Assessing interaction in case-control studies: type I errors when using both additive and multiplicative scales

Epidemiologic researchers often explore effect modification in case-control studies on more than one statistical scale, an approach that one expects would increase the rate of false-positive findings of interaction. For example, researchers have measured effect modification by using both a multiplicative interaction coefficient (M) in a logistic regression model and a measure of interaction on the additive scale such as the interaction coefficient from an additive relative risk regression model (A). We performed computer simulations to investigate the degree to which type I error may be inflated when statistical interactions are evaluated by using both M and A. The overall type I error rate was often greater than 5% when both tests were performed together. These results provide empiric evidence of the limited validity of a common approach to assessing etiologic effect modification. When the scale has not been specified before analysis, interaction hypothesis tests of effect modification should be interpreted particularly cautiously. Researchers are not justified in choosing the interaction test with the lowest P value.     

队列研究资料相加交互作用可信区间的Bootstrap法估计

交互作用评估是流行病学数据分析的重要环节,病因学研究中得到广泛应用的指数模型如logistic回归或Cox比例风险模型,常将危险因素的乘积项纳入模型,其乘积项系数反映了因素间的相乘交互作用,而在公共卫生方面交互作用分析应基于加法模型才更合适.文中根据Rothman提出的评估相加交互作用的指标,通过一个队列研究实例拟合Cox比例风险模型,应用RR值计算两因素的相加交互作用指标,并利用内置Bootstrap功能的S-Plus软件,较为方便地得到Bootstrap法估计的可信区间,避免队列研究资料应用OR值计算导致的估值偏差,且有更高的估计精度.相加和相乘交互作用分析的组合模式相当复杂,当两者冲突时宜选择加法模型.     

队列研究资料相加交互作用可信区间的Bootstrap法估计

交互作用评估是流行病学数据分析的重要环节,病因学研究中得到广泛应用的指数模型如logistic回归或Cox比例风险模型,常将危险因素的乘积项纳入模型,其乘积项系数反映了因素间的相乘交互作用,而在公共卫生方面交互作用分析应基于加法模型才更合适.文中根据Rothman提出的评估相加交互作用的指标,通过一个队列研究实例拟合Cox比例风险模型,应用RR值计算两因素的相加交互作用指标,并利用内置Bootstrap功能的S-Plus软件,较为方便地得到Bootstrap法估计的可信区间,避免队列研究资料应用OR值计算导致的估值偏差,且有更高的估计精度.相加和相乘交互作用分析的组合模式相当复杂,当两者冲突时宜选择加法模型.     

队列研究资料相加交互作用可信区间的Bootstrap法估计

交互作用评估是流行病学数据分析的重要环节,病因学研究中得到广泛应用的指数模型如logistic回归或Cox比例风险模型,常将危险因素的乘积项纳入模型,其乘积项系数反映了因素间的相乘交互作用,而在公共卫生方面交互作用分析应基于加法模型才更合适.文中根据Rothman提出的评估相加交互作用的指标,通过一个队列研究实例拟合Cox比例风险模型,应用RR值计算两因素的相加交互作用指标,并利用内置Bootstrap功能的S-Plus软件,较为方便地得到Bootstrap法估计的可信区间,避免队列研究资料应用OR值计算导致的估值偏差,且有更高的估计精度.相加和相乘交互作用分析的组合模式相当复杂,当两者冲突时宜选择加法模型.     

A weighting approach to causal effects and additive interaction in case-control studies: marginal structural linear odds models

Estimates of additive interaction from case-control data are often obtained by logistic regression; such models can also be used to adjust for covariates. This approach to estimating additive interaction has come under some criticism because of possible misspecification of the logistic model: If the underlying model is linear, the logistic model will be misspecified. The authors propose an inverse probability of treatment weighting approach to causal effects and additive interaction in case-control studies. Under the assumption of no unmeasured confounding, the approach amounts to fitting a marginal structural linear odds model. The approach allows for the estimation of measures of additive interaction between dichotomous exposures, such as the relative excess risk due to interaction, using case-control data without having to rely on modeling assumptions for the outcome conditional on the exposures and covariates. Rather than using conditional models for the outcome, models are instead specified for the exposures conditional on the covariates. The approach is illustrated by assessing additive interaction between genetic and environmental factors using data from a case-control study.     

