Unveiling challenges in Mendelian randomization for gene-environment interaction.

Gene-environment (GxE) interactions play a crucial role in understanding the complex etiology of various traits, but assessing them using observational data can be challenging due to unmeasured confounders for lifestyle and environmental risk factors. Mendelian randomization (MR) has emerged as a valuable method for assessing causal relationships based on observational data. This approach utilizes genetic variants as instrumental variables (IVs) with the aim of providing a valid statistical test and estimation of causal effects in the presence of unmeasured confounders. MR has gained substantial popularity in recent years largely due to the success of genome-wide association studies. Many methods have been developed for MR; however, limited work has been done on evaluating GxE interaction. In this paper, we focus on two primary IV approaches: the two-stage predictor substitution and the two-stage residual inclusion, and extend them to accommodate GxE interaction under both the linear and logistic regression models for continuous and binary outcomes, respectively. Comprehensive simulation study and analytical derivations reveal that resolving the linear regression model is relatively straightforward. In contrast, the logistic regression model presents a considerably more intricate challenge, which demands additional effort.

An accelerated failure time regression model for illness-death data: A frailty approach.

This work presents a new model and estimation procedure for the illness-death survival data where the hazard functions follow accelerated failure time (AFT) models. A shared frailty variate induces positive dependence among failure times of a subject for handling the unobserved dependency between the nonterminal and the terminal failure times given the observed covariates. The motivation behind the proposed modeling approach is to leverage the well-known interpretability advantage of AFT models with respect to the observed covariates, while also benefiting from the simple and intuitive interpretation of the hazard functions. A semiparametric maximum likelihood estimation procedure is developed via a kernel smoothed-aided expectation-maximization algorithm, and variances are estimated by weighted bootstrap. We consider existing frailty-based illness-death models and place particular emphasis on highlighting the contribution of our current research. The breast cancer data of the Rotterdam tumor bank are analyzed using the proposed as well as existing illness-death models. The results are contrasted and evaluated based on a new graphical goodness-of-fit procedure. Simulation results and data analysis nicely demonstrate the practical utility of the shared frailty variate with the AFT regression model under the illness-death framework.

The Role of 68 Ga-FAPI PET/CT in Detection of Metastatic Lobular Breast Cancer.

PURPOSE: Invasive lobular breast cancer (ILC) may be hard to detect using conventional imaging modalities and usually shows less avidity to 18 F-FDG PET/CT. 68 Ga-fibroblast activation protein inhibitor (FAPI) PET/CT has shown promising results in detecting non- 18 F-FDG-avid cancers. We aimed to assess the feasibility of detecting metastatic disease in patients with non- 18 F-FDG-avid ILC. METHODS: This prospective study included patients with metastatic ILC, infiltrative to soft tissues, which was not 18 F-FDG avid. The patients underwent 68 Ga-FAPI PET/CT for evaluation, which was correlated with the fully diagnostic CT performed at the same time. RESULTS: Seven women (aged 57 ± 10 years) were included. Among the 30 organs and structures found to be involved by tumor, the number of findings observed by FAPI PET/CT was significantly higher than that observed by CT alone ( P = 0.022), especially in infiltrative soft tissue and serosal locations. CONCLUSIONS: This small pilot trial suggests a role for 68 Ga-FAPI PET/CT in ILC, which needs to be confirmed by subsequent trials.

Efficient study design to estimate population means with multiple measurement instruments.

Outcomes from studies assessing exposure often use multiple measurements. In previous work, using a model first proposed by Buonoccorsi (1991), we showed that combining direct (eg, biomarkers) and indirect (eg, self-report) measurements provides a more accurate picture of true exposure than estimates obtained when using a single type of measurement. In this article, we propose a tool for efficient design of studies that include both direct and indirect measurements of a relevant outcome. Based on data from a pilot or preliminary study, the tool, which is available online as a shiny app at https://michalbitan.shinyapps.io/shinyApp/, can be used to compute: (1) the sample size required for a statistical power analysis, while optimizing the percent of participants who should provide direct measures of exposure (biomarkers) in addition to the indirect (self-report) measures provided by all participants; (2) the ideal number of replicates; and (3) the allocation of resources to intervention and control arms. In addition we show how to examine the sensitivity of results to underlying assumptions. We illustrate our analysis using studies of tobacco smoke exposure and nutrition. In these examples, a near-optimal allocation of the resources can be found even if the assumptions are not precise.

