Some capabilities for model-based and model-free linkage analysis using the program package S.A.G.E. (Statistical Analysis for Genetic Epidemiology)

For both model-free and model-based linkage analysis the S.A.G.E. (Statistical Analysis for Genetic Epidemiology) program package has some unique capabilities in analyzing both continuous traits and binary traits with variable age of onset. Here we highlight model-based linkage analysis of a quantitative trait (plasma dopamine β hydroxylase) that is known to be largely determined by monogenic inheritance, using a prior segregation analysis to produce the best fitting model for the trait. For a binary trait with variable age of onset (schizophrenia), we illustrate how using age of onset information to obtain a quantitative susceptibility trait leads to more statistically significant linkage signals, suggesting better power.     

Simple Plans or Sophisticated Habits? State,Transition and Learning Interactions in the Two-Step Task

The recently developed ‘two-step’ behavioural task promises to differentiate model-based from model-free reinforcement learning, while generating neurophysiologically-friendly decision datasets with parametric variation of decision variables. These desirable features have prompted its widespread adoption. Here, we analyse the interactions between a range of different strategies and the structure of transitions and outcomes in order to examine constraints on what can be learned from behavioural performance. The task involves a trade-off between the need for stochasticity, to allow strategies to be discriminated, and a need for determinism, so that it is worth subjects’ investment of effort to exploit the contingencies optimally. We show through simulation that under certain conditions model-free strategies can masquerade as being model-based. We first show that seemingly innocuous modifications to the task structure can induce correlations between action values at the start of the trial and the subsequent trial events in such a way that analysis based on comparing successive trials can lead to erroneous conclusions. We confirm the power of a suggested correction to the analysis that can alleviate this problem. We then consider model-free reinforcement learning strategies that exploit correlations between where rewards are obtained and which actions have high expected value. These generate behaviour that appears model-based under these, and also more sophisticated, analyses. Exploiting the full potential of the two-step task as a tool for behavioural neuroscience requires an understanding of these issues.     

Examining the effect of linkage disequilibrium on multipoint linkage analysis

Most linkage programs assume linkage equilibrium among multiple linked markers. This assumption may lead to bias for tightly linked markers where strong linkage disequilibrium (LD) exists. We used simulated data from Genetic Analysis Workshop 14 to examine the possible effect of LD on multipoint linkage analysis. Single-nucleotide polymorphism packets from a non-disease-related region that was generated with LD were used for both model-free and parametric linkage analyses. Results showed that high LD among markers can induce false-positive evidence of linkage for affected sib-pair analysis when parental data are missing. Bias can be eliminated with parental data and can be reduced when additional markers not in LD are included in the analyses.     

Power comparison of parametric and nonparametric linkage tests in small pedigrees

When the mode of inheritance of a disease is unknown, the LOD-score method of linkage analysis must take into account uncertainties in model parameters. We have previously proposed a parametric linkage test called "MFLOD," which does not require specification of disease model parameters. In the present study, we introduce two new model-free parametric linkage tests, known as "MLOD" and "MALOD." These tests are defined, respectively, as the LOD score and the admixture LOD score, maximized (subject to the same constraints as MFLOD) over disease-model parameters. We compared the power of these three parametric linkage tests and that of two nonparametric linkage tests, NPLall and NPLpairs, which are implemented in GENEHUNTER. With the use of small pedigrees and a fully informative marker, we found the powers of MLOD, NPLall, and NPLpairs to be almost equivalent to each other and not far below that of a LOD-score analysis performed under the assumption the correct genetic parameters. Thus, linkage analysis is not much hindered by uncertain mode of inheritance. The results also suggest that both parametric and nonparametric methods are suitable for linkage analysis of complex disorders in small pedigrees. However, whether these results apply to large pedigrees remains to be answered.     

Linkage analysis in the presence of errors IV: joint pseudomarker analysis of linkage and/or linkage disequilibrium on a mixture of pedigrees and singletons when the mode of inheritance cannot be accurately specified

