Correcting for measurement error in individual-level covariates in nonlinear mixed effects models

The nonlinear mixed effects model is used to represent data in pharmacokinetics, viral dynamics, and other areas where an objective is to elucidate associations among individual-specific model parameters and covariates; however, covariates may be measured with error. For additive measurement error, we show substitution of mismeasured covariates for true covariates may lead to biased estimators for fixed effects and random effects covariance parameters, while regression calibration may eliminate bias in fixed effects but fail to correct that in covariance parameters. We develop methods to take account of measurement error that correct this bias and may be implemented with standard software, and we demonstrate their utility via simulation and application to data from a study of HIV dynamics.     

SIMEX variance component tests in generalized linear mixed measurement error models

In the analysis of clustered data with covariates measured with error, a problem of common interest is to test for correlation within clusters and heterogeneity across clusters. We examined this problem in the framework of generalized linear mixed measurement error models. We propose using the simulation extrapolation (SIMEX) method to construct a score test for the null hypothesis that all variance components are zero. A key feature of this SIMEX score test is that no assumptions need to be made regarding the distributions of the random effects and the unobserved covariates. We illustrate this test by analyzing Framingham heart disease data and evaluate its performance by simulation. We also propose individual SIMEX score tests for testing the variance components separately. Both tests can be easily implemented using existing statistical software.     

Incorporating individual error rate into association test of unmatched case-control design

OBJECTIVES: Genotyping error commonly occurs and could reduce the power and bias statistical inference in genetics studies. In addition to genotypes, some automated biotechnologies also provide quality measurement of each individual genotype. We studied the relationship between the quality measurement and genotyping error rate. Furthermore, we propose two association tests incorporating the genotyping quality information with the goal to improve statistical power and inference. METHODS: 50 pairs of DNA sample duplicates were typed for 232 SNPs by BeadArray technology. We used scatter plot, smoothing function and generalized additive models to investigate the relationship between genotype quality score (q) and inconsistency rate (?) among duplicates. We constructed two association tests: (1) weighted contingency table test (WCT) and (2) likelihood ratio test (LRT) to incorporate individual genotype error rate (epsilon(i)), in unmatched case-control setting. RESULTS: In the 50 duplicates, we found q and ? were in strong negative association, suggesting the genotypes with low quality score were more likely to be mistyped. The WCT improved the statistical power and partially corrects the bias in point estimation. The LRT offered moderate power gain, but was able to correct the bias in odds ratio estimation. The two new methods also performed favorably in some scenarios when epsilon(i) was mis-specified. CONCLUSIONS: With increasing number of genetic studies and application of automated genotyping technology, there is a growing need to adequately account for individual genotype error rate in statistical analysis. Our study represents an initial step to address this need and points out a promising direction for further research.     

Adjustment for local ancestry in genetic association analysis of admixed populations

MOTIVATION: Admixed populations offer a unique opportunity for mapping diseases that have large disease allele frequency differences between ancestral populations. However, association analysis in such populations is challenging because population stratification may lead to association with loci unlinked to the disease locus. Methods and results: We show that local ancestry at a test single nucleotide polymorphism (SNP) may confound with the association signal and ignoring it can lead to spurious association. We demonstrate theoretically that adjustment for local ancestry at the test SNP is sufficient to remove the spurious association regardless of the mechanism of population stratification, whether due to local or global ancestry differences among study subjects; however, global ancestry adjustment procedures may not be effective. We further develop two novel association tests that adjust for local ancestry. Our first test is based on a conditional likelihood framework which models the distribution of the test SNP given disease status and flanking marker genotypes. A key advantage of this test lies in its ability to incorporate different directions of association in the ancestral populations. Our second test, which is computationally simpler, is based on logistic regression, with adjustment for local ancestry proportion. We conducted extensive simulations and found that the Type I error rates of our tests are under control; however, the global adjustment procedures yielded inflated Type I error rates when stratification is due to local ancestry difference.     

Correcting biases in estimates of mortality attributable to obesity

Objective: To assess whether a recent study that found a relatively small number of excess deaths attributable to obesity may have underestimated by not correcting for statistical biases. Research Methods and Procedures: This prospective cohort study used data from the First National Health and Nutrition Examination Survey Epidemiologic Follow‐Up Study. Survival analyses were conducted using 9690 individuals 32 to 87 years of age and 1886 all‐cause deaths during a 9.1‐year follow‐up. Corrections were made for the reputed regression‐dilution bias by using the average BMI during the decade before follow‐up as predictor. Corrections for the reputed reverse‐causation bias were made by excluding participants with a history of serious illness. Attributable fractions were calculated and used to estimate excess deaths. Results: The uncorrected estimate of excess deaths attributable to obesity (BMI ≥30) was 41.9, using 18.5 to 25 kg/m² as ideal‐weight category. Using average BMI as predictor increased the estimate to 93.3. Correcting for reverse‐causation effects increased the estimate further to 131.1 (range, 93.3 to 169.0). The uncorrected hazard ratio, 1.25, was increased to 1.41 by using average BMI as predictor, and then to 2.40 by correcting for reverse causation. Using BMI 21 to 25 kg/m² and 23 to 25 kg/m² as ideal‐weight categories increased the corrected estimates to 144.6 (range, 80.5 to 177.2) and 164.1 (range, 103.8 to 194.9), respectively. Larger increases were found for overweight and Grade 2 to 4 obesity (BMI ≥35 kg/m²). For overweight, the uncorrected estimate using 18.5 to 25 kg/m² as ideal‐weight category was ?88.3 and the corrected estimate using 23 to 25 kg/m² as ideal‐weight category was 205.4 (range, 114.5 to 296.3). Discussion: Correcting for statistical biases and using higher ideal‐weight categories increased the estimate of excess deaths attributable to obesity by ～400% and changed the negative estimate for overweight to a large positive estimate.     

