A haplotype-based test of association using data from cohort and nested case-control epidemiologic studies

Haplotype-based risk models can lead to powerful methods for detecting the association of a disease with a genomic region of interest. In population-based studies of unrelated individuals, however, the haplotype status of some subjects may not be discernible without ambiguity from available locus-specific genotype data. A score test for detecting haplotype-based association using genotype data has been developed in the context of generalized linear models for analysis of data from cross-sectional and retrospective studies. In this article, we develop a test for association using genotype data from cohort and nested case-control studies where subjects are prospectively followed until disease incidence or censoring (end of follow-up) occurs. Assuming a proportional hazard model for the haplotype effects, we derive an induced hazard function of the disease given the genotype data, and hence propose a test statistic based on the associated partial likelihood. The proposed test procedure can account for differential follow-up of subjects, can adjust for possibly time-dependent environmental co-factors and can make efficient use of valuable age-at-onset information that is available on cases. We provide an algorithm for computing the test statistic using readily available statistical software. Utilizing simulated data in the context of two genomic regions GPX1 and GPX3, we evaluate the validity of the proposed test for small sample sizes and study its power in the presence and absence of missing genotype data.     

Statistical analysis for haplotype-based matched case-control studies

Using unphased genotype data, we studied statistical inference for association between a disease and a haplotype in matched case-control studies. Statistical inference for haplotype data is complicated due to ambiguity of genotype phases. An estimating equation-based method is developed for estimating odds ratios and testing disease-haplotype association. The method potentially can also be applied to testing haplotype-environment interaction. Simulation studies show that the proposed method has good performance. The performance of the method in the presence of departures from Hardy-Weinberg equilibrium is also studied.     

Multivariate survival analysis for case-control family data

Multivariate survival data arise from case-control family studies in which the ages at disease onset for family members may be correlated. In this paper, we consider a multivariate survival model with the marginal hazard function following the proportional hazards model. We use a frailty-based approach in the spirit of Glidden and Self (1999) to account for the correlation of ages at onset among family members. Specifically, we first estimate the baseline hazard function nonparametrically by the innovation theorem, and then obtain maximum pseudolikelihood estimators for the regression and correlation parameters plugging in the baseline hazard function estimator. We establish a connection with a previously proposed generalized estimating equation-based approach. Simulation studies and an analysis of case-control family data of breast cancer illustrate the methodology's practical utility.     

Genetic association analysis of human longevity in cohort studies of elderly subjects: an example of the PON1 gene in the Danish 1905 birth cohort

Although the case-control or the cross-sectional design has been popular in genetic association studies of human longevity, such a design is prone to false positive results due to sampling bias and a potential secular trend in gene-environment interactions. To avoid these problems, the cohort or follow-up study design has been recommended. With the observed individual survival information, the Cox regression model has been used for single-locus data analysis. In this article, we present a novel survival analysis model that combines population survival with individual genotype and phenotype information in assessing the genetic association with human longevity in cohort studies. By monitoring the changes in the observed genotype frequencies over the follow-up period in a birth cohort, we are able to assess the effects of the genotypes and/or haplotypes on individual survival. With the estimated parameters, genotype- and/or haplotype-specific survival and hazard functions can be calculated without any parametric assumption on the survival distribution. In addition, our model estimates haplotype frequencies in a birth cohort over the follow-up time, which is not observable in the multilocus genotype data. A computer simulation study was conducted to specifically assess the performance and power of our haplotype-based approach for given risk and frequency parameters under different sample sizes. Application of our method to paraoxonase 1 genotype data detected a haplotype that significantly reduces carriers' hazard of death and thus reveals and stresses the important role of genetic variation in maintaining human survival at advanced ages.     

