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1.  The impact of complex informative missingness on the validity of the transmission/disequilibrium test (TDT) 
BMC Proceedings  2007;1(Suppl 1):S26.
The transmission/disequilibrium test was introduced to test for linkage and association between a marker and a putative disease locus using case-parent triads. Several extensions have been proposed to accommodate incomplete triads. Some strategies assumed that parental genotypes were missing completely at random and some methods allowed informative missingness for parental genotypes. However, the above tests assumed that offspring genotypes were missing completely at random and concluded that the transmission/disequilibrium test remained a valid test by excluding incomplete triads from the analysis. In this article, the conditional distribution of ascertained triads allowing informative missingness for offspring genotypes, as well as their parental genotypes, was derived and several tests under such scenarios were evaluated. In simulations, independent triads from the Genetic Analysis Workshop 15 simulated data (Problem 3) was ascertained. When offspring genotypes were missing informatively, simulation results revealed inflated type I error and/or reduced power for the transmission/disequilibrium test excluding incomplete triads.
PMCID: PMC2367473  PMID: 18466523
2.  A hybrid design: case-parent triads supplemented by control-mother dyads 
Genetic epidemiology  2009;33(2):136.
Hybrid designs arose from an effort to combine the benefits of family-based and population-based study designs. A recently proposed hybrid approach augments case-parent triads with population-based control-parent triads, genotyping everyone except the control offspring. Including parents of controls substantially improves statistical efficiency for testing and estimating both offspring and maternal genetic relative risk parameters relative to using case-parent triads alone. Moreover, it allows testing of required assumptions. Nevertheless, control fathers can be hard to recruit, whereas control offspring and their mothers may be readily available. Consequently, we propose an alternative hybrid design where offspring-mother pairs, instead of parents, serve as population-based controls. We compare the power of our proposed method with several competitors and show that it performs well in various scenarios, though it is slightly less powerful than the hybrid design that uses control parents. We describe approaches for checking whether population stratification will bias inferences that use controls and whether the mating symmetry assumption holds. Surprisingly, if mating symmetry is violated, even though mating-type parameters cannot be directly estimated using control-mother dyads alone, and maternal effects cannot be estimated using case-parent triads alone, combining both sources of data allows estimation of all the parameters. This hybrid design can also be used to study environmental influences on disease risk and gene-by-environment interactions.
PMCID: PMC2819841  PMID: 18759250
genetic relative risk; maternal effect; Single Nucleotide Polymorphism (SNP); association studies; family-based design; population-based design; Poisson regression; early-onset disease
3.  The null distribution of likelihood-ratio statistics in the conditional-logistic linkage model 
Frontiers in Genetics  2013;4:244.
Olson's conditional-logistic model retains the nice property of the LOD score formulation and has advantages over other methods that make it an appropriate choice for complex trait linkage mapping. However, the asymptotic distribution of the conditional-logistic likelihood-ratio (CL-LR) statistic with genetic constraints on the model parameters is unknown for some analysis models, even in the case of samples comprising only independent sib pairs. We derive approximations to the asymptotic null distributions of the CL-LR statistics and compare them with the empirical null distributions by simulation using independent affected sib pairs. Generally, the empirical null distributions of the CL-LR statistics match well the known or approximated asymptotic distributions for all analysis models considered except for the covariate model with a minimum-adjusted binary covariate. This work will provide useful guidelines for linkage analysis of real data sets for the genetic analysis of complex traits, thereby contributing to the identification of genes for disease traits.
PMCID: PMC3832807  PMID: 24312121
linkage analysis; affected sib pairs; identity-by-descent; conditional-logistic model; genetic constraints; null distribution; likelihood-ratio statistics
4.  Genetic Determinants of Facial Clefting: Analysis of 357 Candidate Genes Using Two National Cleft Studies from Scandinavia 
PLoS ONE  2009;4(4):e5385.
Facial clefts are common birth defects with a strong genetic component. To identify fetal genetic risk factors for clefting, 1536 SNPs in 357 candidate genes were genotyped in two population-based samples from Scandinavia (Norway: 562 case-parent and 592 control-parent triads; Denmark: 235 case-parent triads).
