SNP Set Association Analysis for Familial Data

Genome‐wide association studies (GWAS) are a popular approach for identifying common genetic variants and epistatic effects associated with a disease phenotype. The traditional statistical analysis of such GWAS attempts to assess the association between each individual single‐nucleotide polymorphism (SNP) and the observed phenotype. Recently, kernel machine‐based tests for association between a SNP set (e.g., SNPs in a gene) and the disease phenotype have been proposed as a useful alternative to the traditional individual‐SNP approach, and allow for flexible modeling of the potentially complicated joint SNP effects in a SNP set while adjusting for covariates. We extend the kernel machine framework to accommodate related subjects from multiple independent families, and provide a score‐based variance component test for assessing the association of a given SNP set with a continuous phenotype, while adjusting for additional covariates and accounting for within‐family correlation. We illustrate the proposed method using simulation studies and an application to genetic data from the Genetic Epidemiology Network of Arteriopathy (GENOA) study.     

A multiple imputation approach for clustered interval‐censored survival data

Multivariate interval‐censored failure time data arise commonly in many studies of epidemiology and biomedicine. Analysis of these type of data is more challenging than the right‐censored data. We propose a simple multiple imputation strategy to recover the order of occurrences based on the interval‐censored event times using a conditional predictive distribution function derived from a parametric gamma random effects model. By imputing the interval‐censored failure times, the estimation of the regression and dependence parameters in the context of a gamma frailty proportional hazards model using the well‐developed EM algorithm is made possible. A robust estimator for the covariance matrix is suggested to adjust for the possible misspecification of the parametric baseline hazard function. The finite sample properties of the proposed method are investigated via simulation. The performance of the proposed method is highly satisfactory, whereas the computation burden is minimal. The proposed method is also applied to the diabetic retinopathy study (DRS) data for illustration purpose and the estimates are compared with those based on other existing methods for bivariate grouped survival data. Copyright © 2010 John Wiley & Sons, Ltd.     

GEE‐Based SNP Set Association Test for Continuous and Discrete Traits in Family‐Based Association Studies

Family‐based genetic association studies of related individuals provide opportunities to detect genetic variants that complement studies of unrelated individuals. Most statistical methods for family association studies for common variants are single marker based, which test one SNP a time. In this paper, we consider testing the effect of an SNP set, e.g., SNPs in a gene, in family studies, for both continuous and discrete traits. Specifically, we propose a generalized estimating equations (GEEs) based kernel association test, a variance component based testing method, to test for the association between a phenotype and multiple variants in an SNP set jointly using family samples. The proposed approach allows for both continuous and discrete traits, where the correlation among family members is taken into account through the use of an empirical covariance estimator. We derive the theoretical distribution of the proposed statistic under the null and develop analytical methods to calculate the P‐values. We also propose an efficient resampling method for correcting for small sample size bias in family studies. The proposed method allows for easily incorporating covariates and SNP‐SNP interactions. Simulation studies show that the proposed method properly controls for type I error rates under both random and ascertained sampling schemes in family studies. We demonstrate through simulation studies that our approach has superior performance for association mapping compared to the single marker based minimum P‐value GEE test for an SNP‐set effect over a range of scenarios. We illustrate the application of the proposed method using data from the Cleveland Family GWAS Study.     

Testing Allele Transmission of an SNP Set Using a Family‐Based Generalized Genetic Random Field Method

Family‐based association studies are commonly used in genetic research because they can be robust to population stratification (PS). Recent advances in high‐throughput genotyping technologies have produced a massive amount of genomic data in family‐based studies. However, current family‐based association tests are mainly focused on evaluating individual variants one at a time. In this article, we introduce a family‐based generalized genetic random field (FB‐GGRF) method to test the joint association between a set of autosomal SNPs (i.e., single‐nucleotide polymorphisms) and disease phenotypes. The proposed method is a natural extension of a recently developed GGRF method for population‐based case‐control studies. It models offspring genotypes conditional on parental genotypes, and, thus, is robust to PS. Through simulations, we presented that under various disease scenarios the FB‐GGRF has improved power over a commonly used family‐based sequence kernel association test (FB‐SKAT). Further, similar to GGRF, the proposed FB‐GGRF method is asymptotically well‐behaved, and does not require empirical adjustment of the type I error rates. We illustrate the proposed method using a study of congenital heart defects with family trios from the National Birth Defects Prevention Study (NBDPS).     

