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PubMed2004

Statistical and substantive inferences in public health: issues in the application of multilevel models.

Multilevel statistical models have become increasingly popular among public health researchers over the past decade. Yet the enthusiasm with which these models are being adopted may obscure rather than solve some problems of statistical and substantive inference. We discuss the three most common applications of multilevel models in public health: (a) cluster-randomized trials, (b) observational studies of the multilevel etiology of health and disease, and (c) assessments of health care provider performance. In each area of investigation, we describe how multilevel models are being applied, comment on the validity of the statistical and substantive inferences being drawn, and suggest ways in which the strengths of multilevel models might be more fully exploited. We conclude with a call for more careful thinking about multilevel causal inference.

Bayes Theorem↗
PubMed1988

Properties of the urn randomization in clinical trials.

In this article we review the important statistical properties of the urn randomization (design) for assigning patients to treatment groups in a clinical trial. The urn design is the most widely studied member of the family of adaptive biased-coin designs. Such designs are a compromise between designs that yield perfect balance in treatment assignments and complete randomization which eliminates experimental bias. The urn design forces a small-sized trial to be balanced but approaches complete randomization as the size of the trial (n) increases. Thus, the urn design is not as vulnerable to experimental bias as are other restricted randomization procedures. In a clinical trial it may be difficult to postulate that the study subjects constitute a random sample from a well-defined homogeneous population. In this case, a randomization model provides a preferred basis for statistical inference. We describe the large-sample permutational null distributions of linear rank statistics for testing the equality of treatment groups based on the urn design. In general, these permutation tests may be different from those based on the population model, which is equivalent to assuming complete randomization. Poststratified subgroup analyses can also be performed on the basis of the urn design permutational distribution. This provides a basis for analyzing the subset of patients with observed responses when some patients' responses can be assumed to be missing-at-random. For multiple mutually exclusive strata, these tests are correlated. For this case, a combined covariate-adjusted test of treatment effect is described. Finally, we show how to generalize the urn design to a prospectively stratified trial with a fairly large number of strata.

Clinical Trials as Topic↗
PubMed2003

Theoretical basis of the Beavis effect.

The core of statistical inference is based on both hypothesis testing and estimation. The use of inferential statistics for QTL identification thus includes estimation of genetic effects and statistical tests. Typically, QTL are reported only when the test statistics reach a predetermined critical value. Therefore, the estimated effects of detected QTL are actually sampled from a truncated distribution. As a result, the expectations of detected QTL effects are biased upward. In a simulation study, William D. Beavis showed that the average estimates of phenotypic variances associated with correctly identified QTL were greatly overestimated if only 100 progeny were evaluated, slightly overestimated if 500 progeny were evaluated, and fairly close to the actual magnitude when 1000 progeny were evaluated. This phenomenon has subsequently been called the Beavis effect. Understanding the theoretical basis of the Beavis effect will help interpret QTL mapping results and improve success of marker-assisted selection. This study provides a statistical explanation for the Beavis effect. The theoretical prediction agrees well with the observations reported in Beavis's original simulation study. Application of the theory to meta-analysis of QTL mapping is discussed.

Chromosome Mapping↗
PubMed1994

[How to assess the size of a clinical trial?].

The interpretation of the results of a clinical trial, an experimental method now recognised as the agreed technique for studying new therapeutic modes of treatment in man, is based on a statistical study of data collected on a sample of patients enrolled in the study and treated till its fulfillment. This interpretation is often made using statistical inference techniques based on the construction of a decision rule associated with a statistical hypothesis test; this hypothesis test serves to formalize a research question in a precise manner, and allows the null hypothesis H0 to be tested against an alternative hypothesis H1. The decision rule will be constructed using a probability distribution, which assumes control against type I error, and consists of falsely rejecting the null hypothesis. However, the control of the risk of type II error, made error where one mistakenly takes a decision not to reject the null hypothesis, can only be achieved using a sufficiently large sample. The correct evaluation of the sample size is thus paramount if one does not wish to be doomed to the failure of a study, by including an insufficient number of patients to achieve the aimed objective. The aim of this report is to review how this evaluation can be due, in a practical manner without proof, in the context of simple situations which are used when Phase II or III clinical trials are put into action.

Clinical Trials as Topic↗
PubMed2002

Exact unconditional inference for risk ratio in a correlated 2 x 2 table with structural zero.