Methodology/Principal Findings
We used two complementary statistical methods, TRIMM and HAPLIN, to look for associations across these two national samples. TRIMM tests for association in each gene by using multi-SNP genotypes from case-parent triads directly without the need to infer haplotypes. HAPLIN on the other hand estimates the full haplotype distribution over a set of SNPs and estimates relative risks associated with each haplotype. For isolated cleft lip with or without cleft palate (I-CL/P), TRIMM and HAPLIN both identified significant associations with IRF6 and ADH1C in both populations, but only HAPLIN found an association with FGF12. For isolated cleft palate (I-CP), TRIMM found associations with ALX3, MKX, and PDGFC in both populations, but only the association with PDGFC was identified by HAPLIN. In addition, HAPLIN identified an association with ETV5 that was not detected by TRIMM.
Strong associations with seven genes were replicated in the Scandinavian samples and our approach effectively replicated the strongest previously known association in clefting—with IRF6. Based on two national cleft cohorts of similar ancestry, two robust statistical methods and a large panel of SNPs in the most promising cleft candidate genes to date, this study identified a previously unknown association with clefting for ADH1C and provides additional candidates and analytic approaches to advance the field.
PMCID: PMC2671138  PMID: 19401770
5.  Calculating Asymptotic Significance Levels of the Constrained Likelihood Ratio Test with Application to Multivariate Genetic Linkage Analysis 
The asymptotic distribution of the multivariate variance component linkage analysis likelihood ratio test has provoked some contradictory accounts in the literature. In this paper we confirm that some previous results are not correct by deriving the asymptotic distribution in one special case. It is shown that this special case is a good approximation to the distribution in many situations. We also introduce a new approach to simulating from the asymptotic distribution of the likelihood ratio test statistic in constrained testing problems. It is shown that this method is very efficient for small p-values, and is applicable even when the constraints are not convex. The method is related to a multivariate integration problem. We illustrate how the approach can be applied to multivariate linkage analysis in a simulation study. Some more philosophical issues relating to one-sided tests in variance components linkage analysis are discussed.
PMCID: PMC2861321  PMID: 19799558
6.  Association analysis of complex diseases using triads, parent-child dyads and singleton monads 
BMC Genetics  2013;14:78.
Triad families are routinely used to test association between genetic variants and complex diseases. Triad studies are important and popular since they are robust in terms of being less prone to false positives due to population structure. In practice, one may collect not only complete triads, but also incomplete families such as dyads (affected child with one parent) and singleton monads (affected child without parents). Since there is a lack of convenient algorithms and software to analyze the incomplete data, dyads and monads are usually discarded. This may lead to loss of power and insufficient utilization of genetic information in a study.
We develop likelihood-based statistical models and likelihood ratio tests to test for association between complex diseases and genetic markers by using combinations of full triads, parent-child dyads, and affected singleton monads for a unified analysis. A likelihood is calculated directly to facilitate the data analysis without imputation and to avoid computational complexity. This makes it easy to implement the models and to explain the results.
By simulation studies, we show that the proposed models and tests are very robust in terms of accurately controlling type I error evaluations, and are powerful by empirical power evaluations. The methods are applied to test for association between transforming growth factor alpha (TGFA) gene and cleft palate in an Irish study.
PMCID: PMC3844511  PMID: 24007308
Association mapping of complex diseases; Likelihood ratio tests; Transmission disequilibrium tests
7.  Application of a novel hybrid study design to explore gene-environment interactions in orofacial clefts 
Annals of Human Genetics  2012;76(3):221-236.
Orofacial clefts are common birth defects with strong evidence for both genetic and environmental causal factors. Candidate-gene studies combined with exposures known to influence the outcome provide a highly targeted approach to detecting GxE interactions. We developed a new statistical approach that combines the case-control and offspring-parent triad designs into a “hybrid design” to search for GxE interactions among 334 autosomal cleft candidate genes and maternal first-trimester exposure to smoking, alcohol, coffee, folic acid supplements, dietary folate, and vitamin A. The study population comprised 425 case-parent triads of isolated clefts and 562 control-parent triads derived from a nationwide study of orofacial clefts in Norway (1996-2001). A full maximum-likelihood model was used in combination with a Wald test statistic to screen for statistically significant GxE interaction between strata of exposed and unexposed mothers. In addition, we performed pathway-based analyses on 28 detoxification genes and 21 genes involved in folic acid metabolism. With the possible exception of the T-box 4 gene (TBX4) and dietary folate interaction in isolated CPO, there was little evidence overall of GxE interaction in our data. This study is the largest to date aimed at detecting interactions between orofacial clefts candidate genes and well-established risk exposures.
