Ecologic versus individual-level sources of bias in ecologic estimates of contextual health effects

A number of authors have attempted to defend ecologic (aggregate) studies by claiming that the goal of those studies is estimation of ecologic (contextual or group-level) effects rather than individual-level effects. Critics of these attempts point out that ecologic effect estimates are inevitably used as estimates of individual effects, despite disclaimers. A more subtle problem is that ecologic variation in the distribution of individual effects can bias ecologic estimates of contextual effects. The conditions leading to this bias are plausible and perhaps even common in studies of ecosocial factors and health outcomes because social context is not randomized across typical analysis units (administrative regions). By definition, ecologic data contain only marginal observations on the joint distribution of individually defined confounders and outcomes, and so identify neither contextual nor individual-level effects. While ecologic studies can still be useful given appropriate caveats, their problems are better addressed by multilevel study designs, which obtain and use individual as well as group-level data. Nonetheless, such studies often share certain special problems with ecologic studies, including problems due to inappropriate aggregation and problems due to temporal changes in covariate distributions.

On the bias produced by quality scores in meta-analysis, and a hierarchical view of proposed solutions

Results from better quality studies should in some sense be more valid or more accurate than results from other studies, and as a consequence should tend to be distributed differently from results of other studies. To date, however, quality scores have been poor predictors of study results. We discuss possible reasons and remedies for this problem. It appears that 'quality' (whatever leads to more valid results) is of fairly high dimension and possibly non-additive and nonlinear, and that quality dimensions are highly application-specific and hard to measure from published information. Unfortunately, quality scores are often used to contrast, model, or modify meta-analysis results without regard to the aforementioned problems, as when used to directly modify weights or contributions of individual studies in an ad hoc manner. Even if quality would be captured in one dimension, use of quality scores in summarization weights would produce biased estimates of effect. Only if this bias were more than offset by variance reduction would such use be justified. From this perspective, quality weighting should be evaluated against formal bias-variance trade-off methods such as hierarchical (random-coefficient) meta-regression. Because it is unlikely that a low-dimensional appraisal will ever be adequate (especially over different applications), we argue that response-surface estimation based on quality items is preferable to quality weighting. Quality scores may be useful in the second stage of a hierarchical response-surface model, but only if the scores are reconstructed to maximize their correlation with bias.

Putting background information about relative risks into conjugate prior distributions

In Bayesian and empirical Bayes analyses of epidemiologic data, the most easily implemented prior specifications use a multivariate normal distribution for the log relative risks or a conjugate distribution for the discrete response vector. This article describes problems in translating background information about relative risks into conjugate priors and a solution. Traditionally, conjugate priors have been specified through flattening constants, an approach that leads to conflicts with the true prior covariance structure for the log relative risks. One can, however, derive a conjugate prior consistent with that structure by using a data-augmentation approximation to the true log relative-risk prior, although a rescaling step is needed to ensure the accuracy of the approximation. These points are illustrated with a logistic regression analysis of neonatal-death risk.

Attributable fractions: bias from broad definition of exposure

In certain special situations, simplification of an exposure measure into a dichotomy results in no bias from nondifferential misclassification when estimating the attributable fraction for "any exposure." This fact has led to recommendations to use a broad definition of exposure when estimating attributable fractions. I here review the assumptions underlying exposure simplification, focusing on the assumptions that the source and target populations have the same exposure distribution and that complete risk removal is possible. I argue that attributable fraction estimates based on dichotomization can be especially sensitive to violations of these assumptions, and hence misleading for projecting the impact of exposure reduction. I conclude that it is important to obtain and use detailed exposure and covariate information for attributable-fraction estimation.

Data augmentation priors for Bayesian and semi-Bayes analyses of conditional-logistic and proportional-hazards regression

Data augmentation priors have a long history in Bayesian data analysis. Formulae for such priors have been derived for generalized linear models, but their accuracy depends on two approximation steps. This note presents a method for using offsets as well as scaling factors to improve the accuracy of the approximations in logistic regression. This method produces an exceptionally simple form of data augmentation that allows it to be used with any standard package for conditional-logistic or proportional-hazards regression to perform Bayesian and semi-Bayes analyses of matched and survival data. The method is illustrated with an analysis of a matched case-control study of diet and breast cancer.