A General Efficient and Flexible Approach for Genome‐Wide Association Analyses of Imputed Genotypes in Family‐Based Designs

Genotype imputation is a critical technique for following up genome‐wide association studies. Efficient methods are available for dealing with the probabilistic nature of imputed single nucleotide polymorphisms (SNPs) in population‐based designs, but not for family‐based studies. We have developed a new analytical approach (FBATdosage), using imputed allele dosage in the general framework of family‐based association tests to bridge this gap. Simulation studies showed that FBATdosage yielded highly consistent type I error rates, whatever the level of genotype uncertainty, and a much higher power than the best‐guess genotype approach. FBATdosage allows fast linkage and association testing of several million of imputed variants with binary or quantitative phenotypes in nuclear families of arbitrary size with arbitrary missing data for the parents. The application of this approach to a family‐based association study of leprosy susceptibility successfully refined the association signal at two candidate loci, C1orf141‐IL23R on chromosome 1 and RAB32‐C6orf103 on chromosome 6.     

Martingale residual‐based method to control for confounders measured only in a validation sample in time‐to‐event analysis

Unmeasured confounding remains an important problem in observational studies, including pharmacoepidemiological studies of large administrative databases. Several recently developed methods utilize smaller validation samples, with information on additional confounders, to control for confounders unmeasured in the main, larger database. However, up‐to‐date applications of these methods to survival analyses seem to be limited to propensity score calibration, which relies on a strong surrogacy assumption. We propose a new method, specifically designed for time‐to‐event analyses, which uses martingale residuals, in addition to measured covariates, to enhance imputation of the unmeasured confounders in the main database. The method is applicable for analyses with both time‐invariant data and time‐varying exposure/confounders. In simulations, our method consistently eliminated bias because of unmeasured confounding, regardless of surrogacy violation and other relevant design parameters, and almost always yielded lower mean squared errors than other methods applicable for survival analyses, outperforming propensity score calibration in several scenarios. We apply the method to a real‐life pharmacoepidemiological database study of the association between glucocorticoid therapy and risk of type II diabetes mellitus in patients with rheumatoid arthritis, with additional potential confounders available in an external validation sample. Compared with conventional analyses, which adjust only for confounders measured in the main database, our estimates suggest a considerably weaker association. Copyright © 2016 John Wiley & Sons, Ltd.     

Family-based association test for time-to-onset data with time-dependent differences between the hazard functions

In genetic association studies, the differences between the hazard functions for the individual genotypes are often time-dependent. We address the non-proportional hazards data by using the weighted logrank approach by Fleming and Harrington [1981]:Commun Stat-Theor M 10:763-794. We introduce a weighted FBAT-Logrank whose weights are based on a non-parametric estimator for the genetic marker distribution function under the alternative hypothesis. We show that the computation of the marker distribution under the alternative does not bias the significance level of any subsequently computed FBAT-statistic. Hence, we use the estimated marker distribution to select the Fleming-Harrington weights so that the power of the weighted FBAT-Logrank test is maximized. In simulation studies and applications to an asthma study, we illustrate the practical relevance of the new methodology. In addition to power increases of 100% over the original FBAT-Logrank test, we also gain insight into the age at which a genotype exerts the greatest influence on disease risk.     

Testing goodness of fit in regression: a general approach for specified alternatives

When fitting generalized linear models or the Cox proportional hazards model, it is important to have tools to test for lack of fit. Because lack of fit comes in all shapes and sizes, distinguishing among different types of lack of fit is of practical importance. We argue that an adequate diagnosis of lack of fit requires a specified alternative model. Such specification identifies the type of lack of fit the test is directed against so that if we reject the null hypothesis, we know the direction of the departure from the model. The goodness‐of‐fit approach of this paper allows to treat different types of lack of fit within a unified general framework and to consider many existing tests as special cases. Connections with penalized likelihood and random effects are discussed, and the application of the proposed approach is illustrated with medical examples. Tailored functions for goodness‐of‐fit testing have been implemented in the R package globaltest . Copyright © 2012 John Wiley & Sons, Ltd.     

