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PubMed1996

Statistical analysis of the standardized mortality ratio and life expectancy.

A new theoretical relation that does not require the constant age-specific mortality ratio assumption is established between the standardized mortality ratio (SMR) and the life expectancy. A set of regression equations is developed from the theoretical relation to derive estimates of the future expectation of life from estimates of the SMR. Curves are presented showing the changes in life expectancy that are associated with a given SMR for individuals aged 25, 45, and 65 years. These results will provide practical applications in estimating remaining life expectancy in epidemiologic studies in which the SMR is the summary statistic. An application is shown for studies in occupational health to develop and illustrate the method.

Adult↗

PubMed2025

Towards improved fine-mapping of candidate causal variants.

Fine-mapping in genome-wide association studies aims to identify potentially causal genetic variants among a set of candidate variants that are often highly correlated with each other owing to linkage disequilibrium. A variety of statistical approaches are used in fine-mapping, almost all of which are based on a multiple regression framework to model the relationship between genotype and phenotype, while accommodating specific assumptions about the distribution of variant effect sizes and using different inference algorithms. Owing to their modelling flexibility and the ease of making inferential statements, these approaches are predominantly Bayesian in nature. Recently, these approaches have been improved by refining modelling assumptions, integrating additional information, accommodating summary statistics, and developing scalable computational algorithms that improve computation efficiency and fine-mapping resolution.

Humans↗

PubMed2000

Responsiveness of fibromyalgia clinical trial outcome measures.

OBJECTIVE: To assess the responsiveness of the Fibromyalgia Impact Questionnaire (FIQ), patient ratings of pain intensity, number of tender points, and total tender point pain intensity score to perceived changes in clinical status in patients with fibromyalgia (FM). METHODS: Using data from a randomized placebo controlled study evaluating efficacy of magnetic therapy in patients with FM, the ability of primary outcomes to detect clinically meaningful changes over a 6 month period was assessed by: (1) degree of association between outcome change scores and patient global ratings of symptom change (Spearman rank-order correlations); (2) ability of these scores to discriminate among groups of patients whose perceived health status had changed to varying degrees (ANOVA); (3) ability of these scores, individually and jointly, to discriminate between patients who had reported improvement and those who did not (logistic regression); (4) effect size, standardized response mean, and Guyatt's statistic were calculated to quantify responsiveness. RESULTS: Correlations showed the outcome measures were moderately responsive to perceived symptomatic change. For FIQ, pain intensity ratings and number of tender points, differences in change scores between globally improved and unchanged groups and between globally improved and worsened groups were significant; for total tender point pain intensity, the globally improved differed from worsened group. FIQ outperformed the other measures in discriminating between patients who reported improvement from those who did not. Summary statistics were consistent with discriminatory analyses, indicating the measures were sensitive to improvement, but relatively unresponsive to decline. CONCLUSION: The FIQ was the most responsive measure to perceived clinical improvement and we recommend its inclusion as a primary endpoint in FM clinical trials.

Adult↗

PubMed2002

African-American ethnicity, socioeconomic status, and breast cancer survival: a meta-analysis of 14 studies involving over 10,000 African-American and 40,000 White American patients with carcinoma of the breast.

BACKGROUND: African-American women are at increased risk for breast cancer mortality compared with white American women, and the extent to which socioeconomic factors account for this outcome disparity is unclear. METHODS: A MEDLINE search was conducted to identify published studies that used a Cox proportional hazards regression model to evaluate the outcome of African-American women and white American women with breast carcinoma after adjusting for socioeconomic status. A meta-analysis was performed using specialized statistical software; the random-effects method of statistical evaluation was used because of the a priori impression that the studies reviewed would be at least moderately heterogeneous in study design and patient populations. RESULTS: The initial literature search yielded 3962 studies. Fourteen studies met all criteria for inclusion in the meta-analysis, resulting in a sample size of 10,001 African-American patients and 42,473 white American patients with breast carcinoma. There was substantial variation in the method used for defining socioeconomic status. Summary statistics revealed a significant odds ratio of 1.22 (95% confidence interval, 1.13-1.30) for the adverse effect of African-American ethnicity on breast cancer mortality. Subset meta-analyses yielded similar results, supporting the robustness of this finding. CONCLUSIONS: This meta-analysis revealed that African-American ethnicity is an independent predictor of a worse breast cancer outcome. The pooled analysis has added strength because of the aggregate sample size and indicates that the true biologic and/or therapeutic determinants of disparities in breast cancer outcome for different ethnic groups and for different socioeconomic strata are incompletely understood.