Sensitivity analysis, Monte Carlo risk analysis, and Bayesian uncertainty assessment

Standard statistical methods understate the uncertainty one should attach to effect estimates obtained from observational data. Among the methods used to address this problem are sensitivity analysis, Monte Carlo risk analysis (MCRA), and Bayesian uncertainty assessment. Estimates from MCRAs have been presented as if they were valid frequentist or Bayesian results, but examples show that they need not be either in actual applications. It is concluded that both sensitivity analyses and MCRA should begin with the same type of prior specification effort as Bayesian analysis.

Confounding in health research

Consideration of confounding is fundamental to the design, analysis, and interpretation of studies intended to estimate causal effects. Unfortunately, the word confounding has been used synonymously with several other terms, and it has been used to refer to at least four distinct concepts. This paper provides an overview of confounding and related concepts based on a counterfactual model of causation. In this context, which predominates in nonexperimental research, confounding is a source of bias in the estimation of causal effects. Special attention is given to the history of definitions of confounding, the distinction between confounding and confounders, problems in the control of confounding, the relations of confounding to exchangeability and collapsibility, and confounding in randomized trials.

Estimation of population attributable fractions from fitted incidence ratios and exposure survey data, with an application to electromagnetic fields and childhood leukemia

Standard presentations of epidemiological results focus on incidence-ratio estimates derived from regression models fit to specialized study data. These data are often highly nonrepresentative of populations for which public-health impacts must be evaluated. Basic methods are provided for interval estimation of attributable fractions from model-based incidence-ratio estimates combined with independent survey estimates of the exposure distribution in the target population of interest. These methods are illustrated in estimation of the potential impact of magnetic-field exposures on childhood leukemia in the United States, based on pooled data from 11 case-control studies and a U.S. sample survey of magnetic-field exposures.

Side effects and time course of response in a placebo-controlled trial of fluoxetine for the treatment of geriatric depression

A high rate of improvement among patients who receive placebo in controlled trials of antidepressants can complicate the evaluation of true drug effect. Placebo response may be a reaction to the psychosocial factors of study participation or a function of changes in the natural course of depression. Drug side effects may also influence patients' expectations, and they should be distinguished from the somatic symptoms associated with major depression. The authors reanalyzed data from a large, multicenter, placebo-controlled clinical trial of fluoxetine treatment of geriatric depression to evaluate similarities and differences between responders and nonresponders in both treatment groups. Specifically, the authors examined weekly somatic complaints as possible predictors of response and of dropout, as well as the time course and onset of response. Fluoxetine was superior to placebo on all outcome measures. Among somatic complaints associated with fluoxetine response, headache before and after randomization was associated with a good response and anxiety after randomization was associated with a poor response. Somnolence before and after randomization was associated with a good placebo response. Early and persistent improvement occurred among similar proportions of responders in both groups. The difference between fluoxetine and placebo seemed to be a persistent response beginning during the 4th week. Pretreatment somnolence was associated with early, persistent improvement in both groups and may serve as a marker for placebo response.

Multilevel modeling in epidemiology with GLIMMIX

Previous work has shown that multilevel modeling can be a valuable technique for epidemiologic analysis. The complexity of using this approach, however, continues to restrict its general application. A critical factor is the lack of flexible and appropriate software for multilevel modeling. SAS provides a macro, GLIMMIX, that can be used for multilevel modeling, but that is not sufficient for a complete epidemiologic analysis. We here provide additional code to obtain epidemiologic output from GLIMMIX, illustrated with new data on diet and breast cancer from the European Community Multicenter Study on Antioxidants, Myocardial Infarction, and Breast Cancer (EURAMIC). Our results give epidemiologists an easily used tool for fitting multilevel models.