Efficient semiparametric estimation of haplotype-disease associations in case-cohort and nested case-control studies

Estimating the effects of haplotypes on the age of onset of a disease is an important step toward the discovery of genes that influence complex human diseases. A haplotype is a specific sequence of nucleotides on the same chromosome of an individual and can only be measured indirectly through the genotype. We consider cohort studies which collect genotype data on a subset of cohort members through case-cohort or nested case-control sampling. We formulate the effects of haplotypes and possibly time-varying environmental variables on the age of onset through a broad class of semiparametric regression models. We construct appropriate nonparametric likelihoods, which involve both finite- and infinite-dimensional parameters. The corresponding nonparametric maximum likelihood estimators are shown to be consistent, asymptotically normal, and asymptotically efficient. Consistent variance-covariance estimators are provided, and efficient and reliable numerical algorithms are developed. Simulation studies demonstrate that the asymptotic approximations are accurate in practical settings and that case-cohort and nested case-control designs are highly cost-effective. An application to a major cardiovascular study is provided.     

Inference on haplotype effects in case-control studies using unphased genotype data

A variety of statistical methods exist for detecting haplotype-disease association through use of genetic data from a case-control study. Since such data often consist of unphased genotypes (resulting in haplotype ambiguity), such statistical methods typically apply the expectation-maximization (EM) algorithm for inference. However, the majority of these methods fail to perform inference on the effect of particular haplotypes or haplotype features on disease risk. Since such inference is valuable, we develop a retrospective likelihood for estimating and testing the effects of specific features of single-nucleotide polymorphism (SNP)-based haplotypes on disease risk using unphased genotype data from a case-control study. Our proposed method has a flexible structure that allows, among other choices, modeling of multiplicative, dominant, and recessive effects of specific haplotype features on disease risk. In addition, our method relaxes the requirement of Hardy-Weinberg equilibrium of haplotype frequencies in case subjects, which is typically required of EM-based haplotype methods. Also, our method easily accommodates missing SNP information. Finally, our method allows for asymptotic, permutation-based, or bootstrap inference. We apply our method to case-control SNP genotype data from the Finland-United States Investigation of Non-Insulin-Dependent Diabetes Mellitus (FUSION) Genetics study and identify two haplotypes that appear to be significantly associated with type 2 diabetes. Using the FUSION data, we assess the accuracy of asymptotic P values by comparing them with P values obtained from a permutation procedure. We also assess the accuracy of asymptotic confidence intervals for relative-risk parameters for haplotype effects, by a simulation study based on the FUSION data.     

Retrospective analysis of haplotype-based case control studies under a flexible model for gene environment association

Genetic epidemiologic studies often involve investigation of the association of a disease with a genomic region in terms of the underlying haplotypes, that is the combination of alleles at multiple loci along homologous chromosomes. In this article, we consider the problem of estimating haplotype-environment interactions from case-control studies when some of the environmental exposures themselves may be influenced by genetic susceptibility. We specify the distribution of the diplotypes (haplotype pair) given environmental exposures for the underlying population based on a novel semiparametric model that allows haplotypes to be potentially related with environmental exposures, while allowing the marginal distribution of the diplotypes to maintain certain population genetics constraints such as Hardy-Weinberg equilibrium. The marginal distribution of the environmental exposures is allowed to remain completely nonparametric. We develop a semiparametric estimating equation methodology and related asymptotic theory for estimation of the disease odds ratios associated with the haplotypes, environmental exposures, and their interactions, parameters that characterize haplotype-environment associations and the marginal haplotype frequencies. The problem of phase ambiguity of genotype data is handled using a suitable expectation-maximization algorithm. We study the finite-sample performance of the proposed methodology using simulated data. An application of the methodology is illustrated using a case-control study of colorectal adenoma, designed to investigate how the smoking-related risk of colorectal adenoma can be modified by "NAT2," a smoking-metabolism gene that may potentially influence susceptibility to smoking itself.     

流行病学研究中的嵌套病例对照研究

自从1975年由Thomas提出以来，嵌套病例对照研究（nested case-control study）方法在流行病学和生存分析的研究中应用日益广泛，近几年来，随机点过程理论的发展促进了这一方法中的理论问题的解决，从而为这一方法的进一步研究奠定了理论基础，本文综述近年来嵌套病例对照研究方法的新进展，指出目前仍待研究的一些问题，并就一种特殊情况给出了Mantel-Haenszel型推断方法。     

Causal mediation analysis in nested case-control studies using conditional logistic regression

The paper proposes an approach to causal mediation analysis in nested case-control study designs, often incorporated with countermatching schemes using conditional likelihood, and we compare the method's performance to that of mediation analysis using the Cox model for the full cohort with a continuous or dichotomous mediator. Simulation studies are conducted to assess our proposed method and investigate the efficiency relative to the cohort. We illustrate the method using actual data from two studies of potential mediation of radiation risk conducted within the Adult Health Study cohort of atomic-bomb survivors. The performance becomes comparable to that based on the full cohort, illustrating the potential for valid mediation analysis based on the reduced data obtained through the nested case-control design.     

