The effect of risk factor misclassification on the partial population attributable risk

The partial population attributable risk (pPAR) is used to quantify the population‐level impact of preventive interventions in a multifactorial disease setting. In this paper, we consider the effect of nondifferential risk factor misclassification on the direction and magnitude of bias of pPAR estimands and related quantities. We found that the bias in the uncorrected pPAR depends nonlinearly and nonmonotonically on the sensitivities, specificities, relative risks, and joint prevalence of the exposure of interest and background risk factors, as well as the associations between these factors. The bias in the uncorrected pPAR is most dependent on the sensitivity of the exposure. The magnitude of bias varies over a large range, and in a small region of the parameter space determining the pPAR, the direction of bias is away from the null. In contrast, the crude PAR can only be unbiased or biased towards the null by risk factor misclassification. The semiadjusted PAR is calculated using the formula for the crude PAR but plugs in the multivariate‐adjusted relative risk. Because the crude and semiadjusted PARs continue to be used in public health research, we also investigated the magnitude and direction of the bias that may arise when using these formulae instead of the pPAR. These PAR estimators and their uncorrected counterparts were calculated in a study of risk factors for colorectal cancer in the Health Professionals Follow‐up Study, where it was found that because of misclassification, the pPAR for low folate intake was overestimated with a relative bias of 48%, when red meat and alcohol intake were treated as misclassified risk factors that are not modified, and when red meat was treated as the modifiable risk factor, the estimated value of the pPAR went from 14% to 60%, further illustrating the extent to which misclassification can bias estimates of the pPAR.     

Effect of exposure misclassification on the mean squared error of population attributable risk and prevented fraction estimates

Previous work has considered the effect of exposure misclassification on the bias of population attributable risk (AR) estimates, but little is known about the corresponding effects on their precision or mean squared error (MSE). This paper considers AR estimation in typical scenarios for case-control and cohort studies. The analogous index used when exposure reduces the risk--the prevented fraction (PF)--is also investigated. It is shown, through both theoretical and simulation results, that even with quite modest levels of exposure misclassification, the MSE can increase substantially, relative to the variance of AR estimated without measurement error. When exposure assessment is perfectly sensitive, there is no bias in AR but lack of measurement specificity can still cause a substantial loss of precision. In a few cases, the AR or PF with misclassified exposure can actually have smaller MSE; these exceptional cases arise when sensitivity is poor and the bias in AR or PF is relatively large. We conclude that while bias can be reduced by defining exposure on a highly sensitive basis, one must also consider the deleterious effect on precision by doing so. Loss of precision in the AR and PF estimates can be safely ignored only when the exposure measure is very accurate.     

Unbiased vs. Conservative estimators of etiological fractions: Examples of misclassification from studies of occupational lung cancer

Theoretical studies emphasize the importance of making unbiased etiological fraction estimates. In empirical works, however, the published estimates are usually conservative. The purpose of the present report is to study, empirically, the numerical magnitude of such conservative biases. Examples from the literature on occupational exposure and lung cancer are reported. It is demonstrated that conservative bias may decrease a numerical estimate by more than a factor 10 and that decreases by a factor 2 or 3 are not unusual. It is concluded that it is important, in future review studies, to pay attention to the magnitude of the conservative biases in the published empirical estimates and to put most emphasis on the least biased estimates in the review process.     

A practical approach to estimating the true effect of exposure despite imprecise exposure classification

Accurate information on actual exposure to some possibly toxic agent usually is not available in long-term occupational studies. Any strategy for assigning exposure levels or categories necessarily results in misclassification, where some individuals classified as exposed have no real exposure and some individuals classified as not exposed have some exposure to the agent. Both misclassification errors serve to reduce the estimate of risk associated with exposure. The question arises, “How much does the true risk depart from the observed estimate given an assumed level of misclassification?” This paper quantifies the effect of such misclassification on several forms of standardized risk ratios. Our results express the true risk as a function of the apparent risk based on imprecise exposure classification and parameters representing the proportion of each of the groups that are correctly classified. In any practical situation, the apparent risk can be computed based on whatever classification scheme is being used. On the other hand, the proportions of the imprecisely classified groups actually exposed cannot. However, the investigator may have information or may make assumptions for likely ranges of values for these proportions. Given the apparent risk, estimated true risks can be calculated and plotted or represented in tabular form as a function of the proportions of actual exposure. The resulting graph or table enables the investigator to read off the range of possible true risk values based on what he is prepared to believe or what other information indicates about the range of proportions of misclassified subjects. For instance, results for a typical value of apparent risk of 1.8 show that the true risk may be twice the apparent risk with only 23% misclassification in each exposure group. The value of the true risk that would be necessary to be consistent with a given apparent risk increases rapidly as the extent of misclassification increases. We also show that, if the extent of misclassification is large, the apparent relative risk is close to 1.0 regardless of the actual value of the true risk. Therefore, a small apparent risk does not necessarily indicate that there is no occupational hazard.     