A pooled analysis of magnetic fields, wire codes, and childhood leukemia. Childhood Leukemia-EMF Study Group

We obtained original individual data from 15 studies of magnetic fields or wire codes and childhood leukemia, and we estimated magnetic field exposure for subjects with sufficient data to do so. Summary estimates from 12 studies that supplied magnetic field measures exhibited little or no association of magnetic fields with leukemia when comparing 0.1-0.2 and 0.2-0.3 microtesla (microT) categories with the 0-0.1 microT category, but the Mantel-Haenszel summary odds ratio comparing >0.3 microT to 0-0.1 microT was 1.7 (95% confidence limits = 1.2, 2.3). Similar results were obtained using covariate adjustment and spline regression. The study-specific relations appeared consistent despite the numerous methodologic differences among the studies. The association of wire codes with leukemia varied considerably across studies, with odds ratio estimates for very high current vs low current configurations ranging from 0.7 to 3.0 (homogeneity P = 0.005). Based on a survey of household magnetic fields, an estimate of the U.S. population attributable fraction of childhood leukemia associated with residential exposure is 3% (95% confidence limits = -2%, 8%). Our results contradict the idea that the magnetic field association with leukemia is less consistent than the wire code association with leukemia, although analysis of the four studies with both measures indicates that the wire code association is not explained by measured fields. The results also suggest that appreciable magnetic field effects, if any, may be concentrated among relatively high and uncommon exposures, and that studies of highly exposed populations would be needed to clarify the relation of magnetic fields to childhood leukemia.

Empirical Bayes adjustments for multiple results in hypothesis-generating or surveillance studies

Traditional methods of adjustment for multiple comparisons (e.g., Bonferroni adjustments) have fallen into disuse in epidemiological studies. However, alternative kinds of adjustment for data with multiple comparisons may sometimes be advisable. When a large number of comparisons are made, and when there is a high cost to investigating false positive leads, empirical or semi-Bayes adjustments may help in the selection of the most promising leads. Here we offer an example of such adjustments in a large surveillance data set of occupation and cancer in Nordic countries, in which we used empirical Bayes (EB) adjustments to evaluate standardized incidence ratios (SIRs) for cancer and occupation among craftsmen and laborers. For men, there were 642 SIRs, of which 138 (21%) had a P < 0.05 (13% positive with SIR > 1.0 and 8% negative with SIR < or = 1.0) when testing the null hypothesis of no cancer/occupation association; some of these were probably due to confounding by nonoccupational risk factors (e.g., smoking). After EB adjustments, there were 95 (15%) SIRs with P < 0.05 (10% positive and 5% negative). For women, there were 373 SIRs, of which 37 (10%) had P < 0.05 before adjustment (6% positive and 4% negative) and 13 (3%) had P < 0.05 after adjustment (2% positive and 1% negative). Several known associations were confirmed after EB adjustment (e.g., pleural cancer among plumbers, original SIR 3.2 (95% confidence interval, 2.5-4.1), adjusted SIR 2.0 (95% confidence interval, 1.6-2.4). EB can produce more accurate estimates of relative risk by shrinking imprecise outliers toward the mean, which may reduce the number of false positives otherwise flagged for further investigation. For example, liver cancer among chimney sweepers was reduced from an original SIR of 2.2 (range, 1.1-4.4) to an adjusted SIR of 1.1 (range, 0.9-1.4). A potentially important future application for EB is studies of gene-environment-disease interactions, in which hundreds of polymorphisms may be evaluated with dozens of environmental risk factors in large cohort studies, producing thousands of associations.

Intrauterine devices and pelvic inflammatory disease: meta-analyses of published studies, 1974-1990

We conducted a meta-analysis of 36 papers published between 1974 and 1990 to estimate the effects of intrauterine device (IUD) use and Dalkon Shield use, in particular, on pelvic inflammatory disease (PID). The number of women studied in each report ranged from 50 to 26,507. For general IUD use, analyses were separated by type of PID (symptomatic or asymptomatic) because of extreme rate-ratio heterogeneity across studies. Dalkon Shield rate ratios were more homogeneous and were considered in a single meta-regression. There was substantial heterogeneity, however, in all three meta-regressions; the rate-ratio estimates ranged from 0.51 to 12 for IUD use and symptomatic PID, from 1.0 to 132 for IUD use and asymptomatic PID, and from 0.32 to 28 for Dalkon-Shield use and PID. This heterogeneity appeared to be due to differences in reference groups, study populations, and characteristics of study design. We observed consistent, positive associations of IUD use with both symptomatic and asymptomatic PID. These associations were largest for the Dalkon Shield.

When should epidemiologic regressions use random coefficients?