Adult↗

PubMed2001

Statistical methods for the analysis and presentation of the results of bone marrow transplants. Part I: unadjusted analysis.

In this paper, we describe modern statistical methods for presentation of the results of studies of bone marrow transplantation. We focus here on 'univariate' or unadjusted techniques to describe the outcomes of such studies. In another paper we will discuss multivariate methods. We discuss the type of data one may have available to make inference about outcomes. We explain the differences between the Kaplan-Meier estimator of the survival function and the cumulative incidence curve, how these curves should be interpreted and when each is the appropriate summary statistic. We discuss the weighted log rank statistic and show how different weights can be used to put emphasis on detecting differences between groups in different time periods. We also present a simple estimate of current leukemia-free survival which is useful in summarizing post-transplant events.

Analysis of Variance↗

PubMed1997

Quantitative synthesis in systematic reviews.

The final common pathway for most systematic reviews is a statistical summary of the data, or meta-analysis. The complex methods used in meta-analyses should always be complemented by clinical acumen and common sense in designing the protocol of a systematic review, deciding which data can be combined, and determining whether data should be combined. Both continuous and binary data can be pooled. Most meta-analyses summarize data from randomized trials, but other applications, such as the evaluation of diagnostic test performance and observational studies, have also been developed. The statistical methods of meta-analysis aim at evaluating the diversity (heterogeneity) among the results of different studies, exploring and explaining observed heterogeneity, and estimating a common pooled effect with increased precision. Fixed-effects models assume that an intervention has a single true effect, whereas random-effects models assume that an effect may vary across studies. Meta-regression analyses, by using each study rather than each patient as a unit of observation, can help to evaluate the effect of individual variables on the magnitude of an observed effect and thus may sometimes explain why study results differ. It is also important to assess the robustness of conclusions through sensitivity analyses and a formal evaluation of potential sources of bias, including publication bias and the effect of the quality of the studies on the observed effect.

Bias↗

PubMed2006

Diagnosis of single-subject and group fMRI data with SPMd.

Except for purely nonparametric methods, statistical methods depend on assumptions about the distribution of the data studied. While these assumptions are easily checked for a single univariate dataset with diagnostic plots, in the massively univariate model used with functional MRI (fMRI) it is impractical to check with a massive number of plots. In previous work we have demonstrated how to diagnose model assumptions and lack-of-fit for single-subject fMRI models using a working assumption of independent errors; our work depended on images and time series of summary statistics that, when simultaneously viewed dynamically, identify problem scans and voxels. In this article we extend our previous work to account for temporal autocorrelation in single-subject models and show how analogous methods can be used on group models where multiple subjects are studied. We apply these methods to the single-subject Functional Image Analysis Contest (FIAC) data and find several anomalies, but none that appear to invalidate the results for that subject. With the group FIAC data we find one subject (and possibly two more) that demonstrate a different pattern of activity. None of our conclusions would be arrived at by simply looking at images of t statistics, demonstrating the importance of model assessment through exploration of the data and diagnosis of model assumptions.

Artifacts↗

PubMed1990

DNA/DNA hybridization studies of the carnivorous marsupials. I: The intergeneric relationships of bandicoots (Marsupialia: Perameloidea).

A complete suite of comparisons among six bandicoot species and one outgroup marsupial was generated using the hydroxyapatite chromatography method of DNA/DNA hybridization; heterologous comparisons were also made with three other bandicoot taxa. Matrices of delta Tm's, delta modes, and delta T50Hs were generated and corrected for nonreciprocity, homoplasy, and, in the case of delta Tm's, normalized percent hybridization; these matrices were analyzed using the FITCH algorithm in Felsenstein's PHYLIP (version 3.1). Uncorrected and nonreciprocity-corrected matrices were also jackknifed and analyzed with FITCH to test for consistency. Finally, sample scores for delta Tm, delta mode, and delta T50H matrices were bootstrapped and then subjected to phylogenetic analysis. These manipulations were carried out, in part, to address criticisms of the statistics used to summarize DNA/DNA hybridization (especially T50H) and the method itself. However, with the exception of an unresolved trichotomy among the two Echymipera species and Peroryctes longicauda, all trees showed the same branchpoints. Except in the case of the tree generated from reciprocal-corrected delta Tm data, nodes were stable under jackknifing; and, again excepting the above-mentioned trichotomy, all nodes were supported by 95% or more of the bootstrapped trees. These results suggest that, despite arguments to the contrary, all three summary statistics can be valid for DNA/DNA hybridization data. Of taxonomic interest is the placement of Echymipera spp. and Peroryctes longicauda together and separate from the more distant Peroryctes raffrayanus; the genus Peroryctes is thus at least paraphyletic. The trees further grouped Echymipera-plus-Peroryctes as the sister group of Isoodon-plus-Perameles. Limited hybridizations with Macrotis lagotis suggest that its current position as representative of an entirely distinct family of perameloids is correct.

