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.

Causal inference for semi-competing risks data.

The causal effects of Apolipoprotein E $\epsilon4$ allele (APOE) on late-onset Alzheimer's disease (AD) and death are complicated to define because AD may occur under one intervention but not under the other, and because AD occurrence may affect age of death. In this article, this dual outcome scenario is studied using the semi-competing risks framework for time-to-event data. Two event times are of interest: a nonterminal event time (age at AD diagnosis), and a terminal event time (age at death). AD diagnosis time is observed only if it precedes death, which may occur before or after AD. We propose new estimands for capturing the causal effect of APOE on AD and death. Our proposal is based on a stratification of the population with respect to the order of the two events. We present a novel assumption utilizing the time-to-event nature of the data, which is more flexible than the often-invoked monotonicity assumption. We derive results on partial identifiability, suggest a sensitivity analysis approach, and give conditions under which full identification is possible. Finally, we present and implement nonparametric and semiparametric estimation methods under right-censored semi-competing risks data for studying the complex effect of APOE on AD and death.

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.

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.

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.

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.

Association Between BNT162b2 Vaccination and Incidence of SARS-CoV-2 Infection in Pregnant Women.

Importance: Data on BNT162b2 messenger RNA (mRNA) vaccine (Pfizer-BioNTech) effectiveness and safety in pregnancy are currently lacking because pregnant women were excluded from the phase 3 trial. Objective: To assess the association between receipt of BNT162b2 mRNA vaccine and risk of SARS-CoV-2 infection among pregnant women. Design, Setting, and Participants: This was a retrospective cohort study within the pregnancy registry of a large state-mandated health care organization in Israel. Pregnant women vaccinated with a first dose from December 19, 2020, through February 28, 2021, were 1:1 matched to unvaccinated women by age, gestational age, residential area, population subgroup, parity, and influenza immunization status. Follow-up ended on April 11, 2021. Exposures: Exposure was defined by receipt of the BNT162b2 mRNA vaccine. To maintain comparability, nonexposed women who were subsequently vaccinated were censored 10 days after their exposure, along with their matched pair. Main Outcomes and Measures: The primary outcome was polymerase chain reaction-validated SARS-CoV-2 infection at 28 days or more after the first vaccine dose. Results: The cohort included 7530 vaccinated and 7530 matched unvaccinated women, 46% and 33% in the second and third trimester, respectively, with a mean age of 31.1 years (SD, 4.9 years). The median follow-up for the primary outcome was 37 days (interquartile range, 21-54 days; range, 0-70). There were 118 SARS-CoV-2 infections in the vaccinated group and 202 in the unvaccinated group. Among infected women, 88 of 105 (83.8%) were symptomatic in the vaccinated group vs 149 of 179 (83.2%) in the unvaccinated group (P ≥ .99). During 28 to 70 days of follow-up, there were 10 infections in the vaccinated group and 46 in the unvaccinated group. The hazards of infection were 0.33% vs 1.64% in the vaccinated and unvaccinated groups, respectively, representing an absolute difference of 1.31% (95% CI, 0.89%-1.74%), with an adjusted hazard ratio of 0.22 (95% CI, 0.11-0.43). Vaccine-related adverse events were reported by 68 patients; none was severe. The most commonly reported symptoms were headache (n = 10, 0.1%), general weakness (n = 8, 0.1%), nonspecified pain (n = 6, <0.1%), and stomachache (n = 5, <0.1%). Conclusions and Relevance: In this retrospective cohort study of pregnant women, BNT162b2 mRNA vaccination compared with no vaccination was associated with a significantly lower risk of SARS-CoV-2 infection. Interpretation of study findings is limited by the observational design.

Estimating the intervention effect in calibration substudies.

Exposure assessment is often subject to measurement errors. We consider here the analysis of studies aimed at reducing exposure to potential health hazards, in which exposure is the outcome variable. In these studies, the intervention effect may be estimated using either biomarkers or self-report data, but it is not common to combine these measures of exposure. Bias in the self-reported measures of exposure is a well-known fact; however, only few studies attempt to correct it. Recently, Keogh et al addressed this problem, presenting a model for measurement error in this setting and investigating how self-report and biomarker data can be combined. Keogh et al find the maximum likelihood estimate for the intervention effect in their model via direct numerical maximization of the likelihood. Here, we exploit an alternative presentation of the model that leads us to a closed formula for the MLE and also for its variance, when the number of biomarker replicates is the same for all subjects in the substudy. The variance formula enables efficient design of such intervention studies. When the number of biomarker replicates is not constant, our approach can be used along with the EM-algorithm to quickly compute the MLE. We compare the MLE to Buonaccorsi's method (Buonaccorsi, 1996) and find that they have similar efficiency when most subjects have biomarker data, but that the MLE has clear advantages when only a small fraction of subjects has biomarker data. This conclusion extends the findings of Keogh et al (2016) and has practical importance for efficiently designing studies.

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.

A quantile regression model for failure-time data with time-dependent covariates.