In this article, we consider small-sample statistical inference for rate ratio (RR) in a correlated 2 x 2 table with a structural zero in one of the off-diagonal cells. Existing Wald's test statistic and logarithmic transformation test statistic will be adopted for this purpose. Hypothesis testing and confidence interval construction based on large-sample theory will be reviewed first. We then propose reliable small-sample exact unconditional procedures for hypothesis testing and confidence interval construction. We present empirical results to evince the better confidence interval performance of our proposed exact unconditional procedures over the traditional large-sample procedures in small-sample designs. Unlike the findings given in Lui (1998, Biometrics 54, 706-711), our empirical studies show that the existing asymptotic procedures may not attain a prespecified confidence level even in moderate sample-size designs (e.g., n = 50). Our exact unconditional procedures on the other hand do not suffer from this problem. Hence, the asymptotic procedures should be applied with caution. We propose two approximate unconditional confidence interval construction methods that outperform the existing asymptotic ones in terms of coverage probability and expected interval width. Also, we empirically demonstrate that the approximate unconditional tests are more powerful than their associated exact unconditional tests. A real data set from a two-step tuberculosis testing study is used to illustrate the methodologies.

Confidence Intervals↗
PubMed2006

Estimation of bias between 2 analytical methods at clinically important ranges.

An approach for estimating bias between 2 analytical methods at different clinical ranges is introduced in this article. The approach models replicated data obtained from the reference and the test method in terms of repeatability and trueness bias. The latter can be partitioned into constant and proportional bias. The approach is based on maximum likelihood estimation and can accommodate normal as well as Poisson and binomial distributions that apply to hematology applications and/or other laboratory methods that count particles per unit of volume and/or time. A full spectrum of statistical inference in the form of confidence intervals for each estimate as well as any statistical hypothesis testing is provided. At the same time these estimates can be practically interpreted and related to any clinical important range or decision point. We recommend this approach as an alternative to the National Committee for Clinical Laboratory Standards (NCCLS) EP9-A2 approach in cases where the application of the NCCLS standard is not appropriate.

Bias↗
PubMed2006

Statistical and Bayesian approaches to RNA secondary structure prediction.

Prediction of RNA secondary structure is a fundamental problem in computational structural biology. For several decades, free energy minimization has been the most popular method for prediction from a single sequence. In recent years, the McCaskill algorithm for computation of partition function and base-pair probabilities has become increasingly appreciated. This paradigm-shifting work has inspired the developments of extended partition function algorithms, statistical sampling and clustering, and application of Bayesian statistical inference. The performance of thermodynamics-based methods is limited by thermodynamic rules and parameters. However, further improvements may come from statistical estimates derived from structural databases for thermodynamics parameters with weak or little experimental data. The Bayesian inference approach appears to be promising in this context.

Algorithms↗
PubMed1998

A comprehensive clinical epidemiological theory based on the concept of the source person-time and four distinct study stages.

The medical community is forced to accelerate the move from opinion-based to evidence-based medicine, that is, to aim at basing all caring and clinical practice on empiri. A clear-cut epistemology would facilitate this process. In this article we present a comprehensive clinical epidemiological theory which can be used for validity issues in caring science, quality of life research, controlled clinical trials and compilations of uncontrolled evidence. The theory is based on four distinct stages that can be identified in a study, whereof the first is demarcation of the source person-time. A source person-time ('study base') can be identified for any study in all disciplines, giving an argument for using this concept as the common reference point for validity issues. Apart from identifying the source person-time, recovery of the actually observed person-time, collection of data and calculation of an ('adjusted') effect parameter (e.g., incidence ratio) are additional stages of a study. When the source person-time is demarcated confounding is introduced, when the actually observed person-time is recovered misrepresentation, in the third stage misclassification and in the fourth analytical alteration of the parameter of effect. The concept of the source person-time can, in addition, link examination of validity in caring and clinical sciences to observational studies, thereby allowing the field to benefit from all theoretical achievements for preventing, handling and understanding systematic errors developed in epidemiology. We conclude it is possible to implement a common terminology of validity for all caring and medical sciences. Drawing causal inferences in these disciplines is not mechanical, it can never, for example, be done with statistical inference. Establishing a causal relation always includes an assessment of the magnitude and direction of systematic errors influencing the adjusted effect parameter. From the presented epistemology it follows that differences in validity from a case history to a large randomized, placebo-controlled and double-blinded study are quantitative rather than qualitative. This realization in turn opens up for a more refined discussion of when a decision is evidence-based rather than opinion-based.

Clinical Trials as Topic↗
PubMed2006

A maximum likelihood framework for protein design.