There is a lot of confusion in the literature about the "differences" between "model-based" and "model-free" methods and about which approach is better suited for detection of the genes predisposing to complex multifactorial phenotypes. By starting from first principles, we demonstrate that the differences between the two approaches have more to do with study design than statistical analysis. When simple data structures are repeatedly ascertained, no assumptions about the genotype-phenotype relationship need to be made for the analysis to be powerful, since simple data structures admit only a small number of df. When more complicated and/or heterogeneous data structures are ascertained, however, the number of df in the underlying probability model is too large to have a powerful, truly "model-free" test. So-called "model-free" methods typically simplify the underlying probability model by implicitly assuming that, in some sense, all meioses connecting two affected individuals are informative for linkage with identical probability and that the affected individuals in a pedigree share as many disease-predisposing alleles as possible. By contrast, "model-based" methods add structure to the underlying parameter space by making assumptions about the genotype-phenotype relationship, making it possible to probabilistically assign disease-locus genotypes to all individuals in the data set on the basis of the observed phenotypes. In this study, we demonstrate the equivalence of these two approaches in a variety of situations and exploit this equivalence to develop more powerful and efficient likelihood-based analogues of "model-free" tests of linkage and/or linkage disequilibrium. Through the use of a "pseudomarker" locus to structure the space of observations, sib-pairs, triads, and singletons can be analyzed jointly, which will lead to tests that are more well-behaved, efficient, and powerful than traditional "model-free" tests such as the affected sib-pair, transmission/disequilibrium, haplotype relative risk, and case-control tests. Also described is an extension of this approach to large pedigrees, which, in practice, is equivalent to affected relative-pair analysis. The proposed methods are equally applicable to two-point and multipoint analysis (using complex-valued recombination fractions).     

A high-density SNP genomewide linkage scan for chronic lymphocytic leukemia-susceptibility loci

Chronic lymphocytic leukemia (CLL) and other B-cell lymphoproliferative disorders (LPDs) show clear evidence of familial aggregation, but the inherited basis is largely unknown. To identify a susceptibility gene for CLL, we conducted a genomewide linkage analysis of 115 pedigrees, using a high-density single-nucleotide polymorphism (SNP) array containing 11,560 markers. Multipoint linkage analyses were undertaken using both nonparametric (model-free) and parametric (model-based) methods. Our results confirm that the presence of high linkage disequilibrium (LD) between SNP markers can lead to inflated nonparametric linkage (NPL) and LOD scores. After the removal of high-LD SNPs, we obtained a maximum NPL of 3.14 (P=.0008) on chromosome 11p11. The same genomic position also yielded the highest multipoint heterogeneity LOD (HLOD) score under both dominant (HLOD 1.95) and recessive (HLOD 2.78) models. In addition, four other chromosomal positions (5q22-23, 6p22, 10q25, and 14q32) displayed HLOD scores >1.15 (which corresponds to a nominal P value <.01). None of the regions coincided with areas of common chromosomal abnormalities frequently observed for CLL. These findings strengthen the argument for an inherited predisposition to CLL and related B-cell LPDs.     

Ignoring linkage disequilibrium among tightly linked markers induces false-positive evidence of linkage for affected sib pair analysis

Most multipoint linkage programs assume linkage equilibrium among the markers being studied. The assumption is appropriate for the study of sparsely spaced markers with intermarker distances exceeding a few centimorgans, because linkage equilibrium is expected over these intervals for almost all populations. However, with recent advancements in high-throughput genotyping technology, much denser markers are available, and linkage disequilibrium (LD) may exist among the markers. Applying linkage analyses that assume linkage equilibrium to dense markers may lead to bias. Here, we demonstrated that, when some or all of the parental genotypes are missing, assuming linkage equilibrium among tightly linked markers where strong LD exists can cause apparent oversharing of multipoint identity by descent (IBD) between sib pairs and false-positive evidence for multipoint model-free linkage analysis of affected sib pair data. LD can also mimic linkage between a disease locus and multiple tightly linked markers, thus causing false-positive evidence of linkage using parametric models, particularly when heterogeneity LOD score approaches are applied. Bias can be eliminated by inclusion of parental genotype data and can be reduced when additional unaffected siblings are included in the analysis.     

Model-Based Reasoning in Humans Becomes Automatic with Training

Model-based and model-free reinforcement learning (RL) have been suggested as algorithmic realizations of goal-directed and habitual action strategies. Model-based RL is more flexible than model-free but requires sophisticated calculations using a learnt model of the world. This has led model-based RL to be identified with slow, deliberative processing, and model-free RL with fast, automatic processing. In support of this distinction, it has recently been shown that model-based reasoning is impaired by placing subjects under cognitive load—a hallmark of non-automaticity. Here, using the same task, we show that cognitive load does not impair model-based reasoning if subjects receive prior training on the task. This finding is replicated across two studies and a variety of analysis methods. Thus, task familiarity permits use of model-based reasoning in parallel with other cognitive demands. The ability to deploy model-based reasoning in an automatic, parallelizable fashion has widespread theoretical implications, particularly for the learning and execution of complex behaviors. It also suggests a range of important failure modes in psychiatric disorders.     

