Estimating Risks and Relative Risks in Case-Base Studies under the Assumptions of Gene-Environment Independence and Hardy-Weinberg Equilibrium

Many diseases result from the interactions between genes and the environment. An efficient method has been proposed for a case-control study to estimate the genetic and environmental main effects and their interactions, which exploits the assumptions of gene-environment independence and Hardy-Weinberg equilibrium. To estimate the absolute and relative risks, one needs to resort to an alternative design: the case-base study. In this paper, the authors show how to analyze a case-base study under the above dual assumptions. This approach is based on a conditional logistic regression of case-counterfactual controls matched data. It can be easily fitted with readily available statistical packages. When the dual assumptions are met, the method is approximately unbiased and has adequate coverage probabilities for confidence intervals. It also results in smaller variances and shorter confidence intervals as compared with a previous method for a case-base study which imposes neither assumption.     

Hierarchical Modeling for Estimating Relative Risks of Rare Genetic Variants: Properties of the Pseudo‐Likelihood Method

Summary Many major genes have been identified that strongly influence the risk of cancer. However, there are typically many different mutations that can occur in the gene, each of which may or may not confer increased risk. It is critical to identify which specific mutations are harmful, and which ones are harmless, so that individuals who learn from genetic testing that they have a mutation can be appropriately counseled. This is a challenging task, since new mutations are continually being identified, and there is typically relatively little evidence available about each individual mutation. In an earlier article, we employed hierarchical modeling ( Capanu et al., 2008 , Statistics in Medicine 27 , 1973–1992) using the pseudo‐likelihood and Gibbs sampling methods to estimate the relative risks of individual rare variants using data from a case–control study and showed that one can draw strength from the aggregating power of hierarchical models to distinguish the variants that contribute to cancer risk. However, further research is needed to validate the application of asymptotic methods to such sparse data. In this article, we use simulations to study in detail the properties of the pseudo‐likelihood method for this purpose. We also explore two alternative approaches: pseudo‐likelihood with correction for the variance component estimate as proposed by Lin and Breslow (1996, Journal of the American Statistical Association 91 , 1007–1016) and a hybrid pseudo‐likelihood approach with Bayesian estimation of the variance component. We investigate the validity of these hierarchical modeling techniques by looking at the bias and coverage properties of the estimators as well as at the efficiency of the hierarchical modeling estimates relative to that of the maximum likelihood estimates. The results indicate that the estimates of the relative risks of very sparse variants have small bias, and that the estimated 95% confidence intervals are typically anti‐conservative, though the actual coverage rates are generally above 90%. The widths of the confidence intervals narrow as the residual variance in the second‐stage model is reduced. The results also show that the hierarchical modeling estimates have shorter confidence intervals relative to estimates obtained from conventional logistic regression, and that these relative improvements increase as the variants become more rare.     

Studies of radon-exposed miner cohorts using a biologically based model: comparison of current Czech and French data with historic data from China and Colorado

Cosmic radiation is an occupational risk factor for commercial aircrews. In this large European cohort study (ESCAPE) its association with cancer mortality was investigated on the basis of individual effective dose estimates for 19,184 male pilots. Mean annual doses were in the range of 2–5 mSv and cumulative lifetime doses did not exceed 80 mSv. All-cause and all-cancer mortality was low for all exposure categories. A significant negative risk trend for all-cause mortality was seen with increasing dose. Neither external and internal comparisons nor nested case-control analyses showed any substantially increased risks for cancer mortality due to ionizing radiation. However, the number of deaths for specific types of cancer was low and the confidence intervals of the risk estimates were rather wide. Difficulties in interpreting mortality risk estimates for time-dependent exposures are discussed.Abbreviations CI confidence interval - CLL chronic lymphatic leukemia - RRC radiation-related cancers - NRRC non-radiation-related cancers - RR relative risk - SMR standardized mortality ratio     