On robustness of marginal regression coefficient estimates and hazard functions in multivariate survival analysis of family data when the frailty distribution is mis-specified

The shared frailty model is an extension of the Cox model to correlated failure times and, essentially, a random effects model for failure time outcomes. In this model, the latent frailty shared by individual members in a cluster acts multiplicatively as a factor on the hazard function and is typically modelled parametrically. One commonly used distribution is gamma, where both shape and scale parameters are set to be the same to allow for unique identification of baseline hazard function. It is popular because it is a conjugate prior, and the posterior distribution possesses the same form as gamma. In addition, the parameter can be interpreted as a time-independent cross-ratio function, a natural extension of odds ratio to failure time outcomes. In this paper, we study the effect of frailty distribution mis-specification on the marginal regression estimates and hazard functions under assumed gamma distribution with an application to family studies. The simulation results show that the biases are generally 10% and lower, even when the true frailty distribution deviates substantially from the assumed gamma distribution. This suggests that the gamma frailty model can be a practical choice in real data analyses if the regression parameters and marginal hazard function are of primary interest and individual cluster members are exchangeable with respect to their dependencies.     

A Novel Test for Testing the Optimally Weighted Combination of Rare and Common Variants Based on Data of Parents and Affected Children

With the development of sequencing technologies, the direct testing of rare variant associations has become possible. Many statistical methods for detecting associations between rare variants and complex diseases have recently been developed, most of which are population‐based methods for unrelated individuals. A limitation of population‐based methods is that spurious associations can occur when there is a population structure. For rare variants, this problem can be more serious, because the spectrum of rare variation can be very different in diverse populations, as well as the current nonexistence of methods to control for population stratification in population‐based rare variant associations. A solution to the problem of population stratification is to use family‐based association tests, which use family members to control for population stratification. In this article, we propose a novel test for Testing the Optimally Weighted combination of variants based on data of Parents and Affected Children (TOW‐PAC). TOW‐PAC is a family‐based association test that tests the combined effect of rare and common variants in a genomic region, and is robust to the directions of the effects of causal variants. Simulation studies confirm that, for rare variant associations, family‐based association tests are robust to population stratification although population‐based association tests can be seriously confounded by population stratification. The results of power comparisons show that the power of TOW‐PAC increases with an increase of the number of affected children in each family and TOW‐PAC based on multiple affected children per family is more powerful than TOW based on unrelated individuals.     

A case‐cohort approach for multi‐state models in hospital epidemiology

Analysing the determinants and consequences of hospital‐acquired infections involves the evaluation of large cohorts. Infected patients in the cohort are often rare for specific pathogens, because most of the patients admitted to the hospital are discharged or die without such an infection. Death and discharge are competing events to acquiring an infection, because these individuals are no longer at risk of getting a hospital‐acquired infection. Therefore, the data is best analysed with an extended survival model – the extended illness‐death model. A common problem in cohort studies is the costly collection of covariate values. In order to provide efficient use of data from infected as well as uninfected patients, we propose a tailored case‐cohort approach for the extended illness‐death model. The basic idea of the case‐cohort design is to only use a random sample of the full cohort, referred to as subcohort, and all cases, namely the infected patients. Thus, covariate values are only obtained for a small part of the full cohort. The method is based on existing and established methods and is used to perform regression analysis in adapted Cox proportional hazards models. We propose estimation of all cause‐specific cumulative hazards and transition probabilities in an extended illness‐death model based on case‐cohort sampling. As an example, we apply the methodology to infection with a specific pathogen using a large cohort from Spanish hospital data. The obtained results of the case‐cohort design are compared with the results in the full cohort to investigate the performance of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Analysis of recurrent gap time data using the weighted risk-set method and the modified within-cluster resampling method

The gap times between recurrent events are often of primary interest in medical and epidemiology studies. The observed gap times cannot be naively treated as clustered survival data in analysis because of the sequential structure of recurrent events. This paper introduces two important building blocks, the averaged counting process and the averaged at-risk process, for the development of the weighted risk-set (WRS) estimation methods. We demonstrate that with the use of these two empirical processes, existing risk-set based methods for univariate survival time data can be easily extended to analyze recurrent gap times. Additionally, we propose a modified within-cluster resampling (MWCR) method that can be easily implemented in standard software. We show that the MWCR estimators are asymptotically equivalent to the WRS estimators. An analysis of hospitalization data from the Danish Psychiatric Central Register is presented to illustrate the proposed methods.     

