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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

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 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.

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.