Bias In Relative Risk Estimates Research Articles

How Independent Are “Independent” Effects? Relative Risk Estimation When Correlated Exposures Are Measured Imprecisely

A relative risk estimate which relates an exposure to risk of disease will tend to be estimated too close to unity if that exposure is subject to random measurement error or intra-subject variability. Independent relative risk estimates, for the effect of one exposure after adjusting for confounding exposures, may be biased in either direction, depending on the amount of measurement imprecision in the exposure of interest and in the confounders. We describe two methods which estimate the bias in multivariate relative risk estimates due to the effect of measurement imprecision in one or more of the exposure variables in the model. Results from the two methods are compared in an example involving HDL cholesterol, triglycerides and coronary heart disease. In this example, the degree of bias in relative risk estimates is shown to be highly dependent on the amount of measurement imprecision ascribed to the exposures. It is concluded that when two exposures are substantially correlated, and one or both is subject to sizeable measurement imprecision, a study in which exposures are measured only once will be inadequate for investigating the independent effect of the exposures. Where feasible, epidemiologists should seek study populations where the correlation between the exposures is smaller.

Missing information caused by death leads to bias in relative risk estimates

ObjectivesIn most clinical and epidemiologic studies, information on disease status is usually collected at regular follow-up visits. Often, this information can only be retrieved in individuals who are alive at follow-up, and studies frequently right censor individuals with missing information because of death in the analysis. Such ad hoc analyses can lead to seriously biased hazard ratio estimates of potential risk factors. We systematically investigate this bias. Study Design and SettingWe illustrate under which conditions the bias can occur. Considering three numerical studies, we characterize the bias, its magnitude, and direction as well as its real-world relevance. ResultsDepending on the situation studied, the bias can be substantial and in both directions. It is mainly caused by differential mortality: if deaths without occurrence of the disease are more pronounced, the risk factor effect is overestimated. However, if the risk for dying after being diseased is prevailing, the effect is mostly underestimated and might even change signs. ConclusionThe bias is a result of both, a too coarse follow-up and an ad hoc Cox analysis in which the data sample is restricted to the observed and known event history. This is especially relevant for studies in which a considerable number of death cases are expected.

Cell Phone Use and Crash Risk

Recent epidemiologic studies have estimated little or no increased risk of automotive crashes related to cell phone conversations by the driver, whereas earlier case-crossover studies estimated the relative risk as close to 4. Did earlier studies introduce a positive bias in relative risk estimates by overestimating driving exposure in control windows? Driving exposures in a "control" window and a corresponding "case" window on the subsequent day were tabulated across 100 days for 439 GPS-instrumented vehicles in the Puget Sound area during 2005-2006. For control windows containing at least some driving, driving exposure was about one-fourth that of case windows. Adjusting for this imbalance reduces relative risk estimates in the earlier case-crossover studies from 4 to 1. Earlier case-crossover studies likely overestimated the relative risk for cell phone conversations while driving by implicitly assuming that driving during a control window was full-time when it may have been only part-time.

Correlated errors in biased surrogates: study designs and methods for measurement error correction

A measurement error model proposed previously allows for correlations between subject-specific biases and between random within-subject errors in the surrogates obtained from two modes of measurement. However, most of these model parameters are not identifiable from the standard validation study design, including, importantly, the attenuation factor needed to correct for bias in relative risk estimates due to measurement error. We propose validation study designs that permit estimation and inference for the attenuation factor and other parameters of interest when these correlations are present. We use an estimating equations framework to develop semi-parametric estimators for these parameters, exploiting instrumental variables techniques. The methods are illustrated through application to data from the Nurses' Health Study and Health Professionals' Follow-up Study, and comparisons are made to more restrictive models.

A sensitivity analysis of bias in relative risk estimates due to disinfection by-product exposure misclassification.

We conducted a sensitivity analysis of relative risk estimates using local area mean disinfection by-product exposures. We used Monte Carlo simulations to generate data representing 100 towns, each with 100 births (n=10,000). Each town was assigned a mean total trihalomethane (TTHM) exposure value (mean=45, SD=28) based on a variable number of sampling locations (range 2-10). True maternal TTHM exposure was randomly assigned from a lognormal distribution using that town's true mean value. We compared the effect of a 20 microg/l increase in TTHM exposure on the risk of small-for-gestational age infancy using the true maternal exposure compared to various weighting measures of the town mean exposures. The exposure metrics included: (1) unweighted town mean, (2) town mean weighted by the inverse variance of the town mean, (3) town mean weighted by the inverse standard deviation of the town mean, (4) town mean weighted by 1-(standard deviation of sites per town/mean across all towns), and (5) a randomly selected value from one of the sites within the town of residence. To estimate the magnitude of misclassification bias from using the town mean concentrations, we compared the true exposure odds ratios (1.00, 1.20, 1.50, and 2.00) to the mean exposure odds ratios from the five exposure scenarios. Misclassification bias from the use of unweighted town mean exposures ranged from 19 to 39%, increasing in proportion to the size of the true effect estimates. Weighted town mean TTHM exposures were less biased than the unweighted estimates of maternal exposure, with bias ranging from 0 to 23%. The weighted town mean analyses showed that attenuation of the true effect of DBP exposure was diminished when town mean concentrations with large variability were downweighted. We observed a trade-off between bias and precision in the weighted exposure analyses, with the least biased effects estimates having the widest confidence intervals. Effect attenuation due to intrasystem variability was most evident in absolute and relative terms for larger odds ratios.