The analysis of case cohort design in the presence of competing risks with application to estimate the risk of delayed cardiac toxicity among Hodgkin Lymphoma survivors

The case‐cohort design is an economical solution to studying the association between an exposure and a rare disease. When the disease of interest has a delayed occurrence, then other types of event may preclude observation of the disease of interest giving rise to a competing risk situation. In this paper, we introduce a modification of the pseudolikelihood proposed by Prentice (Biometrika 1986; 73 :1–11) for the analysis of case‐cohort design, to accommodate the existence of competing risks. The modification is based on the Fine and Gray (J. Amer. Statist. Assoc. 1999; 94 :496–509) approach to enable the modeling of the hazard of subdistribution. We show through simulations that the estimate that maximizes this modified pseudolikelihood is almost unbiased. The predictive probabilities based on the model are close to the theoretical probabilities. The variance for the estimates can be calculated using the jackknife approach. An application of this method on the analysis of late cardiac morbidity among Hodgkin Lymphoma survivors is presented. Copyright © 2010 John Wiley & Sons, Ltd.     

Bayesian variable selection for survival regression in genetics

Variable selection in regression with very big numbers of variables is challenging both in terms of model specification and computation. We focus on genetic studies in the field of survival, and we present a Bayesian-inspired penalized maximum likelihood approach appropriate for high-dimensional problems. In particular, we employ a simple, efficient algorithm that seeks maximum a posteriori (MAP) estimates of regression coefficients. The latter are assigned a Laplace prior with a sharp mode at zero, and non-zero posterior mode estimates correspond to significant single nucleotide polymorphisms (SNPs). Using the Laplace prior reflects a prior belief that only a small proportion of the SNPs significantly influence the response. The method is fast and can handle datasets arising from imputation or resequencing. We demonstrate the localization performance, power and false-positive rates of our method in large simulation studies of dense-SNP datasets and sequence data, and we compare the performance of our method to the univariate Cox regression and to a recently proposed stochastic search approach. In general, we find that our approach improves localization and power slightly, while the biggest advantage is in false-positive counts and computing times. We also apply our method to a real prospective study, and we observe potential association between candidate ABC transporter genes and epilepsy treatment outcomes.     

Design and semiparametric analysis of non‐inferiority trials with active and placebo control for censored time‐to‐event data

The clinical trial design including a test treatment, an active control and a placebo is called the gold standard design. In this paper, we develop a statistical method for planning and evaluating non‐inferiority trials with gold standard design for right‐censored time‐to‐event data. We consider both lost to follow‐up and administrative censoring. We present a semiparametric approach that only assumes the proportionality of the hazard functions. In particular, we develop an algorithm for calculating the minimal total sample size and its optimal allocation to treatment groups such that a desired power can be attained for a specific parameter constellation under the alternative. For the purpose of sample size calculation, we assume the endpoints to be Weibull distributed. By means of simulations, we investigate the actual type I error rate, power and the accuracy of the calculated sample sizes. Finally, we compare our procedure with a previously proposed procedure assuming exponentially distributed event times. To illustrate our method, we consider a double‐blinded, randomized, active and placebo controlled trial in major depression. Copyright © 2013 John Wiley & Sons, Ltd.     

Power of the Mantel–Haenszel and other tests for discrete or grouped time‐to‐event data under a chained binomial model