PMCID: PMC3334353  PMID: 22497478
Birth defects; orofacial cleft; cleft lip; cleft palate; genetic epidemiology
8.  A New Method to Account for Missing Data in Case-Parent Triad Studies 
Human Heredity  2009;68(4):268-277.
The case-parent triad design is commonly used in genetic association studies. Generally, samples are drawn from an affected offspring, manifesting a phenotype of interest, as well as from the parents. The trio genotypes may be analyzed using a variety of available methods, but we focus on log-linear models because they test for genetic association and additionally estimate the relative risks of transmission. The models need to be modified to adjust for missing genotypes. Furthermore, instability in the parameter estimates can arise when certain kinds of genotype combinations do not appear in the dataset.
In this paper, we kill two birds with one stone. We propose a new method to simultaneously account for missing genotype data and genotype combinations with zero counts. This method solves a zero-inflated Poisson (ZIP) regression likelihood. The maximum likelihood estimates yield relative risks and the information matrix gives appropriate variance estimates for inference. A likelihood ratio test determines the significance of genetic association.
We compared the ZIP regression to previously proposed methods in both simulation studies and in a dataset that investigates the risk of orofacial clefts. The ZIP likelihood estimates regression coefficients with less bias than other methods when the minor allele frequency is small.
PMCID: PMC2943516  PMID: 19622893
Log-linear models; Case-parent triad design; Missing data
9.  Power calculations for likelihood ratio tests for offspring genotype risks, maternal effects and parent-of-origin (POO) effects in the presence of missing parental genotypes when unaffected siblings are available 
Genetic epidemiology  2007;31(1):18-30.
Genotype-based likelihood ratio tests (LRT) of association that examine maternal and parent-of-origin effects have been previously developed in the framework of log-linear and conditional logistic regression models. In the situation where parental genotypes are missing, the expectation maximization (EM) algorithm has been incorporated in the log-linear approach to allow incomplete triads to contribute to the likelihood ratio test. We present an extension to this model which we call the Combined_LRT that incorporates additional information from the genotypes of unaffected siblings to improve assignment of incompletely typed families to mating type categories, thereby improving inference of missing parental data. Using simulations involving a realistic array of family structures, we demonstrate the validity of the Combined_LRT under the null hypothesis of no association and provide power comparisons under varying levels of missing data and using sibling genotype data. We demonstrate the improved power of the Combined_LRT compared with the family-based association test (FBAT), another widely used association test. Lastly, we apply the Combined_LRT to a candidate gene analysis in Autism families, some of which have missing parental genotypes. We conclude that the proposed log-linear model will be an important tool for future candidate gene studies, for many complex diseases where unaffected siblings can often be ascertained and where epigenetic factors such as imprinting may play a role in disease etiology.
PMCID: PMC2118060  PMID: 17096358
family-based association; candidate gene tests; imprinting; parent-of-origin; maternal effects
10.  A Likelihood Model That Accounts for Censoring Due to Fetal Loss Can Accurately Test the Effects of Maternal and Fetal Genotype on the Probability of Miscarriage 
Human heredity  2008;67(1):57-65.
Heritable maternal and fetal thrombophilia and/or hypofibrinolysis are important causes of miscarriage. Under the constraint that fetal genotype is observed only after a live birth, estimating risk is complicated. Censoring prevents use of published statistical methodology. We propose techniques to determine whether increases in miscarriage are due to the fetal genotype, maternal genotype, or both.
We propose a study to estimate the risk of miscarriage contributed by an allele, expressed in either dominant or recessive fashion. Using a multinomial likelihood, we derive maximum likelihood estimates of risk for different genotype groups. We describe likelihood ratio tests and a planned hypothesis testing strategy.