Curious phenomena in Bayesian adjustment for exposure misclassification

Many epidemiologic investigations involve some discussion of exposure misclassification, but rarely is there an attempt to adjust for misclassification formally in the statistical analysis. Rather, investigators tend to rely on intuition to comment qualitatively on how misclassification might impact their findings. We point out several ways in which intuition might fail, in the context of unmatched case-control analysis with non-differential exposure misclassification. Particularly, we focus on how intuition can conflict with the results of a Bayesian analysis that accounts for the various uncertainties at hand. First, the Bayesian adjustment for misclassification can weaken the evidence about the direction of an exposure-disease association. Second, admitting uncertainty about the misclassification parameters can lead to narrower interval estimates concerning the association. We focus on the simple setting of unmatched case-control analysis with binary exposure and without adjustment for confounders, though much of our discussion should be relevant more generally.     

The extrapolation of attributable risk to new populations

I develop a method for extrapolation of attributable risk estimated from one population, to other populations with a different rate of risk factor exposure and/or rate of outcome. The method uses the relationship between attributable risk and the product moment correlation.     

The effect of non-differential exposure misclassification on estimates of the attributable and prevented fraction

This paper considers the effect of non-differential exposure misclassification on the population attributable fraction and the population prevented fraction as a function of the sensitivity and specificity of the exposure classification, the true relative risk, and the true prevalence of the exposure. Given a certain set of sensitivity, specificity, and prevalence of the exposure, the apparent attributable fraction is a constant proportion of the true attributable fraction regardless of the true relative risk. This observation does not hold for the apparent prevented fraction and the apparent relative risk, both of which vary with the true relative risk. For both the attributable and the prevented fraction, the sensitivity of the exposure classification has a greater influence on the magnitude of the bias than the specificity; also, the higher the prevalence of the exposure, the larger is the bias caused by the imperfect exposure classification.     

反事实和归因疾病负担研究

反事实(counterfactual)的本质意思是指在实际生活中,某些情况并未发生,即与事实相反.在哲学和统计学界,有很多学者就是借用这个问题来探索事物发生的原因.笔者曾将counterfactual译为虚拟事实,这是沿袭耿直的译法~([1]),但是究其在逻辑学上的起源,会发现一般直译为反事实~([2]),由于无论统计学还是现在的社会学都奉此起源为正溯,故本文也遵从该译法.     

胃癌的环境与遗传危险因素及归因危险度分析

目的分析胃癌的环境与遗传危险因素并进行归因危险度评价。方法采用病例对照研究方法．对南京地区121例原发性胃癌病例进行环境危险因素调查，并对相关酶系基因多态性进行分析．综合评价环境危险因素及遗传危险性在胃癌发生中的归因危险度。结果在南京地区人群中，吸烟、食用腌制食品等两种环境危险因素与遗传危险因子细胞色素氧化酶P4502E1(CYP2E1)和N-乙酰化酶(NAT2)的基因型的人群综合归因危险度达69．7％。胃癌的发生主要是环境危险因素与内在遗传持点共同作用的结果。结论对胃癌的干预应同时考虑环境危险因素和遗传危险性，在了解个体遗传易感性的基础上，对其相应的环境危险因素进行干预，以达到Ⅰ级预防的目的。     

Preventive strategy for hypertension based on attributable risk measures

Objectives To examine the effective preventive strategy for hypertension in a Japanese male population, based on attributable risk measures. Methods A 7-year follow-up study of hypertension among 6,306 middle-aged male office workers in a Japanese telecommunication company. Results In terms of population attributable risk percentage (PAR%), regular alcohol intake and physical inactivity showed great contributions to the development of hypertension in the population no less than obesity. The PAR% of each risk factor varied by age group, and the total PAR% of the three modifiable risk factors was considerably higher in the 30–39 year old group (71%) than in the older groups. Conclusions Reduced alcohol intake and increased physical activity, as well as weight control, may have a larger impact on prevention of hypertension in younger groups than in older groups.     