Since survival data occur over time, often important covariates that we wish to consider also change over time. Such covariates are referred as time-dependent covariates. Quantile regression offers flexible modeling of survival data by allowing the covariates to vary with quantiles. This article provides a novel quantile regression model accommodating time-dependent covariates, for analyzing survival data subject to right censoring. Our simple estimation technique assumes the existence of instrumental variables. In addition, we present a doubly-robust estimator in the sense of Robins and Rotnitzky (1992, Recovery of information and adjustment for dependent censoring using surrogate markers. In: Jewell, N. P., Dietz, K. and Farewell, V. T. (editors), AIDS Epidemiology. Boston: Birkhaäuser, pp. 297-331.). The asymptotic properties of the estimators are rigorously studied. Finite-sample properties are demonstrated by a simulation study. The utility of the proposed methodology is demonstrated using the Stanford heart transplant dataset.

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.

General Semiparametric Shared Frailty Model: Estimation and Simulation with frailtySurv.

The R package frailtySurv for simulating and fitting semi-parametric shared frailty models is introduced. Package frailtySurv implements semi-parametric consistent estimators for a variety of frailty distributions, including gamma, log-normal, inverse Gaussian and power variance function, and provides consistent estimators of the standard errors of the parameters' estimators. The parameters' estimators are asymptotically normally distributed, and therefore statistical inference based on the results of this package, such as hypothesis testing and confidence intervals, can be performed using the normal distribution. Extensive simulations demonstrate the flexibility and correct implementation of the estimator. Two case studies performed with publicly available datasets demonstrate applicability of the package. In the Diabetic Retinopathy Study, the onset of blindness is clustered by patient, and in a large hard drive failure dataset, failure times are thought to be clustered by the hard drive manufacturer and model.

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.

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.

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.

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.

Conditional and Marginal Estimates in Case-Control Family Data - Extensions and Sensitivity Analyses.

This work considers two specific estimation techniques for the family specific proportional hazards model and for the population-averaged proportional hazards model. So far, these two estimation procedures were presented and studied under the gamma frailty distribution mainly because of its simple interpretation and mathematical tractability. Modifications of both procedures for other frailty distributions, such as inverse Gaussian, positive stable and a specific case of discrete distribution, are presented. By extensive simulations, it is shown that under the family specific proportional hazards model, the gamma frailty model appears to be robust to frailty distribution misspecification in both bias and efficiency loss in the marginal parameters. The population-averaged proportional hazards model, is found to be robust under the gamma frailty model misspecification only under moderate or weak dependency within cluster members.

COVID-19 mRNA Vaccination: Age and Immune Status and Its Association with Axillary Lymph Node PET/CT Uptake.

With hundreds of millions of coronavirus disease 2019 (COVID-19) messenger RNA (mRNA)-based vaccine doses planned to be delivered worldwide in the upcoming months, it is important to recognize PET/CT findings in recently vaccinated immunocompetent or immunocompromised patients. We aimed to assess PET/CT uptake in the deltoid muscle and axillary lymph nodes of patients who received a COVID-19 mRNA-based vaccine and to evaluate its association with patient age and immune status. Methods: All consecutive adults who underwent PET/CT scans with any radiotracer at our center during the first month of a national COVID-19 vaccination rollout (between December 23, 2020, and January 27, 2021) and had received the vaccination were included. Data on clinical status, laterality, and time from vaccination were prospectively collected, retrospectively analyzed, and correlated with deltoid muscle and axillary lymph node uptake. Results: Of 426 eligible subjects (median age, 67 ± 12 y; 49% female), 377 (88%) underwent PET/CT with 18F-FDG, and positive axillary lymph node uptake was seen in 45% of them. Multivariate logistic regression analysis revealed a strong inverse association between positive 18F-FDG uptake in ipsilateral lymph nodes and patient age (odds ratio [OR], 0.57; 95% CI, 0.45-0.72; P < 0.001), immunosuppressive treatment (OR, 0.37; 95% CI, 0.20-0.64; P = 0.003), and presence of hematologic disease (OR, 0.44; 95% CI, 0.24-0.8; P = 0.021). No such association was found for deltoid muscle uptake. The number of days from the last vaccination and the number of vaccine doses were also significantly associated with increased odds of positive lymph node uptake. Conclusion: After mRNA-based COVID-19 vaccination, a high proportion of patients showed ipsilateral lymph node axillary uptake, which was more common in immunocompetent patients. This information will help with the recognition of PET/CT pitfalls and may hint about the patient's immune response to the vaccine.

Frailty-based competing risks model for multivariate survival data.

In this work, we provide a new class of frailty-based competing risks models for clustered failure times data. This class is based on expanding the competing risks model of Prentice et al. (1978, Biometrics 34, 541-554) to incorporate frailty variates, with the use of cause-specific proportional hazards frailty models for all the causes. Parametric and nonparametric maximum likelihood estimators are proposed. The main advantages of the proposed class of models, in contrast to the existing models, are: (1) the inclusion of covariates; (2) the flexible structure of the dependency among the various types of failure times within a cluster; and (3) the unspecified within-subject dependency structure. The proposed estimation procedures produce the most efficient parametric and semiparametric estimators and are easy to implement. Simulation studies show that the proposed methods perform very well in practical situations.