Parameter estimation is accurate (bias < 0.0011, root mean squared error <0.0780, n = 500). We used simulation to estimate power for studies of three gene mutations: the 4G hypofibrinolytic mutation in the plasminogen activator inhibitor gene (PAI-1), the prothrombin G20210A mutation, and the Factor V Leiden mutation. With 500 families, our methods have approximately 90% power to detect an increase in the miscarriage rate of 0.2, above a background rate of 0.2.
Our statistical method can determine whether increases in miscarriage are due to fetal genotype, maternal genotype, or both despite censoring.
PMCID: PMC2755496  PMID: 18931510
PAI-1; Pregnancy loss; Thrombophilia; Hypofibrinolysis; Genetics
11.  A Likelihood Model That Accounts for Censoring Due to Fetal Loss Can Accurately Test the Effects of Maternal and Fetal Genotype on the Probability of Miscarriage 
Human Heredity  2008;67(1):57-65.
Heritable maternal and fetal thrombophilia and/or hypofibrinolysis are important causes of miscarriage. Under the constraint that fetal genotype is observed only after a live birth, estimating risk is complicated. Censoring prevents use of published statistical methodology. We propose techniques to determine whether increases in miscarriage are due to the fetal genotype, maternal genotype, or both.
We propose a study to estimate the risk of miscarriage contributed by an allele, expressed in either dominant or recessive fashion. Using a multinomial likelihood, we derive maximum likelihood estimates of risk for different genotype groups. We describe likelihood ratio tests and a planned hypothesis testing strategy.
Parameter estimation is accurate (bias <0.0011, root mean squared error <0.0780, n = 500). We used simulation to estimate power for studies of three gene mutations: the 4G hypofibrinolytic mutation in the plasminogen activator inhibitor gene (PAI-1), the prothrombin G20210A mutation, and the Factor V Leiden mutation. With 500 families, our methods have approximately 90% power to detect an increase in the miscarriage rate of 0.2, above a background rate of 0.2.
Our statistical method can determine whether increases in miscarriage are due to fetal genotype, maternal genotype, or both despite censoring.
PMCID: PMC2755496  PMID: 18931510
PAI-1; Pregnancy loss; Thrombophilia; Hypofibrinolysis; Genetics
12.  A transmission disequilibrium test for general pedigrees that is robust to the presence of random genotyping errors and any number of untyped parents 
Two issues regarding the robustness of the original transmission disequilibrium test (TDT) developed by Spielman et al are: (i) missing parental genotype data and (ii) the presence of undetected genotype errors. While extensions of the TDT that are robust to items (i) and (ii) have been developed, there is to date no single TDT statistic that is robust to both for general pedigrees. We present here a likelihood method, the TDTae, which is robust to these issues in general pedigrees. The TDTae assumes a more general disease model than the traditional TDT, which assumes a multiplicative inheritance model for genotypic relative risk. Our model is based on Weinberg’s work. To assess robustness, we perform simulations. Also, we apply our method to two data sets from actual diseases: psoriasis and sitosterolemia. Maximization under alternative and null hypotheses is performed using Powell’s method. Results of our simulations indicate that our method maintains correct type I error rates at the 1, 5, and 10% levels of significance. Furthermore, a Kolmorogov–Smirnoff Goodness of Fit test suggests that the data are drawn from a central χ2 with 2 df, the correct asymptotic null distribution. The psoriasis results suggest two loci as being significantly linked to the disease, even in the presence of genotyping errors and missing data, and the sitosterolemia results show a P-value of 1.5 × 10−9 for the marker locus nearest to the sitosterolemia disease genes. We have developed software to perform TDTae calculations, which may be accessed from our ftp site.
PMCID: PMC1356564  PMID: 15162128
Keywords: misclassification; genetics; statistics
13.  Candidate gene analysis of spontaneous preterm delivery: New insights from re-analysis of a case-control study using case-parent triads and control-mother dyads 
BMC Medical Genetics  2011;12:174.
Spontaneous preterm delivery (PTD) has a multifactorial etiology with evidence of a genetic contribution to its pathogenesis. A number of candidate gene case-control studies have been performed on spontaneous PTD, but the results have been inconsistent, and do not fully assess the role of how two genotypes can impact outcome. To elucidate this latter point we re-analyzed data from a previously published case-control candidate gene study, using a case-parent triad design and a hybrid design combining case-parent triads and control-mother dyads. These methods offer a robust approach to genetic association studies for PTD compared to traditional case-control designs.