Weight calibration to improve the efficiency of pure risk estimates from case-control samples nested in a cohort

Cohort studies provide information on relative hazards and pure risks of disease. For rare outcomes, large cohorts are needed to have sufficient numbers of events, making it costly to obtain covariate information on all cohort members. We focus on nested case-control designs that are used to estimate relative hazard in the Cox regression model. In 1997, Langholz and Borgan showed that pure risk can also be estimated from nested case-control data. However, these approaches do not take advantage of some covariates that may be available on all cohort members. Researchers have used weight calibration to increase the efficiency of relative hazard estimates from case-cohort studies and nested cased-control studies. Our objective is to extend weight calibration approaches to nested case-control designs to improve precision of estimates of relative hazards and pure risks. We show that calibrating sample weights additionally against follow-up times multiplied by relative hazards during the risk projection period improves estimates of pure risk. Efficiency improvements for relative hazards for variables that are available on the entire cohort also contribute to improved efficiency for pure risks. We develop explicit variance formulas for the weight-calibrated estimates. Simulations show how much precision is improved by calibration and confirm the validity of inference based on asymptotic normality. Examples are provided using data from the American Association of Retired Persons Diet and Health Cohort Study.     

Cohort case-control design and analysis for clustered failure-time data

Cohort case-control design is an efficient and economical design to study risk factors for disease incidence or mortality in a large cohort. In the last few decades, a variety of cohort case-control designs have been developed and theoretically justified. These designs have been exclusively applied to the analysis of univariate failure-time data. In this work, a cohort case-control design adapted to multivariate failure-time data is developed. A risk set sampling method is proposed to sample controls from nonfailures in a large cohort for each case matched by failure time. This method leads to a pseudolikelihood approach for the estimation of regression parameters in the marginal proportional hazards model (Cox, 1972, Journal of the Royal Statistical Society, Series B 34, 187-220), where the correlation structure between individuals within a cluster is left unspecified. The performance of the proposed estimator is demonstrated by simulation studies. A bootstrap method is proposed for inferential purposes. This methodology is illustrated by a data example from a child vitamin A supplementation trial in Nepal (Nepal Nutrition Intervention Project-Sarlahi, or NNIPS).     

Proportional Hazards Regression for the Analysis of Clustered Survival Data from Case–Cohort Studies

Summary Case–cohort sampling is a commonly used and efficient method for studying large cohorts. Most existing methods of analysis for case–cohort data have concerned the analysis of univariate failure time data. However, clustered failure time data are commonly encountered in public health studies. For example, patients treated at the same center are unlikely to be independent. In this article, we consider methods based on estimating equations for case–cohort designs for clustered failure time data. We assume a marginal hazards model, with a common baseline hazard and common regression coefficient across clusters. The proposed estimators of the regression parameter and cumulative baseline hazard are shown to be consistent and asymptotically normal, and consistent estimators of the asymptotic covariance matrices are derived. The regression parameter estimator is easily computed using any standard Cox regression software that allows for offset terms. The proposed estimators are investigated in simulation studies, and demonstrated empirically to have increased efficiency relative to some existing methods. The proposed methods are applied to a study of mortality among Canadian dialysis patients.     

On estimating HLA/disease association with application to a study of aplastic anemia

A multiplicative model is described relating HLA typing information to disease incidence. A likelihood-based method for estimating parameters in this model is proposed for use with data sets in which HLA haplotype information is available on a series of cases and their parents. This approach is extended to incorporate information from a matched control series for the purpose of estimating HLA and environmental risk factor effects simultaneously. The method is applied to data from aplastic anemia patients treated by bone marrow transplantation and the results are compared to unmatched case-control analyses using the same case series and several different control series.     