Estimates of absolute cause-specific risk in cohort studies

In this paper we study methods for estimating the absolute risk of an event c1 in a time interval [t1, t2], given that the individual is at risk at t1 and given the presence of competing risks. We discuss some advantages of absolute risk for measuring the prognosis of an individual patient and some difficulties of interpretation for comparing two treatment groups. We also discuss the importance of the concept of absolute risk in evaluating public health measures to prevent disease. Variance calculations permit one to gauge the relative importance of random and systematic errors in estimating absolute risk. Efficiency calculations were also performed to determine how much precision is lost in estimating absolute risk with a nonparametric approach or with a flexible piecewise exponential model rather than a simple exponential model, and other calculations indicate the extent of bias that arises with the simple exponential model when that model is invalid. Such calculations suggest that the more flexible models will be useful in practice. Simulations confirm that asymptotic methods yield reliable variance estimates and confidence interval coverages in samples of practical size.     

Phylogenetic dating with confidence intervals using mean path lengths

The mean path length (MPL) method, a simple method for dating nodes in a phylogenetic tree, is presented. For small trees the age estimates and corresponding confidence intervals, calibrated with fossil data, can be calculated by hand, and for larger trees a computer program gives the results instantaneously (a Pascal program is available upon request). Necessary input data are a rooted phylogenetic tree with edge lengths (internode lengths) approximately corresponding to the number of substitutions between the nodes. Given this, the MPL method produces relative age estimates with confidence intervals for all nodes of the tree. With the age of one or several nodes of the tree being known from reference fossils, the relative age estimates induce absolute age estimates and confidence intervals of the nodes of the tree. The MPL method relies on the assumptions that substitutions occur randomly and independently in different sites in the DNA sequence and that the substitution rates are approximately constant in time, i.e., assuming a molecular clock. A method is presented for identification of the nodes in the tree at which significant deviations from the clock assumption occur, such that dating may be done using different rates in different parts of the tree. The MPL method is illustrated with the Liliales, a group of monocot flowering plants.     

Confidence Intervals for Relative Risks in Disease Mapping

Several analysis of the geographic variation of mortality rates in space have been proposed in the literature. Poisson models allowing the incorporation of random effects to model extra‐variability are widely used. The typical modelling approach uses normal random effects to accommodate local spatial autocorrelation. When spatial autocorrelation is absent but overdispersion persists, a discrete mixture model is an alternative approach. However, a technique for identifying regions which have significant high or low risk in any given area has not been developed yet when using the discrete mixture model. Taking into account the importance that this information provides to the epidemiologists to formulate hypothesis related to the potential risk factors affecting the population, different procedures for obtaining confidence intervals for relative risks are derived in this paper. These methods are the standard information‐based method and other four, all based on bootstrap techniques, namely the asymptotic‐bootstrap, the percentile‐bootstrap, the BC‐bootstrap and the modified information‐based method. All of them are compared empirically by their application to mortality data due to cardiovascular diseases in women from Navarra, Spain, during the period 1988–1994. In the small area example considered here, we find that the information‐based method is sensible at estimating standard errors of the component means in the discrete mixture model but it is not appropriate for providing standard errors of the estimated relative risks and hence, for constructing confidence intervals for the relative risk associated to each region. Therefore, the bootstrap‐based methods are recommended for this matter. More specifically, the BC method seems to provide better coverage probabilities in the case studied, according to a small scale simulation study that has been carried out using a scenario as encountered in the analysis of the real data.     

Comparison of confidence intervals for adjusted attributable risk estimates under multinomial sampling

The epidemiologic concept of the adjusted attributable risk is a useful approach to quantitatively describe the importance of risk factors on the population level. It measures the proportional reduction in disease probability when a risk factor is eliminated from the population, accounting for effects of confounding and effect-modification by nuisance variables. The computation of asymptotic variance estimates for estimates of the adjusted attributable risk is often done by applying the delta method. Investigations on the delta method have shown, however, that the delta method generally tends to underestimate the standard error, leading to biased confidence intervals. We compare confidence intervals for the adjusted attributable risk derived by applying computer intensive methods like the bootstrap or jackknife to confidence intervals based on asymptotic variance estimates using an extensive Monte Carlo simulation and within a real data example from a cohort study in cardiovascular disease epidemiology. Our results show that confidence intervals based on bootstrap and jackknife methods outperform intervals based on asymptotic theory. Best variants of computer intensive confidence intervals are indicated for different situations.     