The study participants were obtained from the Norwegian Mother and Child Cohort Study (MoBa). A total of 196 case triads and 211 control dyads were selected for the analysis. A case-parent triad design as well as a hybrid design was used to analyze 1,326 SNPs from 159 candidate genes. We compared our results to those from a previous case-control study on the same samples. Haplotypes were analyzed using a sliding window of three SNPs and a pathway analysis was performed to gain biological insight into the pathophysiology of preterm delivery.
The most consistent significant fetal gene across all analyses was COL5A2. The functionally similar COL5A1 was significant when combining fetal and maternal genotypes. PON1 was significant with analytical approaches for single locus association of fetal genes alone, but was possibly confounded by maternal effects. Focal adhesion (hsa04510), Cell Communication (hsa01430) and ECM receptor interaction (hsa04512) were the most constant significant pathways.
This study suggests a fetal association of COL5A2 and a combined fetal-maternal association of COL5A1 with spontaneous PTD. In addition, the pathway analysis implied interactions of genes affecting cell communication and extracellular matrix.
PMCID: PMC3260094  PMID: 22208904
case-parent triad analysis; hybrid design; haplotype; pathway analysis; COL5A2; COL5A1
14.  Detection of imprinting and heterogeneous maternal effects on high blood pressure using Framingham Heart Study data 
BMC Proceedings  2009;3(Suppl 7):S125.
Both imprinting and maternal effects could lead to parent-of-origin patterns in complex traits of human disorders. Statistical methods that differentiate these two effects and identify them simultaneously by using family-based data from retrospective studies are available. The usual data structures include case-parents triads and nuclear families with multiple affected siblings. We develop a likelihood-based method to detect imprinting and maternal effects simultaneously using data from prospective studies. The proposed method utilizes both affected and unaffected siblings in nuclear families by modeling familial genotypes and offspring's disease status jointly. Maternal effect is usually modeled as a fixed effect under the assumption that maternal variant allele(s) has (have) identical effect on any offspring. However, recent studies report that different people may carry different amounts of substances encoded by the mother's variant allele(s) (called maternal microchimerism), which could result in heterogeneity of maternal effects. The proposed method incorporates the heterogeneity of maternal effects by adding a random component to the logit of the penetrance. Our method was applied to the Framingham Heart Study data in two steps to detect single-nucleotide polymorphisms (SNPs) that may be associated with high blood pressure. In the first step, SNPs that affect susceptibility of high blood pressure through minor allele, genomic imprinting, or maternal effects were identified by using the proposed model without the random effect component. In the second step, we fitted the mixed effect model to the identified SNPs that have significant maternal effect to detect heterogeneity of the maternal effects.
PMCID: PMC2795898  PMID: 20017991
15.  Genome wide study of maternal and parent-of-origin effects on the etiology of orofacial clefts 
We performed a genome wide association analysis of maternally-mediated genetic effects and parent-of-origin effects on risk of orofacial clefting using over 2,000 case-parent triads collected through an international cleft consortium. We used log-linear regression models to test individual SNPs. For SNPs with a p-value <10−5 for maternal genotypic effects, we also applied a haplotype-based method, TRIMM, to extract potential information from clusters of correlated SNPs. None of the SNPs were significant at the genome wide level. Our results suggest neither maternal genome nor parent of origin effects play major roles in the etiology of orofacial clefting in our sample. This finding is consistent with previous genetic studies and recent population-based cohort studies in Norway and Denmark, which showed no apparent difference between mother-to-offspring and father-to-offspring recurrence of clefting. We, however, cannot completely rule out maternal genome or parent of origin effects as risk factors because very small effects might not be detectable with our sample size, they may influence risk through interactions with environmental exposures or may act through a more complex network of interacting genes. Thus the most promising SNPs identified by this study may still be worth further investigation.