Family-based association tests for genomewide association scans

With millions of single-nucleotide polymorphisms (SNPs) identified and characterized, genomewide association studies have begun to identify susceptibility genes for complex traits and diseases. These studies involve the characterization and analysis of very-high-resolution SNP genotype data for hundreds or thousands of individuals. We describe a computationally efficient approach to testing association between SNPs and quantitative phenotypes, which can be applied to whole-genome association scans. In addition to observed genotypes, our approach allows estimation of missing genotypes, resulting in substantial increases in power when genotyping resources are limited. We estimate missing genotypes probabilistically using the Lander-Green or Elston-Stewart algorithms and combine high-resolution SNP genotypes for a subset of individuals in each pedigree with sparser marker data for the remaining individuals. We show that power is increased whenever phenotype information for ungenotyped individuals is included in analyses and that high-density genotyping of just three carefully selected individuals in a nuclear family can recover >90% of the information available if every individual were genotyped, for a fraction of the cost and experimental effort. To aid in study design, we evaluate the power of strategies that genotype different subsets of individuals in each pedigree and make recommendations about which individuals should be genotyped at a high density. To illustrate our method, we performed genomewide association analysis for 27 gene-expression phenotypes in 3-generation families (Centre d'Etude du Polymorphisme Humain pedigrees), in which genotypes for ~860,000 SNPs in 90 grandparents and parents are complemented by genotypes for ~6,700 SNPs in a total of 168 individuals. In addition to increasing the evidence of association at 15 previously identified cis-acting associated alleles, our genotype-inference algorithm allowed us to identify associated alleles at 4 cis-acting loci that were missed when analysis was restricted to individuals with the high-density SNP data. Our genotype-inference algorithm and the proposed association tests are implemented in software that is available for free.     

Matching strategies for genetic association studies in structured populations

Association studies in populations that are genetically heterogeneous can yield large numbers of spurious associations if population subgroups are unequally represented among cases and controls. This problem is particularly acute for studies involving pooled genotyping of very large numbers of single-nucleotide-polymorphism (SNP) markers, because most methods for analysis of association in structured populations require individual genotyping data. In this study, we present several strategies for matching case and control pools to have similar genetic compositions, based on ancestry information inferred from genotype data for approximately 300 SNPs tiled on an oligonucleotide-based genotyping array. We also discuss methods for measuring the impact of population stratification on an association study. Results for an admixed population and a phenotype strongly confounded with ancestry show that these simple matching strategies can effectively mitigate the impact of population stratification.     

Accounting for bias from sequencing error in population genetic estimates

Sequencing error presents a significant challenge to population genetic analyses using low-coverage sequence in general and single-pass reads in particular. Bias in parameter estimates becomes severe when the level of polymorphism (signal) is low relative to the amount of error (noise). Choosing an arbitrary quality score cutoff yields biased estimates, particularly with newer, non-Sanger sequencing technologies that have different quality score distributions. We propose a rule of thumb to judge when a given threshold will lead to significant bias and suggest alternative approaches that reduce bias.     

Correcting for measurement error in fractional polynomial models using Bayesian modelling and regression calibration,with an application to alcohol and mortality

Exposure measurement error can result in a biased estimate of the association between an exposure and outcome. When the exposure–outcome relationship is linear on the appropriate scale (e.g. linear, logistic) and the measurement error is classical, that is the result of random noise, the result is attenuation of the effect. When the relationship is non‐linear, measurement error distorts the true shape of the association. Regression calibration is a commonly used method for correcting for measurement error, in which each individual's unknown true exposure in the outcome regression model is replaced by its expectation conditional on the error‐prone measure and any fully measured covariates. Regression calibration is simple to execute when the exposure is untransformed in the linear predictor of the outcome regression model, but less straightforward when non‐linear transformations of the exposure are used. We describe a method for applying regression calibration in models in which a non‐linear association is modelled by transforming the exposure using a fractional polynomial model. It is shown that taking a Bayesian estimation approach is advantageous. By use of Markov chain Monte Carlo algorithms, one can sample from the distribution of the true exposure for each individual. Transformations of the sampled values can then be performed directly and used to find the expectation of the transformed exposure required for regression calibration. A simulation study shows that the proposed approach performs well. We apply the method to investigate the relationship between usual alcohol intake and subsequent all‐cause mortality using an error model that adjusts for the episodic nature of alcohol consumption.     