Animals↗

PubMedDate not supplied

Application of peak expiratory flow in epidemiologic studies of occupation.

Investigation of the use of PEF in the measurement of airway variability over a single day or several weeks suggests that serial measures of PEF may prove useful in detecting short-term adverse responses to a variety of environmental agents. Several investigators have already shown how the visual inspection of temporal trends can prove useful in identifying individuals with occupational asthma. The use of statistical summaries of diurnal variation, i.e., the amplitude as a percent of the daily mean, may provide important added information about airway reactivity in response to occupational exposures in a variety of populations. Indeed, there are several groups of investigators presently examining more refined ways, including autoregressive time series models, of linking short-term temporal patterns in serial measurements of PEF with simultaneously measured short-term exposures. As our understanding of the sources and nature of the variability in PEF improves, together with refinements in the statistical techniques used to describe the temporal data, serial measures of PEF are likely to see a far broader application in the study of acute respiratory hazards. Does the utility of PEF as a pulmonary function measurement stem solely from ease of collection and the consequent increase in the amount of data one can gather, or is the PEF a distinctly different and inherently useful measure of pulmonary function? This question cannot yet be answered. The increasing availability of accurate reliable hand-held spirometers means that one can now plan studies using the powerful repeated measures designs previously feasible only with the peak flow meter (see article on Instrumentation, pp 397-408, in this issue). These data will enable side-by-side comparisons of PEF, FEV1, maximum mid-expiratory flow, and other parameters collected simultaneously. Will the FEV1 once again become the preferred measure of airflow? Time will tell.

Bias↗

PubMed2006

Simulation of correlated continuous and categorical variables using a single multivariate distribution.

Clinical trial simulations make use of input/output models with covariate effects; the virtual patient population generated for the simulation should therefore display physiologically reasonable covariate distributions. Covariate distribution modeling is one method used to create sets of covariate values (vectors) that characterize individual virtual patients, which should be representative of real subjects participating in clinical trials. Covariates can be continuous (e.g., body weight, age) or categorical (e.g., sex, race). A modeling method commonly used for incorporating both continuous and categorical covariates, the Discrete method, requires the patient population to be divided into subgroups for each unique combination of categorical covariates, with separate multivariate functions for the continuous covariates in each subset. However, when there are multiple categorical covariates this approach can result in subgroups with very few representative patients, and thus, insufficient data to build a model that characterizes these patient groups. To resolve this limitation, an application of a statistical methodology (Continuous method) was conceived to enable sampling of complete covariate vectors, including both continuous and categorical covariates, from a single multivariate function. The Discrete and Continuous methods were compared using both simulated and real data with respect to their ability to generate virtual patient distributions that match a target population. The simulated data sets consisted of one categorical and two correlated continuous covariates. The proportion of patients in each subgroup, correlation between the continuous covariates, and ratio of the means of the continuous covariates in the subgroups were varied. During evaluation, both methods accurately generated the summary statistics and proper proportions of the target population. In general, the Continuous method performed as well as the Discrete method, except when the subgroups, defined by categorical value, had markedly different continuous covariate means, for which, in the authors' experience, there are few clinically relevant examples. The Continuous method allows analysis of the full population instead of multiple subgroups, reducing the number of analyses that must be performed, and thereby increasing efficiency. More importantly, analyzing a larger pool of data increases the precision of the covariance estimates of the covariates, thus improving the accuracy of the description of the covariate distribution in the simulated population.

Clinical Trials as Topic↗

PubMed1997

Group sequential monitoring of distribution-free analyses of repeated measures.