Holocaust Experience and Mortality Patterns: 4-Decade Follow-up in a Population-Based Cohort.

Research on mortality associated with exposure to the Holocaust is relevant for a better understanding of the effects of genocides on survivors. To our knowledge, previous studies have not investigated the long-term cause-specific mortality of Holocaust survivors. We compared mortality rates among Israelis born in European countries controlled by the Nazis during World War II with those among Israelis of European descent who did not have this exposure. Records of 22,671 people (45% women; 5,042 survivors) from the population-based Jerusalem Perinatal Study (1964-1976) were linked to the Israeli Population Registry, which was updated through 2016. Cox models were used for analysis, with 2-sided tests of statistical significance. Risk of all-cause mortality was higher among exposed women (hazard ratio (HR) = 1.15, 95% confidence interval (CI): 1.05, 1.27) than in unexposed women. No association was found between Holocaust exposure and male all-cause mortality. In both sexes, survivors had higher cancer-specific mortality (HR = 1.17 (95% CI: 1.01, 1.35) in women and HR = 1.14 (95% CI: 1.01, 1.28) in men). Exposed men also had excess mortality due to coronary heart disease (HR = 1.39, 95% CI: 1.09, 1.77) and lower mortality from other known causes combined (HR = 0.86, 95% CI: 0.75, 0.99). In summary, experiencing the Holocaust was associated with excess all-cause and cancer-specific mortality in women and cancer- and coronary heart disease-specific mortality in men.

Practical implementation of frailty models in Mendelian risk prediction.

There are numerous statistical models used to identify individuals at high risk of cancer due to inherited mutations. Mendelian models predict future risk of cancer by using family history with estimated cancer penetrances (age- and sex-specific risk of cancer given the genotype of the mutations) and mutation prevalences. However, there is often residual risk heterogeneity across families even after accounting for the mutations in the model, due to environmental or unobserved genetic risk factors. We aim to improve Mendelian risk prediction by incorporating a frailty model that contains a family-specific frailty vector, impacting the cancer hazard function, to account for this heterogeneity. We use a discrete uniform population frailty distribution and implement a marginalized approach that averages each family's risk predictions over the family's frailty distribution. We apply the proposed approach to improve breast cancer prediction in BRCAPRO, a Mendelian model that accounts for inherited mutations in the BRCA1 and BRCA2 genes to predict breast and ovarian cancer. We evaluate the proposed model's performance in simulations and real data from the Cancer Genetics Network and show improvements in model calibration and discrimination. We also discuss alternative approaches for incorporating frailties and their strengths and limitations.

Nonparametric Adjustment for Measurement Error in Time-to-Event Data: Application to Risk Prediction Models.

Mismeasured time to event data used as a predictor in risk prediction models will lead to inaccurate predictions. This arises in the context of self-reported family history, a time to event predictor often measured with error, used in Mendelian risk prediction models. Using validation data, we propose a method to adjust for this type of error. We estimate the measurement error process using a nonparametric smoothed Kaplan-Meier estimator, and use Monte Carlo integration to implement the adjustment. We apply our method to simulated data in the context of both Mendelian and multivariate survival prediction models. Simulations are evaluated using measures of mean squared error of prediction (MSEP), area under the response operating characteristics curve (ROC-AUC), and the ratio of observed to expected number of events. These results show that our method mitigates the effects of measurement error mainly by improving calibration and total accuracy. We illustrate our method in the context of Mendelian risk prediction models focusing on misreporting of breast cancer, fitting the measurement error model on data from the University of California at Irvine, and applying our method to counselees from the Cancer Genetics Network. We show that our method improves overall calibration, especially in low risk deciles.

On Estimation of the Hazard Function from Population-based Case-Control Studies.

