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Paul Gustafson

Publications and source records attributed to Paul Gustafson.

15 recordsLinked to original sources
PubMed2007

Bayesian sensitivity analysis for unmeasured confounding in observational studies.

We consider Bayesian sensitivity analysis for unmeasured confounding in observational studies where the association between a binary exposure, binary response, measured confounders and a single binary unmeasured confounder can be formulated using logistic regression models. A model for unmeasured confounding is presented along with a family of prior distributions that model beliefs about a possible unknown unmeasured confounder. Simulation from the posterior distribution is accomplished using Markov chain Monte Carlo. Because the model for unmeasured confounding is not identifiable, standard large-sample theory for Bayesian analysis is not applicable. Consequently, the impact of different choices of prior distributions on the coverage probability of credible intervals is unknown. Using simulations, we investigate the coverage probability when averaged with respect to various distributions over the parameter space. The results indicate that credible intervals will have approximately nominal coverage probability, on average, when the prior distribution used for sensitivity analysis approximates the sampling distribution of model parameters in a hypothetical sequence of observational studies. We motivate the method in a study of the effectiveness of beta blocker therapy for treatment of heart failure.

Adrenergic beta-Antagonists↗
PubMed2006

An innovative application of Bayesian disease mapping methods to patient safety research: a Canadian adverse medical event study.

Recently developed disease mapping and ecological regression methods have become important techniques in studies of disease epidemiology and in health services research. This increase in importance is partially a result of the development of Bayesian statistical methodologies that make it possible to study associations between health problems and risk factors at an aggregate (i.e. areal) level while taking into account such matters as unmeasured confounding and spatial relationships. In this paper we present a demonstration of the joint use of empirical Bayes (EB) and full Bayesian inferential techniques in a small area study of adverse medical events (also known as 'iatrogenic injury') in British Columbia, Canada. In particular, we illustrate a unified Bayesian hierarchical spatial modelling framework that enables simultaneous examinations of potential associations between adverse medical event occurrence and regional characteristics, age effects, residual variation and spatial autocorrelation. We propose an analytic strategy for complementary use of EB and FB inferential techniques for risk assessment and model selection, presenting an EB-FB combined approach that draws on the strengths of each method while minimizing inherent weaknesses. The work was motivated by the need to explore relatively efficient ways to analyse regional variations of health services outcomes and resource utilization when a considerable amount of statistical modelling and inference are required.

Adolescent↗
PubMed2006

Accounting for independent nondifferential misclassification does not increase certainty that an observed association is in the correct direction.

Researchers sometimes argue that their exposure-measurement errors are independent of other errors and are nondifferential with respect to disease, resulting in estimation bias toward the null. Among well-known problems with such arguments are that independence and nondifferentiality are harder to satisfy than ordinarily appreciated (e.g., because of correlation of errors in questionnaire items, and because of uncontrolled covariate effects on error rates); small violations of independence or nondifferentiality may lead to bias away from the null; and, if exposure is polytomous, the bias produced by independent nondifferential error is not always toward the null. The authors add to this list by showing that, in a 2 x 2 table (for which independent nondifferential error produces bias toward the null), accounting for independent nondifferential error does not reduce the p value even though it increases the point estimate. Thus, such accounting should not increase certainty that an association is present.

Bias↗
PubMed2006

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.

Anti-Bacterial Agents↗
PubMed2006

Neonatal intensive care unit characteristics affect the incidence of severe intraventricular hemorrhage.

OBJECTIVES: The incidence of intraventricular hemorrhage (IVH), adjusted for known risk factors, varies across neonatal intensive care units (NICU)s. The effect of NICU characteristics on this variation is unknown. The objective was to assess IVH attributable risks at both patient and NICU levels. STUDY DESIGN: Subjects were <33 weeks' gestation, <4 days old on admission in the Canadian Neonatal Network database (all infants admitted in 1996-97 to 17 NICUs). The variation in severe IVH rates was analyzed using Bayesian hierarchical modeling for patient level and NICU level factors. RESULTS: Of 3772 eligible subjects, the overall crude incidence rates of grade 3-4 IVH was 8.3% (NICU range 2.0-20.5%). Male gender, extreme preterm birth, low Apgar score, vaginal birth, outborn birth, and high admission severity of illness accounted for 30% of the severe IVH rate variation; admission day therapy-related variables (treatment of acidosis and hypotension) accounted for an additional 14%. NICU characteristics, independent of patient level risk factors, accounted for 31% of the variation. NICUs with high patient volume and high neonatologist/staff ratio had lower rates of severe IVH. CONCLUSIONS: The incidence of severe IVH is affected by NICU characteristics, suggesting important new strategies to reduce this important adverse outcome.

