-4.48, p = 0.001), HDL phospholipids (ß 0.70, CI 0.36-1.04, p < 0.001). Similar results were observed for the subfractions of HDL1-3. We observed inverse associations between HDL phospholipids and Ki67 (ß -0.25, p = 0.008), and in particular between HDL1's contents of cholesterol, phospholipids, apolipoprotein-A1, apolipoprotein-A2 and Ki67. No association was observed between lipoproteins and ER expression. CONCLUSION: Our findings hypothesize associations between different lipoprotein subfractions, and PgR expression, and Ki 67 % in breast tumors. These findings may have clinical implications, but require confirmation in larger studies.

A general model for likelihood computations of genetic marker data accounting for linkage, linkage disequilibrium, and mutations.

Several applications necessitate an unbiased determination of relatedness, be it in linkage or association studies or in a forensic setting. An appropriate model to compute the joint probability of some genetic data for a set of persons given some hypothesis about the pedigree structure is then required. The increasing number of markers available through high-density SNP microarray typing and NGS technologies intensifies the demand, where using a large number of markers may lead to biased results due to strong dependencies between closely located loci, both within pedigrees (linkage) and in the population (allelic association or linkage disequilibrium (LD)). We present a new general model, based on a Markov chain for inheritance patterns and another Markov chain for founder allele patterns, the latter allowing us to account for LD. We also demonstrate a specific implementation for X chromosomal markers that allows for computation of likelihoods based on hypotheses of alleged relationships and genetic marker data. The algorithm can simultaneously account for linkage, LD, and mutations. We demonstrate its feasibility using simulated examples. The algorithm is implemented in the software FamLinkX, providing a user-friendly GUI for Windows systems (FamLinkX, as well as further usage instructions, is freely available at www.famlink.se ). Our software provides the necessary means to solve cases where no previous implementation exists. In addition, the software has the possibility to perform simulations in order to further study the impact of linkage and LD on computed likelihoods for an arbitrary set of markers.

Models and implementation for relationship problems with dropout.

Allelic dropout in relationship problems may commonly appear in areas such as disaster victim identification and the identification of missing persons. If dropout is not accounted for, the results may be incorrect interpretation of profiles, loss of valuable information and biased results. In this paper, we explore different models for dropout in kinship cases and present an efficient implementation for one of the models. The implementation allows for dropout to be handled simultaneously with phenomena like silent alleles and mutations that may also cause discordances in relationship data, in addition to subpopulation correction. The implemented dropout model is freely available in the new version of the Familias software. The concepts and methods are illustrated on real and simulated data.

Gene variations in oestrogen pathways, CYP19A1, daily 17ß-estradiol and mammographic density phenotypes in premenopausal women.

INTRODUCTION: High mammographic density is an established breast cancer risk factor, and circulating oestrogen influences oestrogen-regulating gene expression in breast cancer development. However, less is known about the interrelationships of common variants in the CYP19A1 gene, daily levels of oestrogens, mammographic density phenotypes and body mass index (BMI) in premenopausal women. METHODS: Based on plausible biological mechanisms related to the oestrogen pathway, we investigated the association of single nucleotide polymorphisms (SNPs) in CYP19A1, 17ß-estradiol and mammographic density in 202 premenopausal women. DNA was genotyped using the Illumina Golden Gate platform. Daily salivary 17ß-estradiol concentrations were measured throughout an entire menstrual cycle. Mammographic density phenotypes were assessed using a computer-assisted method (Madena). We determined associations using multivariable linear and logistic regression models. RESULTS: The minor alleles of rs749292 were positively (P = 0.026), and the minor alleles of rs7172156 were inversely (P = 0.002) associated with daily 17ß-estradiol. We observed an 87% lower level of daily 17ß-estradiol throughout a menstrual cycle in heavier women (BMI >23.6 kg/m(2)) of rs7172156 with minor genotype aa compared with major genotype AA. Furthermore, the rs749292 minor alleles were inversely associated with absolute mammographic density (P = 0.032). Lean women with rs749292 minor alleles had 70 to 80% lower risk for high absolute mammographic density (>32.4 cm(2)); Aa: odds ratio (OR) = 0.23 (95% CI 0.07 to 0.75). Lean women with rs7172156 minor homozygous genotype had OR 5.45 for high absolute mammographic density (aa: OR = 5.45 (95% CI 1.13 to 26.3)). CONCLUSION: Our findings suggest that two SNPs in CYP19A1, rs749292 and rs7172156, are associated with both daily oestrogen levels and mammographic density phenotypes. BMI may modify these associations, but larger studies are needed.

Exclusion probabilities and likelihood ratios with applications to kinship problems.

In forensic genetics, DNA profiles are compared in order to make inferences, paternity cases being a standard example. The statistical evidence can be summarized and reported in several ways. For example, in a paternity case, the likelihood ratio (LR) and the probability of not excluding a random man as father (RMNE) are two common summary statistics. There has been a long debate on the merits of the two statistics, also in the context of DNA mixture interpretation, and no general consensus has been reached. In this paper, we show that the RMNE is a certain weighted average of inverse likelihood ratios. This is true in any forensic context. We show that the likelihood ratio in favor of the correct hypothesis is, in expectation, bigger than the reciprocal of the RMNE probability. However, with the exception of pathological cases, it is also possible to obtain smaller likelihood ratios. We illustrate this result for paternity cases. Moreover, some theoretical properties of the likelihood ratio for a large class of general pairwise kinship cases, including expected value and variance, are derived. The practical implications of the findings are discussed and exemplified.