The population-based case-control study design has been widely used for studying the etiology of chronic diseases. It is well established that the Cox proportional hazards model can be adapted to the case-control study and hazard ratios can be estimated by (conditional) logistic regression model with time as either a matched set or a covariate (Prentice and Breslow, 1978). However, the baseline hazard function, a critical component in absolute risk assessment, is unidentifiable, because the ratio of cases and controls is controlled by the investigators and does not reflect the true disease incidence rate in the population. In this paper we propose a simple and innovative approach, which makes use of routinely collected family history information, to estimate the baseline hazard function for any logistic regression model that is fit to the risk factor data collected on cases and controls. We establish that the proposed baseline hazard function estimator is consistent and asymptotically normal and show via simulation that it performs well in finite samples. We illustrate the proposed method by a population-based case-control study of prostate cancer where the association of various risk factors is assessed and the family history information is used to estimate the baseline hazard function.

Heritability Estimation using a Regularized Regression Approach (HERRA): Applicable to continuous, dichotomous or age-at-onset outcome.

The popular Genome-wide Complex Trait Analysis (GCTA) software uses the random-effects models for estimating the narrow-sense heritability based on GWAS data of unrelated individuals without knowing and identifying the causal loci. Many methods have since extended this approach to various situations. However, since the proportion of causal loci among the variants is typically very small and GCTA uses all variants to calculate the similarities among individuals, the estimation of heritability may be unstable, resulting in a large variance of the estimates. Moreover, if the causal SNPs are not genotyped, GCTA sometimes greatly underestimates the true heritability. We present a novel narrow-sense heritability estimator, named HERRA, using well-developed ultra-high dimensional machine-learning methods, applicable to continuous or dichotomous outcomes, as other existing methods. Additionally, HERRA is applicable to time-to-event or age-at-onset outcome, which, to our knowledge, no existing method can handle. Compared to GCTA and LDAK for continuous and binary outcomes, HERRA often has a smaller variance, and when causal SNPs are not genotyped, HERRA has a much smaller empirical bias. We applied GCTA, LDAK and HERRA to a large colorectal cancer dataset using dichotomous outcome (4,312 cases, 4,356 controls, genotyped using Illumina 300K), the respective heritability estimates of GCTA, LDAK and HERRA are 0.068 (SE = 0.017), 0.072 (SE = 0.021) and 0.110 (SE = 5.19 x 10-3). HERRA yields over 50% increase in heritability estimate compared to GCTA or LDAK.

Propensity scores with misclassified treatment assignment: a likelihood-based adjustment.

Propensity score methods are widely used in comparative effectiveness research using claims data. In this context, the inaccuracy of procedural or billing codes in claims data frequently misclassifies patients into treatment groups, that is, the treatment assignment ($T$) is often measured with error. In the context of a validation data where treatment assignment is accurate, we show that misclassification of treatment assignment can impact three distinct stages of a propensity score analysis: (i) propensity score estimation; (ii) propensity score implementation; and (iii) outcome analysis conducted conditional on the estimated propensity score and its implementation. We examine how the error in $T$ impacts each stage in the context of three common propensity score implementations: subclassification, matching, and inverse probability of treatment weighting (IPTW). Using validation data, we propose a two-step likelihood-based approach which fully adjusts for treatment misclassification bias under subclassification. This approach relies on two common measurement error-assumptions; non-differential measurement error and transportability of the measurement error model. We use simulation studies to assess the performance of the adjustment under subclassification, and also investigate the method's performance under matching or IPTW. We apply the methods to Medicare Part A hospital claims data to estimate the effect of resection versus biopsy on 1-year mortality among $10\,284$ Medicare beneficiaries diagnosed with brain tumors. The ICD9 billing codes from Medicare Part A inaccurately reflect surgical treatment, but SEER-Medicare validation data are available with more accurate information.

A fully nonparametric estimator of the marginal survival function based on case-control clustered age-at-onset data.