Acute Disease↗
PubMed2006

The performance of random coefficient regression in accounting for residual confounding.

Greenland (2000, Biometrics 56, 915-921) describes the use of random coefficient regression to adjust for residual confounding in a particular setting. We examine this setting further, giving theoretical and empirical results concerning the frequentist and Bayesian performance of random coefficient regression. Particularly, we compare estimators based on this adjustment for residual confounding to estimators based on the assumption of no residual confounding. This devolves to comparing an estimator from a nonidentified but more realistic model to an estimator from a less realistic but identified model. The approach described by Gustafson (2005, Statistical Science 20, 111-140) is used to quantify the performance of a Bayesian estimator arising from a nonidentified model. From both theoretical calculations and simulations we find support for the idea that superior performance can be obtained by replacing unrealistic identifying constraints with priors that allow modest departures from those constraints. In terms of point-estimator bias this superiority arises when the extent of residual confounding is substantial, but the advantage is much broader in terms of interval estimation. The benefit from modeling residual confounding is maintained when the prior distributions employed only roughly correspond to reality, for the standard identifying constraints are equivalent to priors that typically correspond much worse.

Bayes Theorem↗
PubMed2005

Extending logistic regression to model diffuse interactions.

In an observational study focussed on association between a health outcome and numerous explanatory variables, the question of interactions can be problematic. Commonly, logistic regression of the outcome on the explanatory variables might be employed. Such modelling often includes an attempt to select some pairwise product interaction terms, from amongst the many such possible pairs. For several reasons, however, this can be unsatisfying. Here we consider a different approach based on a parsimonious extension of a logistic regression model without interaction terms. This extension permits an overall synergism or antagonism in how the explanatory variables combine to associate with the outcome, without any attempt to identify specific variables which give rise to interactive behaviour. We call this diffuse interaction. We elucidate some simple properties of the diffuse interaction model, and give an example of its application to epidemiological data. We also consider asymptotic behaviour in a restricted case of the model, to gain some insight into how well this kind of interaction can be detected from data.

Analysis of Variance↗
PubMed2005

The utility of prior information and stratification for parameter estimation with two screening tests but no gold standard.

When a gold standard screening or diagnostic test is not routinely available, it is common to apply two different imperfect tests to subjects from a study population. There is a considerable literature on estimating relevant parameters from the resultant data. In the situation that test sensitivities and specificities are unknown, several inferential strategies have been proposed. One suggestion is to use rough knowledge about the unknown test characteristics as prior information in a Bayesian analysis. Another suggestion is to obtain the statistical advantage of an identified model by splitting the population into two strata with differing disease prevalences. There is some division of opinion in the epidemiological literature on the relative merits of these two approaches. This article aims to shed light on the issue, by applying some recently developed theory on the performance of Bayesian inference in non-identified statistical models.

Bayes Theorem↗
PubMed2004

Estimation in Bayesian disease mapping.

Recent work on Bayesian inference of disease mapping models discusses the advantages of the fully Bayesian (FB) approach over its empirical Bayes (EB) counterpart, suggesting that FB posterior standard deviations of small-area relative risks are more reflective of the uncertainty associated with the relative risk estimation than counterparts based on EB inference, since the latter fail to account for the variability in the estimation of the hyperparameters. In this article, an EB bootstrap methodology for relative risk inference with accurate parametric EB confidence intervals is developed, illustrated, and contrasted with the hyperprior Bayes. We elucidate the close connection between the EB bootstrap methodology and hyperprior Bayes, present a comparison between FB inference via hybrid Markov chain Monte Carlo and EB inference via penalized quasi-likelihood, and illustrate the ability of parametric bootstrap procedures to adjust for the undercoverage in the "naive" EB interval estimates. We discuss the important roles that FB and EB methods play in risk inference, map interpretation, and real-life applications. The work is motivated by a recent analysis of small-area infant mortality rates in the province of British Columbia in Canada.

Algorithms↗
PubMed2003

Pelvic bone asymmetry in 323 study participants receiving abdominal CT scans.