On confidence intervals for genotype relative risks and attributable risks from case parent trio designs for candidate-gene studies

Scherag et al. [Hum Hered 2002;54:210-217] recently proposed point estimates and asymptotic as well as exact confidence intervals for genotype relative risks (GRRs) and the attributable risk (AR) in case parent trio designs using single nucleotide polymorphism (SNP) data. The aim of this study was the investigation of coverage probabilities and bias in estimates if the marker locus is not identical to the disease locus. Using a variety of parameter constellations, including marker allele frequencies identical to and different from the SNP at the disease locus, we performed an analytical study to quantify the bias and a Monte-Carlo simulation study for quantifying both bias and coverage probabilities. No bias was observed if marker and trait locus coincided. Two parameters had a strong impact on coverage probabilities of confidence intervals and bias in point estimates if they did not coincide: the linkage disequilibrium (LD) parameter delta and the allele frequency at the marker SNP. If marker allele frequencies were different from the allele frequencies at the functional SNP, substantial biases occurred. Further, if delta between the marker and the disease locus was lower than the maximum possible delta, estimates were also biased. In general, biases were towards the null hypothesis for both GRRs and AR. If one GRR was not increased, as e.g. in a recessive genetic model, biases away from the null could be observed. If both GRRs were in identical directions and if both were substantially larger than 1, the bias always was towards the null. When applying point estimates and confidence intervals for GRRs and AR in candidate gene studies, great care is needed. Effect estimates are substantially biased towards the null if either the allele frequencies at the marker SNP and the true disease locus are different or if the LD between the marker SNP and the disease locus is not at its maximum. A bias away from the null occurs only in uncommon study situations; it is small and can therefore be ignored for applications.     

Cancer mortality following in utero exposure among offspring of female mayak worker cohort members

Little is known about long-term cancer risks following in utero radiation exposure. We evaluated the association between in utero radiation exposure and risk of solid cancer and leukemia mortality among 8,000 offspring, born from 1948-1988, of female workers at the Mayak Nuclear Facility in Ozyorsk, Russia. Mother's cumulative gamma radiation uterine dose during pregnancy served as a surrogate for fetal dose. We used Poisson regression methods to estimate relative risks (RRs) and 95% confidence intervals (CIs) of solid cancer and leukemia mortality associated with in utero radiation exposure and to quantify excess relative risks (ERRs) as a function of dose. Using currently available dosimetry information, 3,226 (40%) offspring were exposed in utero (mean dose = 54.5 mGy). Based on 75 deaths from solid cancers (28 exposed) and 12 (6 exposed) deaths from leukemia, in utero exposure status was not significantly associated with solid cancer: RR = 0.94, 95% CI 0.58 to 1.49; ERR/Gy = -0.1 (95% CI < -0.1 to 4.1), or leukemia mortality; RR = 1.65, 95% CI 0.52 to 5.27; ERR/Gy = -0.8 (95% CI < -0.8 to 46.9). These initial results provide no evidence that low-dose gamma in utero radiation exposure increases solid cancer or leukemia mortality risk, but the data are not inconsistent with such an increase. As the offspring cohort is relatively young, subsequent analyses based on larger case numbers are expected to provide more precise estimates of adult cancer mortality risk following in utero exposure to ionizing radiation.     

Estimating relative risks from significant family-based association studies

Two approaches are described to estimate relative risks from significant family-based association studies. They can be used to obtain either point estimates or confidence regions. The approaches are evaluated by a simulation study and illustrated by application to a real data set. It is shown that both approaches largely reduce the bias in the relative risk estimates which can occur in case that the significant outcome of the study from which the relative risks are estimated is ignored.     