Consider a popular case-control family study where individuals with a disease under study (case probands) and individuals who do not have the disease (control probands) are randomly sampled from a well-defined population. Possibly right-censored age at onset and disease status are observed for both probands and their relatives. For example, case probands are men diagnosed with prostate cancer, control probands are men free of prostate cancer, and the prostate cancer history of the fathers of the probands is also collected. Inherited genetic susceptibility, shared environment, and common behavior lead to correlation among the outcomes within a family. In this article, a novel nonparametric estimator of the marginal survival function is provided. The estimator is defined in the presence of intra-cluster dependence, and is based on consistent smoothed kernel estimators of conditional survival functions. By simulation, it is shown that the proposed estimator performs very well in terms of bias. The utility of the estimator is illustrated by the analysis of case-control family data of early onset prostate cancer. To our knowledge, this is the first article that provides a fully nonparametric marginal survival estimator based on case-control clustered age-at-onset data.

Function of cancer associated genes revealed by modern univariate and multivariate association tests.

Copy number variation (CNV) plays a role in pathogenesis of many human diseases, especially cancer. Several whole genome CNV association studies have been performed for the purpose of identifying cancer associated CNVs. Here we undertook a novel approach to whole genome CNV analysis, with the goal being identification of associations between CNV of different genes (CNV-CNV) across 60 human cancer cell lines. We hypothesize that these associations point to the roles of the associated genes in cancer, and can be indicators of their position in gene networks of cancer-driving processes. Recent studies show that gene associations are often non-linear and non-monotone. In order to obtain a more complete picture of all CNV associations, we performed omnibus univariate analysis by utilizing dCov, MIC, and HHG association tests, which are capable of detecting any type of association, including non-monotone relationships. For comparison we used Spearman and Pearson association tests, which detect only linear or monotone relationships. Application of dCov, MIC and HHG tests resulted in identification of twice as many associations compared to those found by Spearman and Pearson alone. Interestingly, most of the new associations were detected by the HHG test. Next, we utilized dCov's and HHG's ability to perform multivariate analysis. We tested for association between genes of unknown function and known cancer-related pathways. Our results indicate that multivariate analysis is much more effective than univariate analysis for the purpose of ascribing biological roles to genes of unknown function. We conclude that a combination of multivariate and univariate omnibus association tests can reveal significant information about gene networks of disease-driving processes. These methods can be applied to any large gene or pathway dataset, allowing more comprehensive analysis of biological processes.

The impact of covariate measurement error on risk prediction.

In the development of risk prediction models, predictors are often measured with error. In this paper, we investigate the impact of covariate measurement error on risk prediction. We compare the prediction performance using a costly variable measured without error, along with error-free covariates, to that of a model based on an inexpensive surrogate along with the error-free covariates. We consider continuous error-prone covariates with homoscedastic and heteroscedastic errors, and also a discrete misclassified covariate. Prediction performance is evaluated by the area under the receiver operating characteristic curve (AUC), the Brier score (BS), and the ratio of the observed to the expected number of events (calibration). In an extensive numerical study, we show that (i) the prediction model with the error-prone covariate is very well calibrated, even when it is mis-specified; (ii) using the error-prone covariate instead of the true covariate can reduce the AUC and increase the BS dramatically; (iii) adding an auxiliary variable, which is correlated with the error-prone covariate but conditionally independent of the outcome given all covariates in the true model, can improve the AUC and BS substantially. We conclude that reducing measurement error in covariates will improve the ensuing risk prediction, unless the association between the error-free and error-prone covariates is very high. Finally, we demonstrate how a validation study can be used to assess the effect of mismeasured covariates on risk prediction. These concepts are illustrated in a breast cancer risk prediction model developed in the Nurses' Health Study.

Calibrated predictions for multivariate competing risks models.

Prediction models for time-to-event data play a prominent role in assessing the individual risk of a disease, such as cancer. Accurate disease prediction models provide an efficient tool for identifying individuals at high risk, and provide the groundwork for estimating the population burden and cost of disease and for developing patient care guidelines. We focus on risk prediction of a disease in which family history is an important risk factor that reflects inherited genetic susceptibility, shared environment, and common behavior patterns. In this work family history is accommodated using frailty models, with the main novel feature being allowing for competing risks, such as other diseases or mortality. We show through a simulation study that naively treating competing risks as independent right censoring events results in non-calibrated predictions, with the expected number of events overestimated. Discrimination performance is not affected by ignoring competing risks. Our proposed prediction methodologies correctly account for competing events, are very well calibrated, and easy to implement.