Regression models with random coefficients arise naturally in both frequentist and Bayesian approaches to estimation problems. They are becoming widely available in standard computer packages under the headings of generalized linear mixed models, hierarchical models, and multilevel models. I here argue that such models offer a more scientifically defensible framework for epidemiologic analysis than the fixed-effects models now prevalent in epidemiology. The argument invokes an antiparsimony principle attributed to L. J. Savage, which is that models should be rich enough to reflect the complexity of the relations under study. It also invokes the countervailing principle that you cannot estimate anything if you try to estimate everything (often used to justify parsimony). Regression with random coefficients offers a rational compromise between these principles as well as an alternative to analyses based on standard variable-selection algorithms and their attendant distortion of uncertainty assessments. These points are illustrated with an analysis of data on diet, nutrition, and breast cancer.

An introduction to instrumental variables for epidemiologists

Instrumental-variable (IV) methods were invented over 70 years ago, but remain uncommon in epidemiology. Over the past decade or so, non-parametric versions of IV methods have appeared that connect IV methods to causal and measurement-error models important in epidemiological applications. This paper provides an introduction to those developments, illustrated by an application of IV methods to non-parametric adjustment for non-compliance in randomized trials.

Fatalities to occupants of cargo areas of pickup trucks

We sought to describe the fatalities to occupants of pickup truck cargo areas and to compare the mortality of cargo area occupants to passengers in the cab. From the Fatality Analysis Reporting System (FARS) files for 1987-1996, we identified occupants of pickup trucks with at least one fatality and at least one passenger in the cargo area. Outcomes of cargo area occupants and passengers in the cab were compared using estimating equations conditional on the crash and vehicle. Thirty-four percent of deaths to cargo occupants were in noncrash events without vehicle deformation. Fifty-five percent of those who died were age 15-29 years and 79% were male. The fatality risk ratio (FRR) comparing cargo area occupants to front seat occupants was 3.0 (95% Confidence Interval [CI] = 2.7-3.4). The risk was 7.9 (95% CI = 6.2-10.1) times that of restrained front seat occupants. The FRR ranged from 92 (95% CI = 47-179) in noncrash events to 1.7 (95% CI = 1.5-1.9) in crashes with severe vehicle deformation. The FRR was 1.8 (95% CI = 1.4-2.3) for occupants of enclosed cargo areas and 3.5 (95% CI = 3.1-4.0) for occupants of open cargo areas. We conclude that passengers in cargo areas of pickup trucks have a higher risk of death than front seat occupants, especially in noncrash events, and that camper shells offer only limited protection for cargo area occupants.

A second look at the relation between colorectal adenomas and consumption of foods containing partially hydrogenated oils

The trans fatty acids in partially hydrogenated vegetable oil may cause colorectal neoplasia by interfering with cell membrane function or eicosanoid metabolism. This possibility provided a rationale for looking at the relation between colorectal adenomas and consumption of foods containing partially hydrogenated vegetable oils in 234 cases and 407 controls recruited from referrals for colonoscopy at University of North Carolina Hospitals in Chapel Hill, between 1988 and 1990. Foods containing partially hydrogenated vegetable oils were divided into four groups: sweetened baked goods, chocolate candy, oils and condiments, and french fries and chips. We observed no evidence of increased adenoma prevalence associated with consumption of fries and chips (200+ vs 0 kcals/day: odds ratio (OR) = 0.70; 95% confidence limits (CL) = 0.27, 1.8) or chocolate candy (50+ vs 0 kcals/day: OR = 0.49; 95% CL = 0.23, 1.1). We did, however, find evidence of increased adenoma prevalence associated with consumption of sweetened baked goods (400+ vs < 100 kcals/day: OR = 1.9; 95% CL = 0.95, 3.8) and oils and condiments (200+ vs < 100 kcals/day: OR = 2.4; 95% CL = 1.3, 4.2).

A retrospective cohort study of implanted medical devices and selected chronic diseases in Medicare claims data

PURPOSE

Several case-control studies have observed associations of implanted medical devices and certain connective-tissue and neurologic diseases. We reexamined these and other associations using cohort comparisons.

METHODS

We compared the incidence of 52 diseases in several retrospective cohorts constructed from Medicare claims data. Six cohorts were defined by implantation of medical devices (silicone, metal bone or joint implants, breast implants, penile implants, pacemakers, artificial heart valves), and four comparison cohorts were defined by surgeries not involving implants.