Prepregnancy Obesity and Risks of Stillbirth

BackgroundWe examined the association of maternal obesity with risk of stillbirth, focusing on whether the pattern of results varied by gestational age or maternal race-ethnicity or parity.MethodsAnalyses included 4,012 stillbirths and 1,121,234 liveborn infants delivered in California from 2007–2010. We excluded stillbirths due to congenital anomalies, women with hypertensive disorders or diabetes, and plural births, to focus on fetuses and women without these known contributing conditions. We used Poisson regression to estimate relative risks (RR) and 95% confidence intervals (CI). Separate models were run for stillbirths delivered at 20–23, 24–27, 28–31, 32–36, 37–41 weeks, relative to liveborn deliveries at 37–41 weeks.ResultsFor stillbirth at 20–23 weeks, RRs were elevated for all race-ethnicity and parity groups. The RR for a 20-unit change in BMI (which reflects the approximate BMI difference between a normal weight and an Obese III woman) was 3.5 (95% CI 2.2, 5.6) for nulliparous white women and ranged from 1.8 to 5.0 for other sub-groups. At 24–27 weeks, the association was significant (p<0.05) only for multiparous non-Hispanic whites; at 28–31 weeks, for multiparous whites and nulliparous whites and blacks; at 32–36 weeks, for multiparous whites and nulliparous blacks; and at 37–41 weeks, for all groups except nulliparous blacks. The pattern of results was similar when restricted to stillbirths due to unknown causes and somewhat stronger when restricted to stillbirths attributable to obstetric causes.ConclusionIncreased risks were observed across all gestational ages, and some evidence of heterogeneity of the associations was observed by race-ethnicity and parity.     

Body Mass Index and All-Cause Mortality in a Large Prospective Cohort of White and Black U.S. Adults

Remaining controversies on the association between body mass index (BMI) and mortality include the effects of smoking and prevalent disease on the association, whether overweight is associated with higher mortality rates, differences in associations by race and the optimal age at which BMI predicts mortality. To assess the relative risk (RR) of mortality by BMI in Whites and Blacks among subgroups defined by smoking, prevalent disease, and age, 891,572 White and 38,119 Black men and women provided height, weight and other information when enrolled in the Cancer Prevention Study II in 1982. Over 28 years of follow-up, there were 434,400 deaths in Whites and 18,702 deaths in Blacks. Cox proportional-hazards regression was used to estimate multivariable-adjusted relative risks (RR) and 95% confidence intervals (CI). Smoking and prevalent disease status significantly modified the BMI-mortality relationship in Whites and Blacks; higher BMI was most strongly associated with higher risk of mortality among never smokers without prevalent disease. All levels of overweight and obesity were associated with a statistically significantly higher risk of mortality compared to the reference category (BMI 22.5–24.9 kg/m²), except among Black women where risk was elevated but not statistically significant in the lower end of overweight. Although absolute mortality rates were higher in Blacks than Whites within each BMI category, relative risks (RRs) were similar between race groups for both men and women (p-heterogeneity by race  = 0.20 for men and 0.23 for women). BMI was most strongly associated with mortality when reported before age 70 years. Results from this study demonstrate for the first time that the BMI-mortality relationship differs for men and women who smoke or have prevalent disease compared to healthy never-smokers. These findings further support recommendations for maintaining a BMI between 20–25 kg/m² for optimal health and longevity.     

Debiased lasso for generalized linear models with a diverging number of covariates

Modeling and drawing inference on the joint associations between single-nucleotide polymorphisms and a disease has sparked interest in genome-wide associations studies. In the motivating Boston Lung Cancer Survival Cohort (BLCSC) data, the presence of a large number of single nucleotide polymorphisms of interest, though smaller than the sample size, challenges inference on their joint associations with the disease outcome. In similar settings, we find that neither the debiased lasso approach (van de Geer et al., 2014), which assumes sparsity on the inverse information matrix, nor the standard maximum likelihood method can yield confidence intervals with satisfactory coverage probabilities for generalized linear models. Under this “large n, diverging p” scenario, we propose an alternative debiased lasso approach by directly inverting the Hessian matrix without imposing the matrix sparsity assumption, which further reduces bias compared to the original debiased lasso and ensures valid confidence intervals with nominal coverage probabilities. We establish the asymptotic distributions of any linear combinations of the parameter estimates, which lays the theoretical ground for drawing inference. Simulations show that the proposed refined debiased estimating method performs well in removing bias and yields honest confidence interval coverage. We use the proposed method to analyze the aforementioned BLCSC data, a large-scale hospital-based epidemiology cohort study investigating the joint effects of genetic variants on lung cancer risks.     