Discerning the ancestry of European Americans in genetic association studies

European Americans are often treated as a homogeneous group, but in fact form a structured population due to historical immigration of diverse source populations. Discerning the ancestry of European Americans genotyped in association studies is important in order to prevent false-positive or false-negative associations due to population stratification and to identify genetic variants whose contribution to disease risk differs across European ancestries. Here, we investigate empirical patterns of population structure in European Americans, analyzing 4,198 samples from four genome-wide association studies to show that components roughly corresponding to northwest European, southeast European, and Ashkenazi Jewish ancestry are the main sources of European American population structure. Building on this insight, we constructed a panel of 300 validated markers that are highly informative for distinguishing these ancestries. We demonstrate that this panel of markers can be used to correct for stratification in association studies that do not generate dense genotype data.     

Nonlinear tests for genomewide association studies

As millions of single-nucleotide polymorphisms (SNPs) have been identified and high-throughput genotyping technologies have been rapidly developed, large-scale genomewide association studies are soon within reach. However, since a genomewide association study involves a large number of SNPs it is therefore nearly impossible to ensure a genomewide significance level of 0.05 using the available statistics, although the multiple-test problems can be alleviated, but not sufficiently, by the use of tagging SNPs. One strategy to circumvent the multiple-test problem associated with genome-wide association tests is to develop novel test statistics with high power. In this report, we introduce several nonlinear tests, which are based on nonlinear transformation of allele or haplotype frequencies. We investigate the power of the nonlinear test statistics and demonstrate that under certain conditions, some nonlinear test statistics have much higher power than the standard chi2-test statistic. Type I error rates of the nonlinear tests are validated using simulation studies. We also show that a class of similarity measure-based test statistics is based on the quadratic function of allele or haplotype frequencies, and thus they belong to nonlinear tests. To evaluate their performance, the nonlinear test statistics are also applied to three real data sets. Our study shows that nonlinear test statistics have great potential in association studies of complex diseases.     

Using measurement error models to account for georeferencing error in species distribution models

Georeferencing error is prevalent in datasets used to model species distributions, inducing uncertainty in covariate values associated with species occurrences that result in biased probability of occurrence estimates. Traditionally, this error has been dealt with at the data‐level by using only records with an acceptable level of error (filtering) or by summarizing covariates at sampling units by using measures of central tendency (averaging). Here we compare those previous approaches to a novel implementation of a Bayesian logistic regression with measurement error (ME), a seldom used method in species distribution modeling. We show that the ME model outperforms data‐level approaches on 1) specialist species and 2) when either sample sizes are small, the georeferencing error is large or when all georeferenced occurrences have a fixed level of error. Thus, for certain types of species and datasets the ME model is an effective method to reduce biases in probability of occurrence estimates and account for the uncertainty generated by georeferencing error. Our approach may be expanded for its use with presence‐only data as well as to include other sources of uncertainty in species distribution models.     

Use of weighted reference panels based on empirical estimates of ancestry for capturing untyped variation

Many association methods use a subset of genotyped single nucleotide polymorphisms (SNPs) to capture or infer genotypes at other untyped SNPs. We and others previously showed that tag SNPs selected to capture common variation using data from The International HapMap Consortium (Nature 437:1299–1320, 2005), The International HapMap Consortium (Nature 449:851–861, 2007) could also capture variation in populations of similar ancestry to HapMap reference populations (de Bakker et al. in Nat Genet 38:1298–1303, 2006; González-Neira et al. in Genome Res 16:323–330, 2006; Montpetit et al. in PLoS Genet 2:282–290, 2006; Mueller et al. in Am J Hum Genet 76:387–398, 2005). To capture variation in admixed populations or populations less similar to HapMap panels, a “cosmopolitan approach,” in which all samples from HapMap are used as a single reference panel, was proposed. Here we refine this suggestion and show that use of a “weighted reference panel,” constructed based on empirical estimates of ancestry in the target population (relative to available reference panels), is more efficient than the cosmopolitan approach. Weighted reference panels capture, on average, only slightly fewer common variants (minor allele frequency > 5%) than the cosmopolitan approach (mean r ² = 0.977 vs. 0.989, 94.5% variation captured vs. 96.8% at r ² > 0.8), across the five populations of the Multiethnic Cohort, but entail approximately 25% fewer tag SNPs per panel (average 538 vs. 718). These results extend a recent study in two Indian populations (Pemberton et al. in Ann Hum Genet 72:535–546, 2008). Weighted reference panels are potentially useful for both the selection of tag SNPs in diverse populations and perhaps in the design of reference panels for imputation of untyped genotypes in genome-wide association studies in admixed populations. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.