European Prospective Investigation into Cancer and Nutrition (EPIC) calibration study: rationale, design and population characteristics.

The European Prospective Investigation into Cancer and Nutrition (EPIC), which covers a large cohort of half a million men and women from 23 European centres in 10 Western European countries, was designed to study the relationship between diet and the risk of chronic diseases, particularly cancer. Information on usual individual dietary intake was assessed using different validated dietary assessment methods across participating countries. In order to adjust for possible systematic over- or underestimation in dietary intake measurements and correct for attenuation bias in relative risk estimates, a calibration approach was developed. This approach involved an additional dietary assessment common across study populations to re-express individual dietary intakes according to the same reference scale. A single 24-hour diet recall was therefore collected, as the EPIC reference calibration method, from a stratified random sample of 36 900 subjects from the entire EPIC cohort, using a software program (EPIC-SOFT) specifically designed to standardise the dietary measurements across study populations. This paper describes the design and populations of the calibration sub-studies set up in the EPIC centres. In addition, to assess whether the calibration sub-samples were representative of the entire group of EPIC cohorts, a series of subjects' characteristics known possibly to influence dietary intakes was compared in both population groups. This was the first time that calibration sub-studies had been set up in a large multi-centre European study. These studies showed that, despite certain inherent methodological and logistic constraints, a study design such as this one works relatively well in practice. The average response in the calibration study was 78.3% and ranged from 46.5% to 92.5%. The calibration population differed slightly from the overall cohort but the differences were small for most characteristics and centres. The overall results suggest that, after adjustment for age, dietary intakes estimated from calibration samples can reasonably be interpreted as representative of the main cohorts in most of the EPIC centres.

Measurement error in epidemiology: the design of validation studies II: bivariate situation.

The bias in relative risk estimates caused by errors in measurement of the relevant exposure is being increasingly recognized in epidemiology. Estimation of the necessary correction factor to remove this bias for univariate exposure has been considered in an earlier paper. We consider here the multivariate situation in which non-differential errors in measurement can lead to incorrect identification of the variable most closely associated with disease. Estimation of the necessary correction factor when the true exposure is unobservable necessarily requires assumptions. We explore the robustness of the estimation to departures from a range of assumptions. The value of good biomarkers is demonstrated. We present a bivariate example in which failure to take account of measurement error leads to the incorrect exposure being identified as the important determinant of disease risk.

Asymptotic Bias and Efficiency In Case-Control Studies of Candidate Genes and Gene-Environment Interactions: Basic Family Designs

Case-control designs that use population controls are compared with those that use controls selected from their relatives (i.e., siblings, cousins, or "pseudosibs" based on parental alleles) for estimating the effect of candidate genes and gene-environment interactions. The authors first evaluate the asymptotic bias in relative risk estimates resulting from using population controls when there is confounding due to population stratification. Using siblings or pseudosibs as controls completely addresses this issue, whereas cousins provide only partial protection from population stratification. Next, they show that the conventional conditional likelihood for matched case-control studies can give asymptotically biased effect estimates when applied to the pseudosib approach; the asymptotic bias is toward the null and disappears with disease rarity. They show how to reparameterize the pseudosib likelihood so this approach gives consistent effect estimates. They then show that the designs using population or pseudosib controls are generally the most efficient for estimating the main effect of a candidate gene, followed in efficiency by the design using cousins. Finally, they show that the design using sibling controls can be quite efficient when studying gene-environment interactions. In addition to asymptotic bias and efficiency issues, family-based designs might benefit from a higher motivation to participate among cases' relatives, but these designs have the disadvantage that many potential cases will be excluded from study by having no available controls.

Correcting for bias in relative risk estimates due to exposure measurement error: a case study of occupational exposure to antineoplastics in pharmacists.