A heterogeneity measure for cluster identification with application to disease mapping

Mapping of disease incidence has long been of importance to epidemiology and public health. In this paper, we consider identification of clusters of spatial units with elevated disease rates and develop a new approach that estimates the relative disease risk in association with potential risk factors and simultaneously identifies clusters corresponding to elevated risks. A heterogeneity measure is proposed to enable the comparison of a candidate cluster and its complement under a pair of complementary models. A quasi-likelihood procedure is developed for estimating the model parameters and identifying the clusters. An advantage of our approach over traditional spatial clustering methods is the identification of clusters that can have arbitrary shapes due to abrupt or noncontiguous changes while accounting for risk factors and spatial correlation. Asymptotic properties of the proposed methodology are established and a simulation study shows empirically sound finite-sample properties. The mapping and clustering of enterovirus 71 infections in Taiwan are carried out for illustration.     

New models for evaluation of radiation-induced lifetime cancer risk and its uncertainty employed in the UNSCEAR 2006 report

Generalized relative and absolute risk models are fitted to the latest Japanese atomic bomb survivor solid cancer and leukemia mortality data (through 2000), with the latest (DS02) dosimetry, by classical (regression calibration) and Bayesian techniques, taking account of errors in dose estimates and other uncertainties. Linear-quadratic and linear-quadratic-exponential models are fitted and used to assess risks for contemporary populations of China, Japan, Puerto Rico, the U.S. and the UK. Many of these models are the same as or very similar to models used in the UNSCEAR 2006 report. For a test dose of 0.1 Sv, the solid cancer mortality for a UK population using the generalized linear-quadratic relative risk model is estimated as 5.4% Sv(-1) [90% Bayesian credible interval (BCI) 3.1, 8.0]. At 0.1 Sv, leukemia mortality for a UK population using the generalized linear-quadratic relative risk model is estimated as 0.50% Sv(-1) (90% BCI 0.11, 0.97). Risk estimates varied little between populations; at 0.1 Sv the central estimates ranged from 3.7 to 5.4% Sv(-1) for solid cancers and from 0.4 to 0.6% Sv(-1) for leukemia. Analyses using regression calibration techniques yield central estimates of risk very similar to those for the Bayesian approach. The central estimates of population risk were similar for the generalized absolute risk model and the relative risk model. Linear-quadratic-exponential models predict lower risks (at least at low test doses) and appear to fit as well, although for other (theoretical) reasons we favor the simpler linear-quadratic models.     

Robust Joint Modeling of Longitudinal Measurements and Competing Risks Failure Time Data

Existing methods for joint modeling of longitudinal measurements and survival data can be highly influenced by outliers in the longitudinal outcome. We propose a joint model for analysis of longitudinal measurements and competing risks failure time data which is robust in the presence of outlying longitudinal observations during follow‐up. Our model consists of a linear mixed effects sub‐model for the longitudinal outcome and a proportional cause‐specific hazards frailty sub‐model for the competing risks data, linked together by latent random effects. Instead of the usual normality assumption for measurement errors in the linear mixed effects sub‐model, we adopt a t ‐distribution which has a longer tail and thus is more robust to outliers. We derive an EM algorithm for the maximum likelihood estimates of the parameters and estimate their standard errors using a profile likelihood method. The proposed method is evaluated by simulation studies and is applied to a scleroderma lung study (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of Thyroid Dysfunction and the Thyroid-Stimulating Hormone Levels on the Risk of Atrial Fibrillation: A Systematic Review and Dose-Response Meta-Analysis from Cohort Studies