Power for time‐to‐event analyses is usually assessed under continuous‐time models. Often, however, times are discrete or grouped, as when the event is only observed when a procedure is performed. Wallenstein and Wittes (Biometrics, 1993) describe the power of the Mantel–Haenszel test for discrete lifetables under their chained binomial model for specified vectors of event probabilities over intervals of time. Herein, the expressions for these probabilities are derived under a piecewise exponential model allowing for staggered entry and losses to follow‐up. Radhakrishna (Biometrics, 1965) showed that the Mantel–Haenszel test is maximally efficient under the alternative of a constant odds ratio and derived the optimal weighted test under other alternatives. Lachin (Biostatistical Methods: The Assessment of Relative Risks, 2011) described the power function of this family of weighted Mantel–Haenszel tests. Prentice and Gloeckler (Biometrics, 1978) described a generalization of the proportional hazards model for grouped time data and the corresponding maximally efficient score test. Their test is also shown to be a weighted Mantel–Haenszel test, and its power function is likewise obtained. There is trivial loss in power under the discrete chained binomial model relative to the continuous‐time case provided that there is a modest number of periodic evaluations. Relative to the case of homogeneity of odds ratios, there can be substantial loss in power when there is substantial heterogeneity of odds ratios, especially when heterogeneity occurs early in a study when most subjects are at risk, but little loss in power when there is heterogeneity late in a study. Copyright © 2012 John Wiley & Sons, Ltd.     

Testing for Rare Variant Associations in the Presence of Missing Data

For studies of genetically complex diseases, many association methods have been developed to analyze rare variants. When variant calls are missing, naïve implementation of rare variant association (RVA) methods may lead to inflated type I error rates as well as a reduction in power. To overcome these problems, we developed extensions for four commonly used RVA tests. Data from the National Heart Lung and Blood Institute‐Exome Sequencing Project were used to demonstrate that missing variant calls can lead to increased false‐positive rates and that the extended RVA methods control type I error without reducing power. We suggest a combined strategy of data filtering based on variant and sample level missing genotypes along with implementation of these extended RVA tests.     

Developing points‐based risk‐scoring systems in the presence of competing risks

Predicting the occurrence of an adverse event over time is an important issue in clinical medicine. Clinical prediction models and associated points‐based risk‐scoring systems are popular statistical methods for summarizing the relationship between a multivariable set of patient risk factors and the risk of the occurrence of an adverse event. Points‐based risk‐scoring systems are popular amongst physicians as they permit a rapid assessment of patient risk without the use of computers or other electronic devices. The use of such points‐based risk‐scoring systems facilitates evidence‐based clinical decision making. There is a growing interest in cause‐specific mortality and in non‐fatal outcomes. However, when considering these types of outcomes, one must account for competing risks whose occurrence precludes the occurrence of the event of interest. We describe how points‐based risk‐scoring systems can be developed in the presence of competing events. We illustrate the application of these methods by developing risk‐scoring systems for predicting cardiovascular mortality in patients hospitalized with acute myocardial infarction. Code in the R statistical programming language is provided for the implementation of the described methods. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.     

Testing association in the presence of linkage--a powerful score for binary traits

We present a score for testing association in the presence of linkage for binary traits. The score is robust to varying degrees of linkage, and it is valid under any ascertainment scheme based on trait values as well as under population stratification. The score test is derived from a mixed effects model where population level association is modeled using a fixed effect and where correlation among related individuals is allowed for by using log-gamma random effects. The score, as presented in this paper, does not assume full information about the inheritance pattern in families or parental genotypes. We compare the score to the semi-parametric family-based association test (FBAT), which has won ground because of its flexible and simple form. We show that a random effects formulation of co-inheritance can improve the power substantially. We apply the method to data from the Collaborative Study on the Genetics of Alcoholism. We compare our findings to previously published results.     

Haplotype sharing correlation analysis using family data: a comparison with family-based association test in the presence of allelic heterogeneity

The haplotype-sharing correlation (HSC) method for association analysis using family data is revisited by introducing a permutation procedure for estimating region-wise significance at each marker on a study segment. In simulation studies, the HSC method has a correct type 1 error rate in both unstructured and structured populations. The HSC signals on disease segments occur in the vicinity of a true disease locus on a restricted region without recombination hotspots. However, the peak signal may not pinpoint the true disease location in a small region with dense markers. The HSC method is shown to have higher power than single- and multilocus family-based association test (FBAT) methods when the true disease locus is unobserved among the study markers, and especially under conditions of weak linkage disequilibrium and multiple ancestral disease alleles. These simulation results suggest that the HSC method has the capacity to identify true disease-associated segments under allelic heterogeneity that go undetected by the FBAT method that compares allelic or haplotypic frequencies.