PMCID: PMC3617127  PMID: 22419666
GWAS; CL/P; CP; maternal genes; parent-of-origin; family-based study; association study
16.  Collapsing SNP Genotypes in Case-Control Genome-Wide Association Studies Increases the Type I Error Rate and Power* 
Genome-wide association studies are now widely used tools to identify genes and/or regions which may contribute to the development of various diseases. With case-control data a 2×3 contingency table can be constructed for each SNP to perform genotype-based tests of association. An increasingly common technique to increase the power to detect an association is to collapse each 2×3 table into a table assuming either a dominant or recessive mode of inheritance (2×2 table). We consider three different methods of determining which genetic model to choose and show that each of these methods of collapsing genotypes increases the type I error rate (i.e., the rate of false positives). However, one of these methods does lead to an increase in power compared with the usual genotype- and allele-based tests for most genetic models.
PMCID: PMC2789285  PMID: 18673292
genome-wide association; type I error rate
17.  Rapid Testing of SNPs and Gene–Environment Interactions in Case–Parent Trio Data Based on Exact Analytic Parameter Estimation 
Biometrics  2011;68(3):766-773.
Case–parent trio studies concerned with children affected by a disease and their parents aim to detect single nucleotide polymorphisms (SNPs) showing a preferential transmission of alleles from the parents to their affected offspring. A popular statistical test for detecting such SNPs associated with disease in this study design is the genotypic transmission/disequilibrium test (gTDT) based on a conditional logistic regression model, which usually needs to be fitted by an iterative procedure. In this article, we derive exact closed-form solutions for the parameter estimates of the conditional logistic regression models when testing for an additive, a dominant, or a recessive effect of a SNP, and show that such analytic parameter estimates also exist when considering gene–environment interactions with binary environmental variables. Because the genetic model underlying the association between a SNP and a disease is typically unknown, it might further be beneficial to use the maximum over the gTDT statistics for the possible effects of a SNP as test statistic. We therefore propose a procedure enabling a fast computation of the test statistic and the permutation-based p-value of this MAX gTDT. All these methods are applied to whole-genome scans of the case–parent trios from the International Cleft Consortium. These applications show our procedures dramatically reduce the required computing time compared to the conventional iterative methods allowing, for example, the analysis of hundreds of thousands of SNPs in a few minutes instead of several hours.
PMCID: PMC3387527  PMID: 22150644
Conditional logistic regression; Family-based design; Genome-wide association studies; Genotypic transmission/disequilibrium test; International Cleft Consortium; MAX test
18.  Reconsidering the asymptotic null distribution of likelihood ratio tests for genetic linkage in multivariate variance components models under complete pleiotropy 
Biostatistics (Oxford, England)  2009;11(2):226-241.
Accurate knowledge of the null distribution of hypothesis tests is important for valid application of the tests. In previous papers and software, the asymptotic null distribution of likelihood ratio tests for detecting genetic linkage in multivariate variance components models has been stated to be a mixture of chi-square distributions with binomial mixing probabilities. For variance components models under the complete pleiotropy assumption, we show by simulation and by theoretical arguments based on the geometry of the parameter space that all aspects of the previously stated asymptotic null distribution are incorrect—both the binomial mixing probabilities and the chi-square components. Correcting the null distribution gives more conservative critical values than previously stated, yielding P values that can easily be 10 times larger. The true mixing probabilities give the highest probability to the case where all variance parameters are estimated positive, and the mixing components show severe departures from chi-square distributions. Thus, the asymptotic null distribution has complex features that raise challenges for the assessment of significance of multivariate linkage findings. We propose a method to generate an asymptotic null distribution that is much faster than other empirical methods such as permutation, enabling us to obtain P values with higher precision more efficiently.
PMCID: PMC2830577  PMID: 20029057
Asymptotic null distribution; Likelihood ratio test; Mixing probabilities; Multivariate linkage; Nonstandard boundary condition; Single-factor model; Variance components
19.  Natural and Orthogonal Interaction framework for modeling gene-environment interactions with application to lung cancer 
Human heredity  2012;73(4):185-194.
We aimed at extending the natural and orthogonal interaction (NOIA) framework, developed for modeling gene-gene interactions in the analysis of quantitative traits, to allow for reduced genetic models, dichotomous traits, and gene-environment interactions. We evaluate the performance of the NOIA statistical models using simulated data and lung cancer data.