RESULTS

We observed associations that were generally consistent with previous reports, including associations of bone and joint implants with connective-tissue diseases, and an association of penile implants with idiopathic progressive neuropathy. We also observed associations of breast implants and pacemakers with connective-tissue diseases.

CONCLUSIONS

For the most part, our study confirms our previous case-control results. Although confounding by presurgical conditions (such as diabetes) remains a plausible explanation of the findings, several associations are worthy of more detailed research.

Small-sample bias and corrections for conditional maximum-likelihood odds-ratio estimators

A number of small-sample corrections have been proposed for the conditional maximum-likelihood estimator of the odds ratio for matched pairs with a dichotomous exposure. I here contrast the rationale and performance of several corrections, specifically those that generalize easily to multiple conditional logistic regression. These corrections or Bayesian analyses with informative priors may serve as diagnostics for small-sample problems. Points are illustrated with a small exact performance comparison and with an example from a study of electrical wiring and childhood leukemia. The former comparison suggests that small-sample bias may be more prevalent than commonly realized.

Problems due to small samples and sparse data in conditional logistic regression analysis

Conditional logistic regression was developed to avoid "sparse-data" biases that can arise in ordinary logistic regression analysis. Nonetheless, it is a large-sample method that can exhibit considerable bias when certain types of matched sets are infrequent or when the model contains too many parameters. Sparse-data bias can cause misleading inferences about confounding, effect modification, dose response, and induction periods, and can interact with other biases. In this paper, the authors describe these problems in the context of matched case-control analysis and provide examples from a study of electrical wiring and childhood leukemia and a study of diet and glioma. The same problems can arise in any likelihood-based analysis, including ordinary logistic regression. The problems can be detected by careful inspection of data and by examining the sensitivity of estimates to category boundaries, variables in the model, and transformations of those variables. One can also apply various bias corrections or turn to methods less sensitive to sparse data than conditional likelihood, such as Bayesian and empirical-Bayes (hierarchical regression) methods.

Principles of multilevel modelling

BACKGROUND

Multilevel modelling, also known as hierarchical regression, generalizes ordinary regression modelling to distinguish multiple levels of information in a model. Use of multiple levels gives rise to an enormous range of statistical benefits. To aid in understanding these benefits, this article provides an elementary introduction to the conceptual basis for multilevel modelling, beginning with classical frequentist, Bayes, and empirical-Bayes techniques as special cases. The article focuses on the role of multilevel averaging ('shrinkage') in the reduction of estimation error, and the role of prior information in finding good averages.

Multilevel modeling and model averaging

Multilevel modeling, also known as hierarchical regression, generalizes ordinary regression modeling to allow explicit and flexible compromises between simple and complex models. This article provides an elementary introduction to multilevel modeling as a model-averaging technique. Model averaging provides an alternative to model selection, and it emphasizes the role of prior information in finding good models.

Side effects as predictors of drug response in obsessive-compulsive disorder

Differences between the side effect profiles of clomipramine (CMI) and the selective serotonin reuptake inhibitors may be important factors in both treatment outcome and patient selection in obsessive-compulsive disorder (OCD). Safety and efficacy data from an industry-sponsored, multicenter clinical trial of CMI were analyzed previously using tabular and multiple regression methods. Good response, defined as at least a 35% drop in final scores on the Yale-Brown Obsessive Compulsive Scale (Y-BOCS), was associated with a later age of OCD onset and certain early side effects that may reflect a sensitivity of responders to CMI's serotonergic actions. The authors conducted a similar analysis of data from an industry-sponsored clinical trial of fluoxetine in OCD. Fluoxetine response did not seem to be associated with age of OCD onset. Good response to both drugs was associated with initial nervousness and sexual complaints. The common side effects of fluoxetine (headache, nausea, and gastrointestinal complaints) did not seem to be associated with treatment response. Slight differences in the protocols of the two clinical trials yielded patient populations that were different in factors found to be associated with treatment outcome: subjects in the fluoxetine study had lower scores on the Y-BOCS, higher scores on the Hamilton Rating Scale for Depression, and an earlier age of OCD onset.