This paper describes 2 statistical methods designed to correct for bias from exposure measurement error in point and interval estimates of relative risk. The first method takes the usual point and interval estimates of the log relative risk obtained from logistic regression and corrects them for nondifferential measurement error using an exposure measurement error model estimated from validation data. The second, likelihood-based method fits an arbitrary measurement error model suitable for the data at hand and then derives the model for the outcome of interest. Data from Valanis and colleagues' study of the health effects of antineoplastics exposure among hospital pharmacists were used to estimate the prevalence ratio of fever in the previous 3 months from this exposure. For an interdecile increase in weekly number of drugs mixed, the prevalence ratio, adjusted for confounding, changed from 1.06 to 1.17 (95% confidence interval [CI] = 1.04, 1.26) after correction for exposure measurement error. Exposure measurement error is often an important source of bias in public health research. Methods are available to correct such biases.

How independent are “independent” effects? relative risk estimation when correlated exposures are measured imprecisely

A relative risk estimate which relates an exposure to risk of disease will tend to be estimated too close to unity if that exposure is subject to random measurement error or intra-subject variability. “Independent” relative risk estimates, for the effect of one exposure after adjusting for confounding exposures, may be biased in either direction, depending on the amount of measurement imprecision in the exposure of interest and in the confounders. We describe two methods which estimate the bias in multivariate relative risk estimates due to the effect of measurement imprecision in one or more of the exposure variables in the model. Results from the two methods are compared in an example involving HDL cholesterol, triglycerides and coronary heart disease. In this example, the degree of bias in relative risk estimates is shown to be highly dependent on the amount of measurement imprecision ascribed to the exposures. It is concluded that when two exposures are substantially correlated, and one or both is subject to sizeable measurement imprecision, a study in which exposures are measured only once will be inadequate for investigating the independent effect of the exposures. Where feasible, epidemiologists should seek study populations where the correlation between the exposures is smaller.

The Effects of Non-Response in a Prospective Study of Cancer: 15-Year Follow-Up

Out of 11,136 Japanese men identified on the island of Oahu, Hawaii in 1965 by the Honolulu Heart Program, 8006 responded to a mailed questionnaire and were examined. Some 1871 responded only to the mailed questionnaire, and 1259 did not respond at all. After 15 years of follow-up, the examined men had significantly lower risk of death from all causes and death from cancer. Minor differences were also noted between the two groups in the risk of cancer of the lung, stomach, colon, and rectum. However, the examined men had a significantly higher risk of prostate cancer. In general, the strength of these non-response effects was mainly due to risk differences in the first five years of the 15-year follow-up period. The relative risk (RR) of each of the seven endpoint events tended towards 1.0 as each of the three successive five-year follow-up intervals were considered. An exception to this was the prostate cancer incidence RR which favoured the unexamined men throughout the entire 15 years, but significantly so only in the last five-year follow-up interval. When the 8006 examined and 1871 unexamined men who responded to the mailed questionnaire were evaluated with respect to the association of cigarette smoking with lung cancer incidence, the RR for smokers was 9.77 for the examined men, and 6.73 for the unexamined men. Since these RRs are not significantly different, there should be little bias in RR estimates of cigarette smoking for lung cancer if the observation was limited to only the examined men. With regard to the association of body mass index (BMI) with colon cancer in older men, the RRs for men in the highest BMI quintile were quite comparable, at 1.37 for the examined group and 1.60 for the unexamined men. We conclude that although some non-response effects on cancer incidence exist in this cohort, they do not appear to be serious enough to have changed conclusions drawn about risk relationships.

Further considerations of difficulties of estimating familial risks from pedigree data.

In elucidating the etiology of complex diseases through various epidemiologic and genetic analyses, it is necessary to define the expected risks for each member of a pedigree collected through an affected individual. It is shown that several factors are to be considered without which such expected risk estimates may be biased. The presence of secular trends in disease incidence introduces a bias in familial relative risk estimates, the magnitude and direction of which may be judged from the nature of the secular trends and the age and cohort composition of the individuals included in the study. Nonrandom follow-up time of the relatives, on the contrary, produces a bias in relative risk estimates, the magnitude and direction of which cannot be ascertained without any prior assumption about the distribution of follow-up time. In addition, competing causes of diseases and risk heterogeneity among different relatives and among families are also sources of indeterminate biases, which must be removed in order to interprete the results of relative risk studies and segregation analysis of discrete disease traits.

Use of predictive value to adjust relative risk estimates biased by misclassification of outcome status.

The bias in relative risk estimates resulting from misclassification of outcome status has been shown to be a function of sensitivity and specificity of the classification procedure and of disease frequency. In epidemiologic studies, it may not be possible to obtain estimates of sensitivity and specificity. This situation frequently arises in studies of risk factors for coronary artery disease, where invasive procedures may be necessary to validate diagnosis. However, an estimate of the predictive value of a positive result in the classification procedure may be far more readily obtained than estimates of sensitivity and specificity. In this paper, exact and approximate formulae for the adjusted relative risk in terms of the predictive value of a positive test are derived. Hypothetical examples of epidemiologic studies of coronary artery disease are provided to illustrate the use of these formulae.