In many clinical trials the principal analysis consists of a 1 degree of freedom test based on an aggregate summary statistic for a set of repeated measures. Various methods have been proposed for the marginal analysis of such repeated measures that entail estimates of a measure of treatment group difference (the treatment effect) at each of K repeated measures and a consistent estimate of the covariance matrix, where asymptotically these estimates are normally distributed. One can then obtain an overall large sample 1-d.f. test of group differences, such as by taking the average of these K estimates. These methods include the Wei-Lachin family of multivariate rank tests and a corresponding multivariate analysis using the Mann-Whitney difference estimator as a measure of treatment group differences. Other methods, such as O'Brien's non-parametric test, are based on a single summary score for each patient, such as the within-patient mean value. These, and other such methods, allow for some observations to be missing at random. Herein I employ sequential data augmentation to conduct group sequential analyses using a 1 degree of freedom test from a multivariate Mann-Whitney analysis and for the O'Brien rank test. Su and Lachin used this method to perform group sequential analyses of a vector of Hodges-Lehmann estimators. By augmentating the data from the sequential looks in a single analysis, one obtains an estimate of the covariance of the estimates at each look, from which one obtains an estimate of the correlations among the sequential 1-d.f. test statistics. I describe a simple secant algorithm to determine the group sequential boundaries based on recursive integration of the standard multivariate normal distribution with the estimated correlation matrix. Although the boundary obtains readily using the method of Slud and Wei, the more flexible method of Lan and DeMets may be preferred. The true information fraction at each look, needed to apply the spending function method of Lan and DeMets, however, is unknown. Thus, I also describe the use of a surrogate measure of information.

Algorithms↗

PubMed2003

Reporting of prognostic markers: current problems and development of guidelines for evidence-based practice in the future.

Prognostic markers help to stratify patients for treatment by identifying patients with different risks of outcome (e.g. recurrence of disease), and are important tools in the management of cancer and many other diseases. Systematic review and meta-analytical approaches to identifying the most valuable prognostic markers are needed because (sometimes conflicting) evidence relating to markers is often published across a number of studies. To investigate the practicality of this approach, an empirical investigation of a systematic review of tumour markers for neuroblastoma was performed; 260 studies of prognostic markers were identified, which considered 130 different markers. The reporting of these studies was often inadequate, in terms of both statistical analysis and presentation, and there was considerable heterogeneity for many important clinical/statistical factors. These problems restricted both the extraction of data and the meta-analysis of results from the primary studies, limiting feasibility of the evidence-based approach.Guidelines for reporting the results of primary prognostic marker studies in cancer, and other diseases, are given in order to facilitate both the interpretation of individual studies and the undertaking of systematic reviews, meta-analysis and, ultimately, evidence-based practice. General availability of full individual patient data is a necessary step forward and would overcome the majority of problems encountered, including poorly reported summary statistics and variability in cutoff level, outcome assessed and adjustment factors used. It would also limit the problem of reporting bias, although publication bias will remain a concern until studies are prospectively registered. Such changes in practice would help important evidence-based reviews to be conducted in order to establish the most appropriate prognostic markers for clinical use, which should ultimately improve patient care.

Biomarkers, Tumor↗

PubMed2003

Summary of historical beryllium uses and airborne concentration levels at Los Alamos National Laboratory.

Beryllium operations and accompanying medical surveillance of workers at Los Alamos National Laboratory began in the 1940s. In 1999 a Former Workers Medical Surveillance Program that includes screening for chronic beryllium disease was initiated. As part of this program, historical beryllium exposure conditions were reconstructed from archived paper and electronic industrial hygiene data sources to improve understanding of past beryllium uses and airborne concentration levels. Archived industrial hygiene sampling reports indicated beryllium was principally used in technical areas-01 and -03, primarily being machined. Beryllium was also used at 15 other technical areas in activities that ranged from explosives detonation to the manufacture of X-ray windows. A total of 4528 personal breathing zone and area air samples for beryllium, combined for purposes of calculating summary statistics, were identified during the records review phase. The geometric mean airborne beryllium concentration for the period 1949-1989 for all technical areas was 0.04 microg Be/m(3) with 97 percent of all sample below the 2.0 microg Be/m(3) occupational exposure limit (OEL). Average beryllium concentrations per decade were less than 1 microg Be/m(3) and annual geometric mean concentrations in technical area-03, the largest user of beryllium, were generally below 0.1 microg Be/m(3), indicating exposure was generally well-controlled, that is, below the OEL. Typical of many retrospective exposure assessments, not all archived data could be extracted and summarized. Despite this, we report a reasonable summary of potential beryllium uses and airborne concentration levels a worker may have encountered from 1949-1989. These data can be used to more effectively identify former worker populations at potential risk for chronic beryllium disease and to offer these workers screening as part of the Former Worker Medical Surveillance Program, and in the event that a case is diagnosed, help to understand historical exposure conditions.