A regularization corrected score method for nonlinear regression models with covariate error.

Many regression analyses involve explanatory variables that are measured with error, and failing to account for this error is well known to lead to biased point and interval estimates of the regression coefficients. We present here a new general method for adjusting for covariate error. Our method consists of an approximate version of the Stefanski-Nakamura corrected score approach, using the method of regularization to obtain an approximate solution of the relevant integral equation. We develop the theory in the setting of classical likelihood models; this setting covers, for example, linear regression, nonlinear regression, logistic regression, and Poisson regression. The method is extremely general in terms of the types of measurement error models covered, and is a functional method in the sense of not involving assumptions on the distribution of the true covariate. We discuss the theoretical properties of the method and present simulation results in the logistic regression setting (univariate and multivariate). For illustration, we apply the method to data from the Harvard Nurses' Health Study concerning the relationship between physical activity and breast cancer mortality in the period following a diagnosis of breast cancer.

Frailty Models for Familial Risk with Application to Breast Cancer.

In evaluating familial risk for disease we have two main statistical tasks: assessing the probability of carrying an inherited genetic mutation conferring higher risk; and predicting the absolute risk of developing diseases over time, for those individuals whose mutation status is known. Despite substantial progress, much remains unknown about the role of genetic and environmental risk factors, about the sources of variation in risk among families that carry high-risk mutations, and about the sources of familial aggregation beyond major Mendelian effects. These sources of heterogeneity contribute substantial variation in risk across families. In this paper we present simple and efficient methods for accounting for this variation in familial risk assessment. Our methods are based on frailty models. We implemented them in the context of generalizing Mendelian models of cancer risk, and compared our approaches to others that do not consider heterogeneity across families. Our extensive simulation study demonstrates that when predicting the risk of developing a disease over time conditional on carrier status, accounting for heterogeneity results in a substantial improvement in the area under the curve of the receiver operating characteristic. On the other hand, the improvement for carriership probability estimation is more limited. We illustrate the utility of the proposed approach through the analysis of BRCA1 and BRCA2 mutation carriers in the Washington Ashkenazi Kin-Cohort Study of Breast Cancer.

Bias correction in the hierarchical likelihood approach to the analysis of multivariate survival data.

Frailty models are useful for measuring unobserved heterogeneity in risk of failures across clusters, providing cluster-specific risk prediction. In a frailty model, the latent frailties shared by members within a cluster are assumed to act multiplicatively on the hazard function. In order to obtain parameter and frailty variate estimates, we consider the hierarchical likelihood (H-likelihood) approach (Ha, Lee and Song, 2001. Hierarchical-likelihood approach for frailty models. Biometrika 88, 233-243) in which the latent frailties are treated as "parameters" and estimated jointly with other parameters of interest. We find that the H-likelihood estimators perform well when the censoring rate is low, however, they are substantially biased when the censoring rate is moderate to high. In this paper, we propose a simple and easy-to-implement bias correction method for the H-likelihood estimators under a shared frailty model. We also extend the method to a multivariate frailty model, which incorporates complex dependence structure within clusters. We conduct an extensive simulation study and show that the proposed approach performs very well for censoring rates as high as 80%. We also illustrate the method with a breast cancer data set. Since the H-likelihood is the same as the penalized likelihood function, the proposed bias correction method is also applicable to the penalized likelihood estimators.

Missing genetic information in case-control family data with general semi-parametric shared frailty model.

Case-control family data are now widely used to examine the role of gene-environment interactions in the etiology of complex diseases. In these types of studies, exposure levels are obtained retrospectively and, frequently, information on most risk factors of interest is available on the probands but not on their relatives. In this work we consider correlated failure time data arising from population-based case-control family studies with missing genotypes of relatives. We present a new method for estimating the age-dependent marginalized hazard function. The proposed technique has two major advantages: (1) it is based on the pseudo full likelihood function rather than a pseudo composite likelihood function, which usually suffers from substantial efficiency loss; (2) the cumulative baseline hazard function is estimated using a two-stage estimator instead of an iterative process. We assess the performance of the proposed methodology with simulation studies, and illustrate its utility on a real data example.

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.