Modeling and E-M estimation of haplotype-specific relative risks from genotype data for a case-control study of unrelated individuals

The US National Cancer Institute has recently sponsored the formation of a Cohort Consortium (http://2002.cancer.gov/scpgenes.htm) to facilitate the pooling of data on very large numbers of people, concerning the effects of genes and environment on cancer incidence. One likely goal of these efforts will be generate a large population-based case-control series for which a number of candidate genes will be investigated using SNP haplotype as well as genotype analysis. The goal of this paper is to outline the issues involved in choosing a method of estimating haplotype-specific risk estimates for such data that is technically appropriate and yet attractive to epidemiologists who are already comfortable with odds ratios and logistic regression. Our interest is to develop and evaluate extensions of methods, based on haplotype imputation, that have been recently described (Schaid et al., Am J Hum Genet, 2002, and Zaykin et al., Hum Hered, 2002) as providing score tests of the null hypothesis of no effect of SNP haplotypes upon risk, which may be used for more complex tasks, such as providing confidence intervals, and tests of equivalence of haplotype-specific risks in two or more separate populations. In order to do so we (1) develop a cohort approach towards odds ratio analysis by expanding the E-M algorithm to provide maximum likelihood estimates of haplotype-specific odds ratios as well as genotype frequencies; (2) show how to correct the cohort approach, to give essentially unbiased estimates for population-based or nested case-control studies by incorporating the probability of selection as a case or control into the likelihood, based on a simplified model of case and control selection, and (3) finally, in an example data set (CYP17 and breast cancer, from the Multiethnic Cohort Study) we compare likelihood-based confidence interval estimates from the two methods with each other, and with the use of the single-imputation approach of Zaykin et al. applied under both null and alternative hypotheses. We conclude that so long as haplotypes are well predicted by SNP genotypes (we use the Rh2 criteria of Stram et al. [1]) the differences between the three methods are very small and in particular that the single imputation method may be expected to work extremely well.     

Inference of haplotype effects in case-control studies using unphased genotype and environmental data

A retrospective likelihood-based approach was proposed to test and estimate the effect of haplotype on disease risk using unphased genotype data with adjustment for environmental covariates. The proposed method was also extended to handle the data in which the haplotype and environmental covariates are not independent. Likelihood ratio tests were constructed to test the effects of haplotype and gene-environment interaction. The model parameters such as haplotype effect size was estimated using an Expectation Conditional-Maximization (ECM) algorithm developed by Meng and Rubin (1993). Model-based variance estimates were derived using the observed information matrix. Simulation studies were conducted for three different genetic effect models, including dominant effect, recessive effect, and additive effect. The results showed that the proposed method generated unbiased parameter estimates, proper type I error, and true beta coverage probabilities. The model performed well with small or large sample sizes, as well as short or long haplotypes.     

HAPLOPOOL: improving haplotype frequency estimation through DNA pools and phylogenetic modeling

MOTIVATION: The search for genetic variants that are linked to complex diseases such as cancer, Parkinson's;, or Alzheimer's; disease, may lead to better treatments. Since haplotypes can serve as proxies for hidden variants, one method of finding the linked variants is to look for case-control associations between the haplotypes and disease. Finding these associations requires a high-quality estimation of the haplotype frequencies in the population. To this end, we present, HaploPool, a method of estimating haplotype frequencies from blocks of consecutive SNPs. RESULTS: HaploPool leverages the efficiency of DNA pools and estimates the population haplotype frequencies from pools of disjoint sets, each containing two or three unrelated individuals. We study the trade-off between pooling efficiency and accuracy of haplotype frequency estimates. For a fixed genotyping budget, HaploPool performs favorably on pools of two individuals as compared with a state-of-the-art non-pooled phasing method, PHASE. Of independent interest, HaploPool can be used to phase non-pooled genotype data with an accuracy approaching that of PHASE. We compared our algorithm to three programs that estimate haplotype frequencies from pooled data. HaploPool is an order of magnitude more efficient (at least six times faster), and considerably more accurate than previous methods. In contrast to previous methods, HaploPool performs well with missing data, genotyping errors and long haplotype blocks (of between 5 and 25 SNPs).     

