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Biomedical subjects

T A Louis

Publications and source records attributed to T A Louis.

61 records · Page 4Linked to original sources

Reducing the number of inferior treatments in clinical trials.

In clinical trials comparing two treatments, one would often like to control the probability of erroneous decision while minimizing not the total sample size but the number of patients given the inferior treatment. To do this obviously requires that one use a datadependent allocation rule for the two treatments rather than the conventional equal sample size scheme, whether fixed or sequential. We show here how this may be done in the case of deciding which of two normally distributed treatment effects has the greater mean, when the variances are assumed to be equal and known. Similar methods can be used under other hypotheses on the underlying probability distributions, and will provide a considerable increase in flexibility in the design of sequential clinical trials.

Clinical Trials as Topic↗

Innovations in bayes and empirical bayes methods: estimating parameters, populations and ranks.

By formalizing the relation among components and 'borrowing information' among them, Bayes and empirical Bayes methods can produce more valid, efficient and informative statistical evaluations than those based on traditional methods. In addition, Bayesian structuring of complicated models and goals guides development of appropriate statistical approaches and generates summaries which properly account for sampling and modelling uncertainty. Computing innovations enable implementation of complex and relevant models, thereby substantially increasing the role of Bayes/empirical Bayes methods in important statistical assessments. Policy-relevant statistical assessments involve synthesis of information from a set of related components such as medical clinics, geographic regions or research studies. Typical assessments include inference for individual parameters, synthesis over the collection of components (for example, the parameter histogram) and comparisons among parameters (for example, ranks). The relative importance of these goals depends on the context. Bayesian structuring provides a guide to valid inference. For example, while posterior means are the 'obvious' and optimal estimates for individual components under squared error loss, their empirical distribution function (EDF) is underdispersed and never valid for estimating the EDF of the true, underlying parameters. Effective histogram estimates result from optimizing a loss function based in a distance between the histogram and its estimate. Similarly, ranking observed data usually produces poor estimates and ranking posterior means can be inappropriate. Effective estimates should be based on a loss function that caters directly to ranks. Using examples of 'borrowing information', shrinkage and the variance/bias trade-off we motivate Bayes and empirical Bayes analysis. Then, we outline the formal approach and discuss 'triple-goal' estimates with values that when ranked produce optimal ranks, for which the EDF is an optimal estimate of the parameter EDF and such that the values themselves are effective estimates of co-ordinate-specific parameters. We use basic models and data analysis examples to highlight the conceptual and structural issues.

Animals↗

Triple-goal estimates for disease mapping.

Maps of regional morbidity and mortality rates play an important role in assessing environmental equity. They provide effective tools for identifying areas with potentially elevated risk, determining spatial trend, and formulating and validating aetiological hypotheses about disease. Bayes and empirical Bayes methods produce stable small-area rate estimates that retain geographic and demographic resolution. The beauty of the Bayesian approach lies in its ability to structure complicated models, inferential goals and analyses. Three inferential goals are relevant to disease mapping and risk assessment: (i) computing accurate estimates of disease rates in small geographic areas; (ii) estimating the distribution of disease rates over the region; (iii) ranking the disease rates so that environmental investigation can be prioritized. No single set of estimates can simultaneously optimize these three goals, and Shen and Louis propose a set of estimates that perform well on all three goals. These are optimal for estimating the distribution of rates and for ranking, and maintain a high accuracy in estimating area-specific rates. However, the Shen/Louis method is sensitive to choice of priors. To address this issue we introduce a robustified version of the method based on a smoothed non-parametric estimate of the prior. We evaluate the performance of this method through a simulation study, and illustrate it using a data set of county-specific lung cancer rates in Ohio.

Algorithms↗

Statistical consulting in clinical research: the two-way street.

Clinical research often rests on statistical interpretation of numerical data. Thus, effective collaboration between clinician and statistician can have central importance. Interaction in the planning phases of a project can identify tractable scientific and statistical problems that will need attention and can help avoid intractable ones. The central need is for clear, broad, specific two-way communication on scientific issues and research roles.

Communication↗

General methods for analysing repeated measures.

We present an overview of issues and methods for analysing repeated measures of a continuous random variable. We discuss modelling the mean vector and covariance structure, statistical efficiency, regression diagnostics, and discrepancies between longitudinal and cross-sectional methods. We illustrate key points with examples and discuss areas requiring further development.

Adult↗

Random effects models with non-parametric priors.

We discuss the performance of non-parametric maximum likelihood (NPML) estimators for the distribution of a univariate random effect in the analysis of longitudinal data. For continuous data, we analyse generated and real data sets, and compare the NPML method to those that assume a Gaussian random effects distribution and to ordinary least squares. For binary outcomes we use generated data to study the moderate and large-sample performance of the NPML compared with a method based on a Gaussian random effect distribution in logistic regression. We find that estimated fixed effects are compatible for all approaches, but that appropriate standard errors for the NPML require adjusting the likelihood-based standard errors. We conclude that the non-parametric approach provides an attractive alternative to Gaussian-based methods, though additional evaluations are necessary before it can be recommended for general use.

Likelihood Functions↗

Environmental justice and statistical summaries of differences in exposure distributions.

Recent regulatory action requires the assessment of environmental justice (equitable protection from the burdens of environmental hazards across sociodemographic subpopulations) in the siting of hazardous waste sites, and prioritization of environmental remediation efforts. Assessments of environmental justice require linking exposure, demographic, and health data. The geographic nature of the data makes the use of geographic information systems attractive for environmental justice assessments. Typical geographic assessments compare the composition of 'exposed' populations, while typical statistical assessments focus on differences in health outcomes between population subgroups, possibly adjusted for exposure. We outline an alternate approach based on summarized differences between exposure distributions within each population subgroup. We illustrate how such summaries provide a tool for site evaluation (e.g., defining exposure inequities resulting from locating a new potential hazard at any of a number of possible sites). In addition, we describe summaries, based on dose-response relationships, to describe risk differences imposed by the observed exposure differences. Reported toxic emissions from Allegheny County, Pennsylvania illustrate the approach.

Bayes Theorem↗