SLC9A6 mutations cause X-linked mental retardation, microcephaly, epilepsy, and ataxia, a phenotype mimicking Angelman syndrome.

Linkage analysis and DNA sequencing in a family exhibiting an X-linked mental retardation (XLMR) syndrome, characterized by microcephaly, epilepsy, ataxia, and absent speech and resembling Angelman syndrome, identified a deletion in the SLC9A6 gene encoding the Na(+)/H(+) exchanger NHE6. Subsequently, other mutations were found in a male with mental retardation (MR) who had been investigated for Angelman syndrome and in two XLMR families with epilepsy and ataxia, including the family designated as having Christianson syndrome. Therefore, mutations in SLC9A6 cause X-linked mental retardation. Additionally, males with findings suggestive of unexplained Angelman syndrome should be considered as potential candidates for SLC9A6 mutations.

Joint DNA-based disaster victim identification.

We address computational and statistical aspects of DNA-based identification of victims in the aftermath of disasters. Current methods and software for such identification typically consider each victim individually, leading to suboptimal power of identification and potential inconsistencies in the statistical summary of the evidence. We resolve these problems by performing joint identification of all victims, using the complete genetic data set. Individual identification probabilities, conditional on all available information, are derived from the joint solution in the form of posterior pairing probabilities. A closed formula is obtained for the a priori number of possible joint solutions to a given DVI problem. This number increases quickly with the number of victims and missing persons, posing computational challenges for brute force approaches. We address this complexity with a preparatory sequential step aiming to reduce the search space. The examples show that realistic cases are handled efficiently. User-friendly implementations of all methods are provided in the R package dvir, freely available on all platforms.

Making decisions in missing person identification cases with low statistical power.

The present work proposes a general strategy for dealing with missing person identification cases through DNA-database search. Our main example is the identification of abducted children in the last civic-dictatorship of Argentina, known as the "Missing Grandchildren of Argentina". Particularly we focus on those pedigrees where few, or only distant relatives of the missing person are available, resulting in low statistical power. For such complex cases we provide a statistical method for selecting a likelihood ratio (LR) threshold for each pedigree based on error rates. Furthermore, we provide an open-source user friendly software for computing LR thresholds and error rates. The strategy described in the paper could be applied to other large-scale cases of DNA-based identification hampered by low statistical power.

Strategies for pairwise searches in forensic kinship analysis.

Testing kinship between pairs of individuals is central to a wide range of applications. We focus on cases where many tests are done jointly. Typical examples include cases where DNA profiles are available from a burial site, a plane crash or a database of convicted offenders. The task is to determine the relationships between DNA profiles or individuals. Our approach generalises previous methods and implementations in several respects. We model general, possibly inbred, pairwise relationships which is important for non-human applications and in archaeological studies of ancient inbred populations. Furthermore, we do not restrict attention to autosomal markers. Some cases, such as distinguishing between maternal and paternal half siblings, can be solved using X-chromosomal markers. When many tests are done, the risk of errors increases. We address this problem by building on the theory of multiple testing and show how optimal thresholds for tests can be determined. We point out that the likelihood ratios in a blind search may be dependent so multiple testing methods and interpretation need to account for this. In addition, we show how a Bayesian approach can be helpful. Our examples, using simulated and real data, demonstrate the practical importance of the methods and implementation is based on freely available software.

Identification of distant family relationships.

MOTIVATION: Family relationships can be estimated from DNA marker data. Applications arise in a large number of areas including evolution and conservation research, genealogical research in human, plant and animal populations, forensic problems and genetic mapping via linkage and association analyses. Traditionally, likelihood-based approaches to relationship estimation have used unlinked genetic markers. Due to the fact that some relationships cannot be distinguished from data at unlinked markers, and given the limited number of such markers available, there are considerable constraints on the type of identification problem that can be satisfactorily addressed with such approaches. The aim of this article is to explore the potential of linked autosomal single nucleotide polymorphism markers in this context. Throughout, we will view the problem of relationship estimation as one of pedigree identification rather than identity-by-descent, and thus focus on applications where determination of the exact relationship is important. RESULTS: We show that the increase in information obtained by exploiting large sets of linked markers substantially increases the number of problems that can be solved. Results are presented based on simulations as well as on real data. AVAILABILITY: The R library FEST is freely available from http://folk.uio.no/thoree/FEST.

A CLEC16A variant confers risk for juvenile idiopathic arthritis and anti-cyclic citrullinated peptide antibody negative rheumatoid arthritis.

OBJECTIVE: Variants in CLEC16A have conferred susceptibility to autoimmune diseases in genome-wide association studies. The present work aimed to investigate the locus' involvements in juvenile idiopathic arthritis (JIA) and further explore the association with rheumatoid arthritis (RA), type 1 diabetes (T1D) and Addison's disease (AD) in the Norwegian population. METHODS: Three single nucleotide polymorphisms (SNPs) were genotyped in patients with RA (n=809), JIA (n=509), T1D (n=1211) and AD (n=414) and in healthy controls (n=2149). RESULTS: All diseases were associated with CLEC16A, but with different SNPs. The intron 22 SNP, rs6498169, was associated with RA (p=0.006) and JIA (p=0.016) and the intron 19 SNPs, rs12708716/rs12917716, with T1D (p=1x10-5) and AD (p=2x10-4). The RA association was confined to the anti-cyclic citrullinated peptide antibody (anti-CCP) negative subgroup (p=2x10-4). CONCLUSION: This is the first report of a CLEC16A association with JIA and a split of the RA association according to anti-CCP status. Different causative variants underlie the rheumatic versus the organ specific diseases.