Model-based influences on humans' choices and striatal prediction errors

The mesostriatal dopamine system is prominently implicated in model-free reinforcement learning, with fMRI BOLD signals in ventral striatum notably covarying with model-free prediction errors. However, latent learning and devaluation studies show that behavior also shows hallmarks of model-based planning, and the interaction between model-based and model-free values, prediction errors, and preferences is underexplored. We designed a multistep decision task in which model-based and model-free influences on human choice behavior could be distinguished. By showing that choices reflected both influences we could then test the purity of the ventral striatal BOLD signal as a model-free report. Contrary to expectations, the signal reflected both model-free and model-based predictions in proportions matching those that best explained choice behavior. These results challenge the notion of a separate model-free learner and suggest a more integrated computational architecture for high-level human decision-making.     

Joint oligogenic segregation and linkage analysis using bayesian Markov chain Monte Carlo methods

One of the most challenging areas in human genetics is the dissection of quantitative traits. In this context, the efficient use of available data is important, including, when possible, use of large pedigrees and many markers for gene mapping. In addition, methods that jointly perform linkage analysis and estimation of the trait model are appealing because they combine the advantages of a model-based analysis with the advantages of methods that do not require prespecification of model parameters for linkage analysis. Here we review a Markov chain Monte Carlo approach for such joint linkage and segregation analysis, which allows analysis of oligogenic traits in the context of multipoint linkage analysis of large pedigrees. We provide an outline for practitioners of the salient features of the method, interpretation of the results, effect of violation of assumptions, and an example analysis of a two-locus trait to illustrate the method.     

Quantifying genomic imprinting in the presence of linkage

Genomic imprinting decreases the power of classical linkage analysis, in which paternal and maternal transmissions of marker alleles are equally weighted. Several methods have been proposed for taking genomic imprinting into account in the model-free linkage analysis of binary traits. However, none of these methods are suitable for the formal identification and quantification of genomic imprinting in the presence of linkage. In addition, the available methods are designed for use with pure sib-pairs, requiring artificial decomposition in cases of larger sibships, leading to a loss of power. We propose here the maximum likelihood binomial method adaptive for imprinting (MLB-I), which is a unified analytic framework giving rise to specific tests in sibships of any size for (i) linkage adaptive to imprinting, (ii) genomic imprinting in the presence of linkage, and (iii) partial versus complete genomic imprinting. In addition, we propose an original measure for quantifying genomic imprinting. We have derived and validated the distribution of the three tests under their respective null hypotheses for various genetic models, and have assessed the power of these tests in simulations. This method can readily be applied to genome-wide scanning, as illustrated here for leprosy sibships. Our approach provides a novel tool for dissecting genomic imprinting in model-free linkage analysis, and will be of considerable value for identifying and evaluating the contribution of imprinted genes to complex diseases.     

Conclusion of LOD-score analysis for family data generated under two-locus models.

The power to detect linkage by the LOD-score method is investigated here for diseases that depend on the effects of two genes. The classical strategy is, first, to detect a major-gene (MG) effect by segregation analysis and, second, to seek for linkage with genetic markers by the LOD-score method using the MG parameters. We already showed that segregation analysis can lead to evidence for a MG effect for many two-locus models, with the estimates of the MG parameters being very different from those of the two genes involved in the disease. We show here that use of these MG parameter estimates in the LOD-score analysis may lead to a failure to detect linkage for some two-locus models. For these models, use of the sib-pair method gives a non-negligible increase of power to detect linkage. The linkage-homogeneity test among subsamples differing for the familial disease distribution provides evidence of parameter misspecification, when the MG parameters are used. Moreover, for most of the models, use of the MG parameters in LOD-score analysis leads to a large bias in estimation of the recombination fraction and sometimes also to a rejection of linkage for the true recombination fraction. A final important point is that a strong evidence of an MG effect, obtained by segregation analysis, does not necessarily imply that linkage will be detected for at least one of the two genes, even with the true parameters and with a close informative marker.     

Dopamine Enhances Model-Based over Model-Free Choice Behavior

Decision making is often considered to arise out of contributions from a model-free habitual system and a model-based goal-directed system. Here, we investigated the effect of a dopamine manipulation on the degree to which either system contributes to instrumental behavior in a two-stage Markov decision task, which has been shown to discriminate model-free from model-based control. We found increased dopamine levels promote model-based over model-free choice.     