BACKGROUND: The aim of protein design is to predict amino-acid sequences compatible with a given target structure. Traditionally envisioned as a purely thermodynamic question, this problem can also be understood in a wider context, where additional constraints are captured by learning the sequence patterns displayed by natural proteins of known conformation. In this latter perspective, however, we still need a theoretical formalization of the question, leading to general and efficient learning methods, and allowing for the selection of fast and accurate objective functions quantifying sequence/structure compatibility. RESULTS: We propose a formulation of the protein design problem in terms of model-based statistical inference. Our framework uses the maximum likelihood principle to optimize the unknown parameters of a statistical potential, which we call an inverse potential to contrast with classical potentials used for structure prediction. We propose an implementation based on Markov chain Monte Carlo, in which the likelihood is maximized by gradient descent and is numerically estimated by thermodynamic integration. The fit of the models is evaluated by cross-validation. We apply this to a simple pairwise contact potential, supplemented with a solvent-accessibility term, and show that the resulting models have a better predictive power than currently available pairwise potentials. Furthermore, the model comparison method presented here allows one to measure the relative contribution of each component of the potential, and to choose the optimal number of accessibility classes, which turns out to be much higher than classically considered. CONCLUSION: Altogether, this reformulation makes it possible to test a wide diversity of models, using different forms of potentials, or accounting for other factors than just the constraint of thermodynamic stability. Ultimately, such model-based statistical analyses may help to understand the forces shaping protein sequences, and driving their evolution.

Amino Acid Sequence↗
PubMed2001

Pathogen testing of ready-to-eat meat and poultry products collected at federally inspected establishments in the United States, 1990 to 1999.

The Food Safety and Inspection Service (FSIS) conducted microbiological testing programs for ready-to-eat (RTE) meat and poultry products produced at approximately 1,800 federally inspected establishments. All samples were collected at production facilities and not at retail. We report results here for the years 1990 through 1999. Prevalence data for Salmonella, Listeria monocytogenes, Escherichia coli O157:H7, or staphylococcal enterotoxins in nine different categories of RTE meat and poultry products are presented and discussed. The prevalence data have certain limitations that restrict statistical inferences, because these RTE product-testing programs are strictly regulatory in nature and not statistically designed. The cumulative 10-year Salmonella prevalences were as follows: jerky, 0.31%; cooked, uncured poultry products, 0.10%; large-diameter cooked sausages, 0.07%; small-diameter cooked sausages, 0.20%; cooked beef, roast beef, and cooked corned beef, 0.22%; salads, spreads, and pâtés, 0.05%; and sliced ham and luncheon meat, 0.22%. The cumulative 3-year Salmonella prevalence for dry and semidry fermented sausages was 1.43%. The cumulative 10-year L. monocytogenes prevalences were as follows: jerky, 0.52%; cooked, uncured poultry products, 2.12%; large-diameter cooked sausages, 1.31%; small-diameter cooked sausages, 3.56%; cooked beef, roast beef, and cooked corned beef, 3.09%; salads, spreads, and pâtés, 3.03%; and sliced ham and luncheon meat, 5.16%. The cumulative 3-year L. monocytogenes prevalence for dry and semidry fermented sausages was 3.25%. None of the RTE products tested for E. coli O157:H7 or staphylococcal enterotoxins was positive. Although FSIS and the industry have made progress in reducing pathogens in these products, additional efforts are ongoing to continually improve the safety of all RTE meat and poultry products manufactured in federally inspected establishments in the United States.

Animals↗
PubMed1997

Estimation of excess risk from case-control data using Aalen's linear regression model.

We introduce methods for statistical inference in Aalen's non-parametric linear regression model of disease incidence (Aalen, 1989, Statistics in Medicine 8, 907-925) from nested case-control data. These methods provide the basis for estimation of excess risk as a linear function of dose and absolute risk for a given exposure history. The methods are illustrated by estimating excess and absolute risks associated with radon exposure and smoking from nested case-control samples from the Colorado Plateau uranium miners cohort.

Adult↗
PubMed2005

Adding confidence to gene expression clustering.

It has been well established that gene expression data contain large amounts of random variation that affects both the analysis and the results of microarray experiments. Typically, microarray data are either tested for differential expression between conditions or grouped on the basis of profiles that are assessed temporally or across genetic or environmental conditions. While testing differential expression relies on levels of certainty to evaluate the relative worth of various analyses, cluster analysis is exploratory in nature and has not had the benefit of any judgment of statistical inference. By using a novel dissimilarity function to ascertain gene expression clusters and conditional randomization of the data space to illuminate distinctions between statistically significant clusters of gene expression patterns, we aim to provide a level of confidence to inferred clusters of gene expression data. We apply both permutation and convex hull approaches for randomization of the data space and show that both methods can provide an effective assessment of gene expression profiles whose coregulation is statistically different from that expected by random chance alone.

Cluster Analysis↗
PubMed1985

The problem of multiple inference in psychiatric research.