Use of external rates in nested case-control studies with application to the international radiation study of cervical cancer patients.

A method is proposed for analysis of nested case-control studies that combines the matched comparison of covariate values between cases and controls and a comparison of the observed numbers of cases in the nesting cohort with expected numbers based on external rates and average relative risks estimated from the controls. The former comparison is based on the conditional likelihood for matched case-control studies and the latter on the unconditional likelihood for Poisson regression. It is shown that the two likelihoods are orthogonal and that their product is an estimator of the full survival likelihood that would have been obtained on the total cohort, had complete covariate data been available. Parameter estimation and significance tests follow in the usual way by maximizing this product likelihood. The method is illustrated using data on leukemia following irradiation for cervical cancer. In this study, the original cohort study showed a clear excess of leukemia in the first 15 years after exposure, but it was not feasible to obtain dose estimates on the entire cohort. However, the subsequent nested case-control study failed to demonstrate significant differences between alternative dose-response relations and effects of time-related modifiers. The combined analysis allows much clearer discrimination between alternative dose-time-response models.     

On Mendelian randomization analysis of case-control study

Mendelian randomization (MR) analysis uses genotypes as instruments to estimate the causal effect of an exposure in the presence of unobserved confounders. The existing MR methods focus on the data generated from prospective cohort studies. We develop a procedure for studying binary outcomes under a case-control design. The proposed procedure is built upon two working models commonly used for MR analyses and adopts a quasi-empirical likelihood framework to address the ascertainment bias from case-control sampling. We derive various approaches for estimating the causal effect and hypothesis testing under the empirical likelihood framework. We conduct extensive simulation studies to evaluate the proposed methods. We find that the proposed empirical likelihood estimate is less biased than the existing estimates. Among all the approaches considered, the Lagrange multiplier (LM) test has the highest power, and the confidence intervals derived from the LM test have the most accurate coverage. We illustrate the use of our method in MR analysis of prostate cancer case-control data with vitamin D level as exposure and three single nucleotide polymorphisms as instruments.     

A marginal likelihood approach for estimating penetrance from kin-cohort designs

The kin-cohort design is a promising alternative to traditional cohort or case-control designs for estimating penetrance of an identified rare autosomal mutation. In this design, a suitably selected sample of participants provides genotype and detailed family history information on the disease of interest. To estimate penetrance of the mutation, we consider a marginal likelihood approach that is computationally simple to implement, more flexible than the original analytic approach proposed by Wacholder et al. (1998, American Journal of Epidemiology 148, 623-629), and more robust than the likelihood approach considered by Gail et al. (1999, Genetic Epidemiology 16, 15-39) to presence of residual familial correlation. We study the trade-off between robustness and efficiency using simulation experiments. The method is illustrated by analysis of the data from the Washington Ashkenazi Study.     

Comparison of cohort and nested case-control designs for estimating the effect of time-varying drug exposure on the risk of adverse event in the presence of ties

Cohort and nested case-control (NCC) designs are frequently used in pharmacoepidemiology to assess the associations of drug exposure that can vary over time with the risk of an adverse event. Although it is typically expected that estimates from NCC analyses are similar to those from the full cohort analysis, with moderate loss of precision, only few studies have actually compared their respective performance for estimating the effects of time-varying exposures (TVE). We used simulations to compare the properties of the resulting estimators of these designs for both time-invariant exposure and TVE. We varied exposure prevalence, proportion of subjects experiencing the event, hazard ratio, and control-to-case ratio and considered matching on confounders. Using both designs, we also estimated the real-world associations of time-invariant ever use of menopausal hormone therapy (MHT) at baseline and updated, time-varying MHT use with breast cancer incidence. In all simulated scenarios, the cohort-based estimates had small relative bias and greater precision than the NCC design. NCC estimates displayed bias to the null that decreased with a greater number of controls per case. This bias markedly increased with higher proportion of events. Bias was seen with Breslow's and Efron's approximations for handling tied event times but was greatly reduced with the exact method or when NCC analyses were matched on confounders. When analyzing the MHT-breast cancer association, differences between the two designs were consistent with simulated data. Once ties were taken correctly into account, NCC estimates were very similar to those of the full cohort analysis.