The NOIA statistical models are developed for the additive, dominant, recessive genetic models, and a binary environmental exposure. Using the Kronecker product rule, a NOIA statistical model is built to model gene-environment interactions. By treating the genotypic values as the logarithm of odds, the NOIA statistical models are extended to the analysis of case-control data.
Our simulations showed that power for testing associations while allowing for interaction using the statistical model is much higher than using functional models for most of the scenarios we simulated. When applied to the lung cancer data, much smaller P-values were obtained using the NOIA statistical model for either the main effects or the SNP-smoking interactions for some of the SNPs tested.
The NOIA statistical models are usually more powerful than the functional models in detecting main effects and interaction effects for both quantitative traits and binary traits.
PMCID: PMC3534768  PMID: 22889990
Statistical power; Genetic association studies; Case-control association analysis; Gene-environment interaction; Environmental risk factor; Association mapping; Orthogonal modeling
20.  Permutation Tests for Random Effects in Linear Mixed Models 
Biometrics  2011;68(2):10.1111/j.1541-0420.2011.01675.x.
Inference regarding the inclusion or exclusion of random effects in linear mixed models is challenging because the variance components are located on the boundary of their parameter space under the usual null hypothesis. As a result, the asymptotic null distribution of the Wald, score, and likelihood ratio tests will not have the typical χ2 distribution. Although it has been proved that the correct asymptotic distribution is a mixture of χ2 distributions, the appropriate mixture distribution is rather cumbersome and nonintuitive when the null and alternative hypotheses differ by more than one random effect. As alternatives, we present two permutation tests, one that is based on the best linear unbiased predictors and one that is based on the restricted likelihood ratio test statistic. Both methods involve weighted residuals, with the weights determined by the among- and within-subject variance components. The null permutation distributions of our statistics are computed by permuting the residuals both within and among subjects and are valid both asymptotically and in small samples. We examine the size and power of our tests via simulation under a variety of settings and apply our test to a published data set of chronic myelogenous leukemia patients.
PMCID: PMC3883440  PMID: 21950470
Hypothesis testing; Longitudinal data; Variance components
21.  Detecting parent of origin and dominant QTL in a two-generation commercial poultry pedigree using variance component methodology 
Variance component QTL methodology was used to analyse three candidate regions on chicken chromosomes 1, 4 and 5 for dominant and parent-of-origin QTL effects. Data were available for bodyweight and conformation score measured at 40 days from a two-generation commercial broiler dam line. One hundred dams were nested in 46 sires with phenotypes and genotypes on 2708 offspring. Linear models were constructed to simultaneously estimate fixed, polygenic and QTL effects. Different genetic models were compared using likelihood ratio test statistics derived from the comparison of full with reduced or null models. Empirical thresholds were derived by permutation analysis.
Dominant QTL were found for bodyweight on chicken chromosome 4 and for bodyweight and conformation score on chicken chromosome 5. Suggestive evidence for a maternally expressed QTL for bodyweight and conformation score was found on chromosome 1 in a region corresponding to orthologous imprinted regions in the human and mouse.
Initial results suggest that variance component analysis can be applied within commercial populations for the direct detection of segregating dominant and parent of origin effects.
PMCID: PMC2637028  PMID: 19284678
22.  Induced smoothing for the semiparametric accelerated failure time model: asymptotics and extensions to clustered data 
Biometrika  2009;96(3):577-590.
This paper extends the induced smoothing procedure of Brown & Wang (2006) for the semiparametric accelerated failure time model to the case of clustered failure time data. The resulting procedure permits fast and accurate computation of regression parameter estimates and standard errors using simple and widely available numerical methods, such as the Newton–Raphson algorithm. The regression parameter estimates are shown to be strongly consistent and asymptotically normal; in addition, we prove that the asymptotic distribution of the smoothed estimator coincides with that obtained without the use of smoothing. This establishes a key claim of Brown & Wang (2006) for the case of independent failure time data and also extends such results to the case of clustered data. Simulation results show that these smoothed estimates perform as well as those obtained using the best available methods at a fraction of the computational cost.
PMCID: PMC3412573  PMID: 23049117
Censoring; Convex optimization; Multivariate survival data; Rank regression
23.  Using Imputed Genotypes for Relative Risk Estimation in Case-Parent Studies 
American Journal of Epidemiology  2011;173(5):553-559.