Evidence for a novel late-onset Alzheimer disease locus on chromosome 19p13.2

Late-onset familial Alzheimer disease (LOFAD) is a genetically heterogeneous and complex disease for which only one locus, APOE, has been definitively identified. Difficulties in identifying additional loci are likely to stem from inadequate linkage analysis methods. Nonparametric methods suffer from low power because of limited use of the data, and traditional parametric methods suffer from limitations in the complexity of the genetic model that can be feasibly used in analysis. Alternative methods that have recently been developed include Bayesian Markov chain-Monte Carlo methods. These methods allow multipoint linkage analysis under oligogenic trait models in pedigrees of arbitrary size; at the same time, they allow for inclusion of covariates in the analysis. We applied this approach to an analysis of LOFAD on five chromosomes with previous reports of linkage. We identified strong evidence of a second LOFAD gene on chromosome 19p13.2, which is distinct from APOE on 19q. We also obtained weak evidence of linkage to chromosome 10 at the same location as a previous report of linkage but found no evidence for linkage of LOFAD age-at-onset loci to chromosomes 9, 12, or 21.     

Transcranial Direct Current Stimulation of Right Dorsolateral Prefrontal Cortex Does Not Affect Model-Based or Model-Free Reinforcement Learning in Humans

There is broad consensus that the prefrontal cortex supports goal-directed, model-based decision-making. Consistent with this, we have recently shown that model-based control can be impaired through transcranial magnetic stimulation of right dorsolateral prefrontal cortex in humans. We hypothesized that an enhancement of model-based control might be achieved by anodal transcranial direct current stimulation of the same region. We tested 22 healthy adult human participants in a within-subject, double-blind design in which participants were given Active or Sham stimulation over two sessions. We show Active stimulation had no effect on model-based control or on model-free (‘habitual’) control compared to Sham stimulation. These null effects are substantiated by a power analysis, which suggests that our study had at least 60% power to detect a true effect, and by a Bayesian model comparison, which favors a model of the data that assumes stimulation had no effect over models that assume stimulation had an effect on behavioral control. Although we cannot entirely exclude more trivial explanations for our null effect, for example related to (faults in) our experimental setup, these data suggest that anodal transcranial direct current stimulation over right dorsolateral prefrontal cortex does not improve model-based control, despite existing evidence that transcranial magnetic stimulation can disrupt such control in the same brain region.     

Further evidence for the increased power of LOD scores compared with nonparametric methods.

In genetic analysis of diseases in which the underlying model is unknown, "model free" methods-such as affected sib pair (ASP) tests-are often preferred over LOD-score methods, although LOD-score methods under the correct or even approximately correct model are more powerful than ASP tests. However, there might be circumstances in which nonparametric methods will outperform LOD-score methods. Recently, Dizier et al. reported that, in some complex two-locus (2L) models, LOD-score methods with segregation analysis-derived parameters had less power to detect linkage than ASP tests. We investigated whether these particular models, in fact, represent a situation that ASP tests are more powerful than LOD scores. We simulated data according to the parameters specified by Dizier et al. and analyzed the data by using a (a) single locus (SL) LOD-score analysis performed twice, under a simple dominant and a recessive mode of inheritance (MOI), (b) ASP methods, and (c) nonparametric linkage (NPL) analysis. We show that SL analysis performed twice and corrected for the type I-error increase due to multiple testing yields almost as much linkage information as does an analysis under the correct 2L model and is more powerful than either the ASP method or the NPL method. We demonstrate that, even for complex genetic models, the most important condition for linkage analysis is that the assumed MOI at the disease locus being tested is approximately correct, not that the inheritance of the disease per se is correctly specified. In the analysis by Dizier et al., segregation analysis led to estimates of dominance parameters that were grossly misspecified for the locus tested in those models in which ASP tests appeared to be more powerful than LOD-score analyses.     

SLEB3 in systemic lupus erythematosus (SLE) is strongly related to SLE families ascertained through neuropsychiatric manifestations

Seizures and psychosis are neuropsychiatric (NP) manifestations of a large number of systemic lupus erythematosus (SLE) patients. Since NP manifestations were part of the SLE phenotype for some, but not all SLE affecteds, we hypothesized that those SLE patient families with NP manifestations might be more genetically homogeneous at loci important to NP-related SLE, and hence have increased power to detect linkage. We identified 23 families of European-American (EA) origin and 20 families of African-American (AA) origin, in which at least one SLE patient in each family was diagnosed with the presence of NP manifestations. A total of 318 microsatellite markers at an average marker density of 11 cM were genotyped. Uncertainty of the genetic model led us to perform the initial genome scan by a multipoint non-parametric allele sharing linkage method. Once the evidence of linkage was suggestive, we then performed parametric model-based linkage by maximizing the relevant parameters to define a parsimonious genetic model. We found the maximum multipoint parametric LOD score was 5.19 and the non-parametric linkage score (Zlr) was 3.12 ( P=9x10(-4)) for EA NP pedigrees at 4p16, previously identified as SLEB3. The segregation behavior of this linked locus suggests a dominant mode of inheritance with an almost 100% homogeneous genetic effect in these pedigrees. The results demonstrated a significant increase of LOD score to detect SLEB3 when the families were further ascertained through NP, compared with the analysis of all EA SLE families together.     