STUDY DESIGN: Retrospective review of all CT scans of pelvis and abdomen performed at our institution in October and November 2000. OBJECTIVE: To determine the prevalence and extent of radiographic pelvic asymmetry in a population of patients not preselected for having low back pain. SUMMARY OF BACKGROUND DATA: Pelvic asymmetry refers to asymmetric positioning of landmarks on the two sides of the pelvis and may have a structural or functional etiology. Pelvic asymmetry can be associated with the presence of true leg length discrepancy, lead to false diagnosis or inaccurate measurement of leg length discrepancy, or itself be independently associated with back pain. Although the prevalence of pelvic asymmetry has been reported in patients with back pain to be 24-91%, its prevalence in the general population is not known. METHODS: A total of 323 consecutive CT scans of the pelvis/abdomen were assessed for pelvic asymmetry by one of three examiners. Pelvic asymmetry was defined as an unequal distance from the iliac crests to the acetabuli bilaterally, measured on the anteroposterior scout view of the CT scan. Measurements made on 30 randomly selected scans by the three examiners were used to assess interrater reliability of the measurement method. RESULTS: Pelvic asymmetry ranged in magnitude from -11 mm to 7 mm [right pelvis (mm) - left pelvis (mm)]. Pelvic asymmetry was >5 mm in 17 of 323 (5.3%) and >10 mm in 2 of 323 (0.6%) of the subjects; 172 of 323 (53.3%) had a smaller right hemipelvis (mean asymmetry = -3.0 mm). A total of 95 of 323 (29.4%) had a smaller left hemipelvis (mean asymmetry = 2.1 mm). The intraclass correlation coefficient [ICC(2,1)] between the three observers was high (0.91). CONCLUSION: Pelvic asymmetry of >5 mm was uncommon, with a prevalence of approximately 5% in the population studied. CT scanography was found to be a practical and reliable method for the assessment of suspected pelvic asymmetry.

Adolescent↗
PubMed2003

A simple approach to fitting Bayesian survival models.

There has been much recent work on Bayesian approaches to survival analysis, incorporating features such as flexible baseline hazards, time-dependent covariate effects, and random effects. Some of the proposed methods are quite complicated to implement, and we argue that as good or better results can be obtained via simpler methods. In particular, the normal approximation to the log-gamma distribution yields easy and efficient computational methods in the face of simple multivariate normal priors for baseline log-hazards and time-dependent covariate effects. While the basic method applies to piecewise-constant hazards and covariate effects, it is easy to apply importance sampling to consider smoother functions.

Bayes Theorem↗
PubMed2002

A Bayesian approach to case-control studies with errors in covariables.

We develop Bayesian methodology for the analysis of case-control data with covariate imprecision. The pretense that the distribution of the imprecisely measured covariate is discrete on a heuristically chosen support set leads to a method which is reasonably simple to implement, and can be applied to different study designs. The methodological development emphasizes the interplay between retrospective and prospective analysis. We illustrate the method on simulated data, and on data from a cancer study where smoking history is the imprecisely measured covariate.

Journal Article↗
PubMed2002

Comparing the effects of continuous and discrete covariate mismeasurement, with emphasis on the dichotomization of mismeasured predictors.

It is well known that imprecision in the measurement of predictor variables typically leads to bias in estimated regression coefficients. We compare the bias induced by measurement error in a continuous predictor with that induced by misclassification of a binary predictor in the contexts of linear and logistic regression. To make the comparison fair, we consider misclassification probabilities for a binary predictor that correspond to dichotomizing an imprecise continuous predictor in lieu of its precise counterpart. On this basis, nondifferential binary misclassification is seen to yield more bias than nondifferential continuous measurement error. However, it is known that differential misclassification results if a binary predictor is actually formed by dichotomizing a continuous predictor subject to nondifferential measurement error. When the postulated model linking the response and precise continuous predictor is correct, this differential misclassification is found to yield less bias than continuous measurement error, in contrast with nondifferential misclassification, i.e., dichotomization reduces the bias due to mismeasurement. This finding, however, is sensitive to the form of the underlying relationship between the response and the continuous predictor. In particular, we give a scenario where dichotomization involves a trade-off between model fit and misclassification bias. We also examine how the bias depends on the choice of threshold in the dichotomization process and on the correlation between the imprecise predictor and a second precise predictor.

Bias↗