Meta-analyses of genome-wide association studies are often based on imputed single nucleotide polymorphism (SNP) data, because component studies were genotyped using different platforms. One would like to include case-parent triad studies along with case-control studies in such meta-analyses. However, there are no published methods for estimating relative risks from imputed data for case-parent triad studies. The authors propose a method for estimating the relative risk for a variant SNP allele based on a log-additive model. Their simulations first confirm that the proposed method performs well with genotyped SNP data. As an empirical test of the method's behavior with imputed SNPs, the authors then apply it to chromosome 22 data from the Mexico City Childhood Asthma Study (1998–2003). For chromosome 22, the authors had data on 7,293 SNPs that were both genotyped and imputed using the software MACH, which relies on linkage disequilibrium with nearby SNPs. Correlation between estimated relative risks based on the actual genotypes and those based on the imputed genotypes was remarkably high (r2 = 0.95), validating this method of relative risk estimation for the case-parent study design. This method should be useful to investigators who wish to conduct meta-analyses using imputed SNP data from both case-parent triad and case-control studies.
PMCID: PMC3291117  PMID: 21296892
epidemiologic methods; genome-wide association study; genotype; imputation; meta-analysis; risk
24.  Deprivation and bronchiolitis. 
OBJECTIVE: To test the hypothesis that socioeconomic deprivation is associated with an increased risk of admission with clinically suspected bronchiolitis. DESIGN: Case-control study. SETTING: Children under 1 year living in Sheffield in 1989-90. SUBJECTS: 307 children resident in Sheffield admitted to Sheffield hospitals with clinically suspected bronchiolitis between 1 October 1989 and 28 February 1990. METHODS: Children admitted with clinically suspected bronchiolitis were ascertained from laboratory records of nasopharyngeal aspirates cultured for respiratory syncytial virus. Case notes were examined to determine whether these children had required medical intervention and postcode of residence was recorded. Controls were selected from the Sheffield child development study (SCDS) data. Postcodes were converted to electoral wards which were assigned Townsend deprivation index scores. Electoral wards were then categorised by Townsend score into five levels of deprivation. Data on family smoking for cases and controls were extracted from the SCDS. RESULTS: Of the 307 children admitted with suspected bronchiolitis during the study period, 127 required one or more medical intervention. The risk of admission with clinically suspected bronchiolitis and with bronchiolitis requiring medical intervention rose with increasing level of deprivation score of electoral ward of residence. Children living in electoral wards in the two more deprived groups were more than 1.5 times as likely to be admitted (odds ratio (OR) 1.67, 95% confidence interval (CI) 1.25 to 2.24) or admitted requiring a medical intervention (OR 1.74, 95% CI 1.16 to 2.62) than children living in other parts of the city. Similar results were obtained after exclusion of children living in homes classified as smoky by the health visitor. CONCLUSION: Residence in an area of social and material deprivation increases the risk of admission with bronchiolitis even after taking account of parental smoking and when only more severe cases were considered.
PMCID: PMC1511601  PMID: 8660048
25.  Detection of Fetomaternal Genotype Associations in Early-Onset Disorders: Evaluation of Different Methods and Their Application to Childhood Leukemia 
Several designs and analytical approaches have been proposed to dissect offspring from maternal genetic contributions to early-onset diseases. However, lack of parental controls halts the direct verification of the assumption of mating symmetry (MS) required to assess maternally-mediated effects. In this study, we used simulations to investigate the performance of existing methods under mating asymmetry (MA) when parents of controls are missing. Our results show that the log-linear, likelihood-based framework using a case-triad/case-control hybrid design provides valid tests for maternal genetic effects even under MA. Using this approach, we examined fetomaternal associations between 29 SNPs in 12 cell-cycle genes and childhood pre-B acute lymphoblastic leukemia (ALL). We identified putative fetomaternal effects at loci CDKN2A rs36228834 (P = .017) and CDKN2B rs36229158 (P = .022) that modulate the risk of childhood ALL. These data further corroborate the importance of the mother's genotype on the susceptibility to early-onset diseases.
PMCID: PMC2896672  PMID: 20617153

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