Genome scanning for linkage: an overview.

Several different methods for linkage analysis are shown to arise from a single likelihood function L for the observed allele-sharing data at multiple markers in a chromosomal region. These include classical parametric lod score methods, nonparametric or "model-free" affected pedigree-member (APM) methods, and the Gaussian process method. Setting the methods in the context of the likelihood function L clarifies their underlying assumptions. A test statistic derived from L, the efficient score statistic, is introduced. It is asymptotically equivalent to the lod score, but it can be easier to compute when the penetrances and frequencies of alleles of the trait gene are not known. APM test statistics and the Gaussian lod score are shown to be special cases of efficient score statistics. This unified framework facilitates exploration of a range of models for the effects of a putative trait-predisposing gene, and it facilitates sensitivity analyses to examine the consequences of model misspecification.     

Attention-deficit/hyperactivity disorder in a population isolate: linkage to loci at 4q13.2, 5q33.3, 11q22, and 17p11

Attention-deficit/hyperactivity disorder (ADHD [MIM 143465]) is the most common behavioral disorder of childhood. Twin, adoption, segregation, association, and linkage studies have confirmed that genetics plays a major role in conferring susceptibility to ADHD. We applied model-based and model-free linkage analyses, as well as the pedigree disequilibrium test, to the results of a genomewide scan of extended and multigenerational families with ADHD from a genetic isolate. In these families, ADHD is highly comorbid with conduct and oppositional defiant disorders, as well as with alcohol and tobacco dependence. We found evidence of linkage to markers at chromosomes 4q13.2, 5q33.3, 8q11.23, 11q22, and 17p11 in individual families. Fine mapping applied to these regions resulted in significant linkage in the combined families at chromosomes 4q13.2 (two-point allele-sharing LOD score from LODPAL = 4.44 at D4S3248), 5q33.3 (two-point allele-sharing LOD score from LODPAL = 8.22 at D5S490), 11q22 (two-point allele-sharing LOD score from LODPAL = 5.77 at D11S1998; multipoint nonparametric linkage [NPL]-log[P value] = 5.49 at approximately 128 cM), and 17p11 (multipoint NPL-log [P value] >12 at approximately 12 cM; multipoint maximum location score 2.48 [alpha = 0.10] at approximately 12 cM; two-point allele-sharing LOD score from LODPAL = 3.73 at D17S1159). Additionally, suggestive linkage was found at chromosome 8q11.23 (combined two-point NPL-log [P value] >3.0 at D8S2332). Several of these regions are novel (4q13.2, 5q33.3, and 8q11.23), whereas others replicate already-published loci (11q22 and 17p11). The concordance between results from different analytical methods of linkage and the replication of data between two independent studies suggest that these loci truly harbor ADHD susceptibility genes.     

The bias introduced by population stratification in IBD based linkage analysis

The lack of replication of model-free linkage analyses performed on complex diseases raises questions about the robustness of these methods to various biases. The confounding effect of population stratification on a genetic association study has long been recognized in the genetic epidemiology community. Because the estimation of the number of alleles shared identical by descent (IBD) does not depend on the marker allele frequency when founders of families are observed, model-free linkage analysis is usually thought to be robust to population stratification. However, for common complex diseases, the genotypes of founders are often unobserved and therefore population stratification has the potential to impair model-free linkage analysis. Here, we demonstrate that, when some or all of the founder genotypes are missing, population stratification can introduce deleterious effects on various model-free linkage methods or designs. For an affected sib pair design, it can cause excess false-positive discoveries even when the trait distribution is homogeneous among subpopulations. After incorporating a control group of discordant sib pairs or for a quantitative trait, two circumstances must be met for population stratification to be a confounder: the distributions for both the marker and the trait must be heterogeneous among subpopulations. When this occurs, the bias can result in either a liberal, and hence invalid, test or a conservative test. Bias can be eliminated or alleviated by inclusion of founders' or other family members' genotype data. When this is not possible, new methods need to be developed to be robust to population stratification.