Novel Likelihood Ratio Tests for Screening Gene‐Gene and Gene‐Environment Interactions With Unbalanced Repeated‐Measures Data

There has been extensive literature on modeling gene‐gene interaction (GGI) and gene‐environment interaction (GEI) in case‐control studies with limited literature on statistical methods for GGI and GEI in longitudinal cohort studies. We borrow ideas from the classical two‐way analysis of variance literature to address the issue of robust modeling of interactions in repeated‐measures studies. While classical interaction models proposed by Tukey and Mandel have interaction structures as a function of main effects, a newer class of models, additive main effects and multiplicative interaction (AMMI) models, do not have similar restrictive assumptions on the interaction structure. AMMI entails a singular value decomposition of the cell residual matrix after fitting the additive main effects and has been shown to perform well across various interaction structures. We consider these models for testing GGI and GEI from two perspectives: likelihood ratio test based on cell means and a regression‐based approach using individual observations. Simulation results indicate that both approaches for AMMI models lead to valid tests in terms of maintaining the type I error rate, with the regression approach having better power properties. The performance of these models was evaluated across different interaction structures and 12 common epistasis patterns. In summary, AMMI model is robust with respect to misspecified interaction structure and is a useful screening tool for interaction even in the absence of main effects. We use the proposed methods to examine the interplay between the hemochromatosis gene and cumulative lead exposure on pulse pressure in the Normative Aging Study.     

Comparison of population- and family-based methods for genetic association analysis in the presence of interacting loci

We compared different ascertainment schemes for genetic association analysis: affected sib-pairs (ASPs), case-parent trios, and unrelated cases and controls. We found, with empirical type 1 diabetes data at four known disease loci, that studies based on case-parent trios and on unmatched cases and controls often gave higher odds ratio estimates and stronger significance test values than ASP designs. We used simulations and a simplified disease model involving two interacting loci, one of large effect and one smaller, to examine interaction models that could cause such an effect. The different ascertainment schemes were compared for power to detect an effect when only the locus of smaller effect was genotyped. ASPs showed the greatest power for association testing under most models of interaction except under additive and certain epistatic crossover models, for which case/controls and case-parent trios did better. All ascertainment schemes gave an unbiased estimation of log genotype relative risks (GRRs) under a multiplicative model. Under nonmultiplicative interactions, GRRs at the minor locus as estimated from ASPs could be biased upwards or downwards, resulting in either an increase or decrease in power compared to the case/control or trio design. For the four known type 1 diabetes loci, we observed decreased risks with ASPs, which could be due to additive interactions with the remaining susceptibility loci. Thus, the optimal ascertainment strategy in genetic association studies depends on the unknown underlying multilocus genetic model, and on whether the goal of the study is to detect an effect or to accurately estimate the resulting disease risks.     

Testing proportionality in the proportional odds model fitted with GEE.

Generalized estimating equations (GEE) methodology as proposed by Liang and Zeger has received widespread use in the analysis of correlated binary data. Miller et al. and Lipsitz et al. extended GEE to correlated nominal and ordinal categorical data; in particular, they used GEE for fitting McCullagh's proportional odds model. In this paper, we consider robust (that is, empirically corrected) and model-based versions of both a score test and a Wald test for assessing the assumption of proportional odds in the proportional odds model fitted with GEE. The Wald test is based on fitting separate multiple logistic regression models for each dichotomization of the response variable, whereas the score test requires fitting just the proportional odds model. We evaluate the proposed tests in small to moderate samples by simulating data from a series of simple models. We illustrate the use of the tests on three data sets from medical studies.     

logistic回归模型中交互作用的分析及评价

流行病学病因学研究常运用logistic回归模型分析影响因素的作用,并利用纳入乘积项的方法分析因素间交互作用,如有统计学意义表示两因素间存在相乘交互作用,但乘积项若无统计学意义并不表示两因素问相加交互作用或生物学交互作用的有无.文中介绍Rothman提出的针对logistic或Cox回归模型的三个评价相加交互作用的指标及其可信区间的计算,并以SPSS 15.0软件应用实例分析得出logistic回归模型的参数估计值和协方差矩阵,引入Andersson等编制的Excel计算表,计算相加交瓦作用指标及其可信区间,用于评价因素间的相加交互作用,为研究人员分析生物学交互作用提供依据.该方法方便快捷,且Excel计算表可在线免费下载.     

Test for additive interaction in proportional hazards models

PURPOSE: We describe a method for testing and estimating a two-way additive interaction between two categorical variables, each of which has greater than or equal to two levels. METHODS: We test additive and multiplicative interactions in the same proportional hazards model and measure additivity by relative excess risk due to interaction (RERI), proportion of disease attributable to interaction (AP), and synergy index (S). A simulation study was used to compare the performance of these measures of additivity. Data from the Atherosclerosis Risk in Communities cohort study with a total of 15,792 subjects were used to exemplify the methods. RESULTS: The test and measures of departure from additivity depend neither on follow-up time nor on the covariates. The simulation study indicates that RERI is the best choice of measures of additivity using a proportional hazards model. The examples indicated that an interaction between two variables can be statistically significant on additive measure (RERI=1.14, p=0.04) but not on multiplicative measure (beta3=0.59, p=0.12) and that additive and multiplicative interactions can be in opposite directions (RERI=0.08, beta3=-0.08). CONCLUSIONS: The method has broader application for any regression models with a rate as the dependent variable. In the case that both additive and multiplicative interactions are statistically significant and in the opposite direction, the interpretation needs caution.