Interval estimation of the attributable risk in case-control studies with matched pairs

OBJECTIVE: The attributable risk (AR), which represents the proportion of cases who can be preventable when we completely eliminate a risk factor in a population, is the most commonly used epidemiological index to assess the impact of controlling a selected risk factor on community health. The goal of this paper is to develop and search for good interval estimators of the AR for case-control studies with matched pairs. METHODS: This paper considers five asymptotic interval estimators of the AR, including the interval estimator using Wald's statistic suggested elsewhere, the two interval estimators using the logarithmic transformations: log(x) and log(1-x), the interval estimator using the logit transformation log(x/(1-x)), and the interval estimator derived from a simple quadratic equation developed in this paper. This paper compares the finite sample performance of these five interval estimators by calculation of their coverage probability and average length in a variety of situations. RESULTS: This paper demonstrates that the interval estimator derived from the quadratic equation proposed here can not only consistently perform well with respect to the coverage probability, but also be more efficient than the interval estimator using Wald's statistic in almost all the situations considered here. This paper notes that although the interval estimator using the logarithmic transformation log(1-x) may also perform well with respect to the coverage probability, using this estimator is likely to be less efficient than the interval estimator using Wald's statistic. Finally, this paper notes that when both the underlying odds ratio (OR) and the prevalence of exposure (PE) in the case group are not large (OR < or =2 and PE < or =0.10), the application of the two interval estimators using the transformations log(x) and log(x/(1-x)) can be misleading. However, when both the underlying OR and PE in the case group are large (OR > or =4 and PE > or =0.50), the interval estimator using the logit transformation can actually outperform all the other estimators considered here in terms of efficiency. CONCLUSIONS: When there is no prior knowledge of the possible range for the underlying OR and PE, the interval estimator derived from the quadratic equation developed here for general use is recommended. When it is known that both the OR and PE in the case group are large (OR > or =4 and PE > or =0.50), it is recommended that the interval estimator using the logit transformation is used.     

儿童哮喘危险因素的Meta分析及归因危险度百分比的探讨

目的:分析儿童哮喘发病相关危险因素,为临床早期干预提供依据.方法;收集国内1995年1月～ 2012年11月公开发表的关于儿童哮喘发病危险因素的研究文献进行Meta分析及人群归因危险度百分比,查找儿童哮喘发病危险因素.结果:个人过敏史、特应性体质、家族哮喘史、一二级家族过敏史、感冒、呼吸道感染、环境因素包括异味、吸烟、吸人物等是发生儿童哮喘的危险因素,母乳喂养是保护因素.危险因素权重估计分别为个人过敏史11.15％,特应性体质14.29％,家族哮喘史19.17％,一二级家族过敏史21.44％,诱因1感冒、呼吸道感染26.22％,诱因2环境异味、吸烟、吸入物等7.73％.结论:对于特应性体质儿童提倡母乳喂养,尽量避免呼吸道感染,避开常见吸人性过敏原或可预防儿童哮喘发生.     

Interval estimation of the attributable risk for multiple exposure levels in case-control studies with confounders

The attributable risk (AR) is one of the most important and commonly-used epidemiological indices to assess the public health importance of an association between a risk factor and a disease. When the underlying risk factor has multiple exposure levels in the presence of confounders, we consider the case-control studies using random sampling to collect the cases and controls here. We develop four asymptotic interval estimators for AR, including the interval estimator using Wald's statistic, the interval estimator using the logarithmic transformation, the interval estimator using the logit transformation, and the interval estimator derived from a quadratic equation. We apply Monte Carlo simulation to evaluate the finite-sample performance of these interval estimators in a variety of situations. We demonstrate that given an adequately large sample size, all the estimators developed here can actually perform reasonably well. We note that the interval estimator using the logit transformation may be of limited use when the number of studied subjects is not large. We also note that the interval estimator using the logarithmic transformation can lose efficiency compared to the interval estimator using Wald's statistic or the interval estimator derived from a quadratic equation developed in this paper. Finally, we use the data taken from a case control study of the oral contraceptive use in myocardial infarction patients with various smoking levels to illustrate he practical usefulness of these estimators.     

The effects of exposure misclassification on estimates of relative risk

In epidemiologic studies, individuals may be misclassified with respect to exposure to a risk factor for disease. Such misclassification causes the relative risk of disease associated with the exposure in the population to be biased toward the null value. Here, a formula is derived for the apparent relative risk under misclassification (R) as a function of the sensitivity (U) and specificity (V) of the test for exposure and of the true relative risk (R) and true prevalence of exposure (P(E] in the population. The relative influence of U and V on the bias in R depends both on R and on P(E), with U tending to be more influential at higher values of P(E). When there is misclassification of exposure, variation in P(E) may bias comparisons of relative risk between groups or exposures, either by producing spurious differences or by masking true differences, and may generate spurious trends associated with a third variable such as age. Because the possible effects of misclassification of exposure on relative risk are complex and not easily generalized, the potential degree of bias should be evaluated individually in each situation.     

Bayesian methods of confidence interval construction for the population attributable risk from cross‐sectional studies

Population attributable risk measures the public health impact of the removal of a risk factor. To apply this concept to epidemiological data, the calculation of a confidence interval to quantify the uncertainty in the estimate is desirable. However, because perhaps of the confusion surrounding the attributable risk measures, there is no standard confidence interval or variance formula given in the literature. In this paper, we implement a fully Bayesian approach to confidence interval construction of the population attributable risk for cross‐sectional studies. We show that, in comparison with a number of standard Frequentist methods for constructing confidence intervals (i.e. delta, jackknife and bootstrap methods), the Bayesian approach is superior in terms of percent coverage in all except a few cases. This paper also explores the effect of the chosen prior on the coverage and provides alternatives for particular situations. Copyright © 2016 John Wiley & Sons, Ltd.     