Random-effects meta-analyses are not always conservative

It is widely held that random-effects summary effect estimates are more conservative than fixed-effects summaries in epidemiologic meta-analysis. This view is based on the fact that random-effects summaries have higher estimated variances and, consequently, wider confidence intervals than fixed-effects summaries when there is evidence of appreciable heterogeneity among the results from the individual studies. In such instances, however, the random-effects point estimates are not invariably closer to the null value nor are their p values invariably larger than those of fixed-effects summaries. Thus, random-effects summaries are not predictably conservative according to either of these two connotations of the term. The authors give an example from a meta-analysis of water chlorination and cancer in which the random-effects summaries are less conservative in both of these alternative senses and possibly more biased than the fixed-effects summaries. The discussion of when to use random effects and when to use fixed effects in computing summary estimates should be replaced by a discussion of whether summary estimates should be computed at all when the studies are not methodologically comparable, when their results are discernibly heterogeneous, or when there is evidence of publication bias.

Relation of probability of causation to relative risk and doubling dose: a methodologic error that has become a social problem

Epidemiologists, biostatisticians, and health physicists frequently serve as expert consultants to lawyers, courts, and administrators. One of the most common errors committed by experts is to equate, without qualification, the attributable fraction estimated from epidemiologic data to the probability of causation requested by courts and administrators. This error has become so pervasive that it has been incorporated into judicial precedents and legislation. This commentary provides a brief overview of the error and the context in which it arises.

Application of the case-specular method to two studies of wire codes and childhood cancers

This paper presents the results of applying the case-specular method to two earlier studies of wire codes and childhood cancers (DA Savitz et al, Am J Epidemiol 1988;128:21-38, and SJ London et al, Am J Epidemiol 1991;9:923-937). The method compares the wire codes of case residences with the wire codes of specular residences constructed by switching the location of the case residence across the center of the street. The method was designed to discriminate between the magnetic field hypothesis, which postulates that childhood cancer is affected by magnetic fields and that wire codes are a proxy for magnetic fields, and the neighborhood hypothesis, which postulates that childhood cancer is affected by some characteristics of the neighborhood other than magnetic fields and that wire codes are a proxy for those characteristics. Although the results from the two applications of the method have limited precision, they support the results originally reported (odds ratios of around 2 for very high current configuration residences and childhood cancers) and do not support suggestions that the associations are due to confounding by socio-economic and neighborhood factors. The results leave open the question of whether or not control selection bias could have influenced the original associations, because there was no convincing evidence that the control-specular matrices were symmetric.

Presenting statistical uncertainty in trends and dose-response relations

When one estimates the effects of a polytomous exposure, it is common practice to express all effects relative to a baseline or reference level. Certain authors have challenged this practice and proposed alternatives, which we review here. One alternative, the "floating absolute risk" method, can supply useful statistics and trend graphs, but it does not yield valid confidence intervals for relative risks. All categorical methods have further shortcomings when the exposure is continuous, however. These shortcomings can be addressed by plotting or tabulating confidence limits for points on a flexible curve fitted to the uncategorized data.

A case-control study of colorectal adenomatous polyps and consumption of foods containing partially hydrogenated oils

The trans fatty acids produced by partially hydrogenating vegetable oils may cause colorectal neoplasia by interfering with cell membrane function or eicosanoid synthesis. This possibility provides a rationale for looking at the relation between colorectal adenomatous polyps and consumption of foods containing partially hydrogenated vegetable oils (PHVOs). A total of 516 cases and 551 controls who underwent screening sigmoidoscopy from 1991-1993 were recruited from a prepaid Los Angeles health plan. Subjects were interviewed and given a self-administered food frequency questionnaire. Food items containing PHVOs were divided into four groups characterized by principal ingredients and preparation methods: sweetened baked goods, candy bars, oils and condiments, and french fries and chips. After adjusting for age, sex, physical activity, body mass index, smoking, total energy, and red meat and vegetable intake, there was a positive association between polyps and sweetened baked goods [350+ versus <50 kcal/day (odds ratio, 2.1; 95% confidence interval, 1.3-3.5)]. No association was found with the other food groups after adjustment for dietary and nondietary covariates. Neither was total dietary trans fatty acid associated with adenomas after adjustment for sweetened baked goods and other covariates. These results do not support the hypothesis that eating foods containing PHVOs increases the risk of colorectal adenomas, but they are consistent with the hypothesis that foods high in fat and sugar and low in fiber and correlated micronutrients increase the risk of adenomas.