This paper deals with the problem of multiple inference in psychiatric research, an issue which arises whenever a researcher has to make more than one statistical inference in a single research study. It frequently arises in psychiatric research because of multivariate study designs, with subjects being measured on more than one dependent variable with the intention of studying differences between groups in mean scores. The disadvantages of the commonly adopted strategy of using multiple univariate tests (e.g. multiple t-tests) are outlined. Two broad strategies--Bonferroni-adjusted univariate tests and multivariate statistical analysis--are introduced. Their advantages and disadvantages are discussed in terms of their usefulness in confirmatory and exploratory research in psychiatry.

Analysis of Variance↗
PubMed1992

Two-level analysis of covariance structures for unbalanced designs with small level-one samples.

The main purpose of this paper is to develop basic statistical theory for two-level analysis of covariance structures. Major asymptotic results for statistical inference, such as the asymptotic distributions of the estimator and the goodness-of-fit test statistic are derived, based on an unbalanced design with only small numbers of level-one units. Computationally, it is shown that the solution can be obtained via standard programs, such as LISREL, EQS and COSAN. The behaviour of the estimates is illustrated by an artificial example and a real-life example. Some possibilities of extending the results to a more general two-level model, and to situations with arbitrary distributions and elliptical distributions are also investigated.

Analysis of Variance↗
PubMed2006

Heterogeneity in fecundability studies: issues and modelling.

Modelization of fecundability stepped recently from demography and population-based contexts to reproductive biology and treatment of infertility. This created a strong call for flexibility and robustness. Indeed, explained and unexplained heterogeneities are non-negligible sources of bias that result in false conclusions as to the determinants of fertility or to the success rates of reproductive techniques, among other examples. There are two main sources of heterogeneity: biological heterogeneity and heterogeneity of sexual behaviour. A uniform presentation of time-to-pregnancy and Barrett-Marshall models is proposed to enlighten their similarities and differences in modelling heterogeneity of fecundability. Mixed models for fecundability studies are presented as tools to allow for unexplained heterogeneity and to quantify heterogeneity of the effect of observed factors and variability of size of this unexplained heterogeneity between subpopulations. Some criteria for the modelling strategy in fecundability studies are suggested with emphasis on the unit-treatment additivity criterion. The strong and complex selection process resulting from heterogeneity is described as well as the selection and cross-selection processes of observed and unobserved fecundability factors. Consequences regarding data collection and statistical inference are discussed. In the current context, a consensus setting general rules for data collection and statistical analysis would be useful to compare the results and increase the reliability of these results in medical practice.

Female↗
PubMed1998

Probability logic and probabilistic induction.

This article reviews some philosophical aspects of probability and describes how probability logic can give precise meanings to the concepts of inductive support, corroboration, refutation, and related notions, as well as provide a foundation for logically sound statistical inference. Probability logic also provides a basis for recognizing prior distributions as an integral component of statistical analysis, rather than the current misleading practice of pretending that statistics applied to observational data are objective. This basis is important, because the use of realistic priors in a statistical analysis can yield more stringent tests of hypotheses and more accurate estimates than conventional procedures.

Epidemiologic Studies↗
PubMedDate not supplied

Parametric inference for epidemic models.

The likelihood function corresponding to epidemic data is often very complicated. We illustrate that the EM algorithm can sometimes help to simplify likelihood inferences. Difficulties with likelihood inferences about parameters of epidemic models have established a role for martingale methods. These are methods of statistical inference based on estimating equations derived from the rich theory of martingales, and they have produced simple methods of inference in a number of important applications to epidemic data. We contrast likelihood methods with martingale methods and determine which specific assumptions cause changes in inferences about the infection potential of a disease. It is found that the martingale-based estimate of the infection potential remains unaltered under a variety of commonly used model specifications but that the precision of this estimate changes as model assumptions are altered.

Algorithms↗
PubMed1991

Statistical conclusion validity. Multiple inferences in rehabilitation research.

The problem of multiple statistical inferences and Type I error rates in rehabilitation research is examined. The Bonferroni method is the most commonly advocated procedure to control Type I error in clinical research. The traditional Bonferroni method is often overly conservative and results in a loss of statistical power when more than a small number of comparisons are evaluated. Adjustments to the Bonferroni method designed to control or reduce the incidence of Type I errors and improve the statistical conclusion validity of rehabilitation research are presented. The adjusted or sharpened Bonferroni methods allow the researcher to control the incidence of Type I errors while maintaining statistical power. Adjustments to the Bonferroni method are simple to compute and applicable to a wide variety of statistical tests. The use of appropriate multiple comparison procedures will reduce the number of Type I errors and improve the statistical conclusion validity of rehabilitation research studies.

Bias↗