ObjectiveTo explore the relationship between thyroid dysfunction, thyroid-stimulating hormone (TSH) levels, and risks of atrial fibrillation (AF) in studies and conduct a dose-response meta-analysis on the correlation between the TSH levels and risk of AF.MethodsThirteen studies from 5 databases with 649 293 subjects (mean age, 65.1 years) were included. The dose-response meta-analysis was conducted by comparing the risk ratios (RRs) and 95% confidence intervals (CIs) for incident AF associated with different levels of TSH (vs TSH level of 0 mU/L) across studies. Data were collected until October 25, 2021.ResultsSubclinical hyperthyroidism, subclinical hypothyroidism, and clinical hyperthyroidism were associated with an increased risk of AF (RR, 1.70; 95% CI, 1.11-2.62; RR, 1.23; 95% CI, 1.05-1.44; and RR, 2.35; 95% CI, 1.07-5.16, respectively), whereas clinical hypothyroidism was not associated with the significantly increased risk of AF (RR, 1.20; 95% CI, 0.72-1.99). A nonlinear relationship was observed in 2 models (crude model, P_nonlinear < .001; adjusted model, P_nonlinear = .0391) between the TSH levels and risks of AF.ConclusionsOur study indicated that subclinical hyperthyroidism, subclinical hypothyroidism, clinical hyperthyroidism were associated with the risk of AF, and the results for the TSH levels and risk of AF were mixed, which showed a U-shaped relationship.     

Should the statistical analyses of twinning-rate data be improved?

Every statistical model is based on explicitly or implicitly formulated assumptions. In this study we address new techniques of calculation of variances and confidence intervals, analyse some statistical methods applied to modelling twinning rates, and investigate whether the improvements give more reliable results. For an observed relative frequency, the commonly used variance formula holds exactly with the assumptions that the repetitions are independent and that the probability of success is constant. The probability of a twin maternity depends not only on genetic predisposition, but also on several demographic factors, particularly ethnicity, maternal age and parity. Therefore, the assumption of constancy is questionable. The effect of grouping on the analysis of regression models for twinning rates is also considered. Our results indicate that grouping influences the efficiency of the estimates but not the estimates themselves. Recently, confidence intervals for proportions of low-incidence events have been a target for revived interest and we present the new alternatives. These confidence intervals are slightly wider and their midpoints do not coincide with the maximum-likelihood estimate of the twinning rate, but their actual coverage is closer to the nominal one than the coverage of the traditional confidence interval. In general, our findings indicate that the traditional methods are mainly satisfactorily robust and give reliable results. However, we propose that new formulae for the confidence intervals should be used. Our results are applied to twin-maternity data from Finland and Denmark.     

Fish Consumption,Mercury Intake,and the Associated Risks to the Kuwaiti Population

This analysis uses recent data on fish consumption among Kuwaitis and on levels of Hg in fish collected from fish markets in Kuwait to estimate the human health risks to the Kuwaiti population due to consumption of fish containing Hg. Mercury is a known human neurotoxicant. Recent, somewhat controversial, evidence suggests that it also may play a role in cardiovascular disease. Our analysis indicates that roughly 5,000 IQ points are lost among the 30,000 Kuwaiti infants born each year and that approximately 15 fatal heart attacks each year among middle-aged and elderly Kuwaitis may be attributed to consumption of methyl Hg in fish. Approximate 90% confidence intervals are from 1,800 to 14,000 IQ points lost annually and from 0 to 72 fatal heart attacks each year. The confidence intervals for neurotoxicity are broad because of uncertainty about the slope of the dose–response and the existence of a threshold. The range of estimates for heart attacks includes zero because of residual uncertainty about the causality of observed associations between methyl Hg exposure and cardiovascular disease. These results do not imply that Kuwaitis should immediately reduce their consumption of fish, but do suggest that a careful risk–risk tradeoff analysis may be warranted.     

On the estimation of average treatment effects with right-censored time to event outcome and competing risks

We are interested in the estimation of average treatment effects based on right-censored data of an observational study. We focus on causal inference of differences between t-year absolute event risks in a situation with competing risks. We derive doubly robust estimation equations and implement estimators for the nuisance parameters based on working regression models for the outcome, censoring, and treatment distribution conditional on auxiliary baseline covariates. We use the functional delta method to show that these estimators are regular asymptotically linear estimators and estimate their variances based on estimates of their influence functions. In empirical studies, we assess the robustness of the estimators and the coverage of confidence intervals. The methods are further illustrated using data from a Danish registry study.