Occupational hydrocarbon exposure and risk of renal cell carcinoma

A population-based case-control study (210 cases and 210 age- sex- and frequency-matched population controls) was conducted to evaluate the association between occupational hydrocarbon exposure and risk of renal cell carcinoma. Retrospective estimates of lifetime occupational hydrocarbon exposure were made without regard to case or control status, and an exposure index was calculated based on time and score combinations. A weak positive association was found for hydrocarbon exposure in males only (odds ratio = 1.6). For those under the age of 60, exposure to moderate levels of hydrocarbons produced the highest risk, while for those over the age of 70 a dose-response relationship was found. Those overweight were at high risk for renal cell carcinoma, and there was positive interaction between hydrocarbon exposure and overweight. Alcohol use alone or in the presence of hydrocarbon exposure decreased the risk significantly.     

Estimation of attributable risk for case-control studies with multiple matching

Kuritz and Landis considered case-control studies with multiple matching and proposed an asymptotic interval estimator of the attributable risk based on Wald's statistic. Using Monte Carlo simulation, Kuritz and Landis demonstrated that their interval estimator could perform well when the number of matched sets was large (>or=100). However, the number of matched sets may often be moderate or small in practice. In this paper, we evaluate the performance of Kuritz and Landis' interval estimator in small or moderate number of matched sets and compare it with four other interval estimators. We note that the coverage probability of Kuritz and Landis' interval estimator tends to be less than the desired confidence level when the probability of exposure among cases is large. In these cases, the interval estimator using the logarithmic transformation and the two interval estimators derived from the quadratic equations developed here can generally improve the coverage probability of Kuritz and Landis' interval estimator, especially for the case of a small number of matched sets. Furthermore, we find that an interval estimator derived from a quadratic equation is consistently more efficient than Kuritz and Landis' interval estimator. The interval estimator using the logit transformation, although which performs poorly when the underlying odds ratio (OR) is close to 1, can be useful when both the probability of exposure among cases and the underlying OR are moderate or large.     

Effects of the analytical treatment of exposure data on associations of cancer and occupational magnetic field exposure

Epidemiological studies of cancer among workers exposed to magnetic fields have yielded inconsistent results. This variability may be partly explained by differences in study methods. To assess sensitivity to such methods, data from a previous study of brain cancer and leukemia among electric power company workers were reanalyzed using alternative models, which incorporated uncertainty about the intensity of historical exposures, alternative cut points for categorizing the exposure variable for analysis, and a range of lags for describing cancer latency. Mortality rate ratios for leukemia ranged from 0.8–1.5. For brain cancer, increasing cumulative magnetic field exposure was associated with increasing mortality in virtually all models, with rate ratios between 1.3–3.4 for the most exposed workers. These rate ratios are consistent with previous analyses suggesting a 1.5–3.0-fold increase in the risk of brain cancer but no association with leukemia, and confirm that the previous results are not dependent on arbitrary decisions in applying the exposure data. Am. J. Ind. Med. 34:49–56, 1998. © 1998 Wiley-Liss, Inc.     

职业接触粉尘与死亡相关的前瞻性队列研究

目的探讨职业接触粉尘对死亡的影响,为现代职业卫生政策法规的制定以及相关工作提供科学依据。方法以1989～1992年广州市实施并建立的职工职业健康监护档案为基础资料,选年龄≥30岁的80987名接尘和无接尘职工为研究对象,进行前瞻性队列研究。结果(1)队列平均43．5岁,主要为工人,中学文化,已婚,接尘率16．3％,吸烟率43．7％,饮酒率33．5％;(2)队列平均随访8年,失访35例,死亡1539人,以恶性肿瘤死亡为主。接尘、无接尘全死因粗死亡率分别为男380．14／10万和314．56／10万,女95．72／10万和98．33／10万。(3)调整相关混杂因素后,接尘者全死因、恶性肿瘤、呼吸系统疾病死亡相对危险度(RR)分别为1．24、1、34和2．41,其中男性矽尘接触者分别为1．57、1．61和5、72,男接尘者肺癌和鼻咽癌死亡相对危险度分别为1、67和1．81,与无接尘者比,RR的增加均有显著性意义。(4)调整相关混杂因素后,接尘者全死因、恶性肿瘤死亡归因危险度百分比(AR％)和人群归因危险度百分比(PAR％)分别为19．5％、3．8％、25．4％和5．3％。结论职业接触粉尘可致全死因死亡尤其是恶性肿瘤和呼吸系统疾病死亡危险性增加。