Air Pollutants, Occupational↗

PubMed1997

Variation in bronchial responsiveness in the European Community Respiratory Health Survey (ECRHS).

Attempts to compare bronchial responsiveness between populations have been hampered by between-study differences in the pharmacological agent of provocation, the method of administration and the summary statistic employed. The European Community Respiratory Health Survey used methacholine challenge delivered by Mefar dosimeter according to a standardized protocol used in 35 centres in 16 countries. Data were obtained from 13,161 men and women, aged 20-44 yrs at the start of the study. The dose of methacholine producing a 20% fall in forced expiratory volume in one second (FEV1) (PD20) and the regression coefficient of percentage decline in FEV1 with log dose, were calculated ("slope", after transformation), with and without calibration of nebulizers by weight and adjustment for nonresponse bias. Standardization for baseline lung function and variation in smoking prevalence was applied to slope. Results were robust to whichever summary measure was used, and to the various adjustments. Responsiveness was low in Iceland and Switzerland, and in most centres in Sweden, Italy and Spain, and high in New Zealand, Australia, the USA, Britain, France, Denmark and Germany. Bronchial responsiveness varies considerably in Europe, and high levels are not confined to the English-speaking world.

Adult↗

PubMed1986

Statistical characterization of the EEG: the use of the power spectrum as a measure of ergodicity.

In order to interpret statistical summaries of treatment-related changes in EEG power spectra, the internal consistency of the set of data from each condition must first be known. A technique for the assessment of such across-record homogeneity (ergodicity) is derived from the defining characteristics of the power spectrum. A simplified graphic approximation is also detailed. Computer simulations and practical validation confirm it as a useful means of evaluating the ergodicity of sets of EEG data.

Electroencephalography↗

PubMed1993

Exploring models for the length of stay distribution.

Diagnosis Related Groups (DRG) are frequently used to standardize the comparison of consumption variables, such as length of stay (LOS). In order to be reliable, this comparison must control for the presence of outliers, i.e. values far removed from the pattern set by the majority of the data. Indeed, outliers can distort the usual statistical summaries, such as means and variances. A common practice is to trim LOS values according to various empirical rules, but there is little theoretical support for choosing between alternative procedures. This pilot study explores the possibility of describing LOS distributions with parametric models which provide the necessary framework for the use of robust methods.

Adolescent↗

PubMed2004

Statistical methods for single-case studies in neuropsychology: comparing the slope of a patient's regression line with those of a control sample.

Performance on some neuropsychological tests is best expressed as the slope of a regression line. Examples include the quantification of performance on tests designed to assess the accuracy of time estimation or distance estimation. The present paper presents methods for comparing a patient's performance with a control or normative sample when performance is expressed as slope. The methods test if there is a significant difference between a patient's slope and those obtained from controls, yield an estimate of the abnormality of the patient's slope, and provide confidence limits on the level of abnormality. The methods can be used with control samples of any size and will therefore be of particular relevance to single-case researchers. A method for comparing the difference between a patient's scores on two measures with the differences observed in controls is also described (one or both measures can be slopes). The methods require only summary statistics (rather than the raw data from the normative or control sample); it is hoped that this feature will encourage the development of norms for tasks that use slopes to quantify performance. Worked examples of the statistical methods are provided using neuropsychological data and a computer program (for PCs) that implements the methods is described and made available.

Controlled Clinical Trials as Topic↗

PubMed2004

Bayesian hierarchical error model for analysis of gene expression data.

MOTIVATION: Analysis of genome-wide microarray data requires the estimation of a large number of genetic parameters for individual genes and their interaction expression patterns under multiple biological conditions. The sources of microarray error variability comprises various biological and experimental factors, such as biological and individual replication, sample preparation, hybridization and image processing. Moreover, the same gene often shows quite heterogeneous error variability under different biological and experimental conditions, which must be estimated separately for evaluating the statistical significance of differential expression patterns. Widely used linear modeling approaches are limited because they do not allow simultaneous modeling and inference on the large number of these genetic parameters and heterogeneous error components on different genes, different biological and experimental conditions, and varying intensity ranges in microarray data. RESULTS: We propose a Bayesian hierarchical error model (HEM) to overcome the above restrictions. HEM accounts for heterogeneous error variability in an oligonucleotide microarray experiment. The error variability is decomposed into two components (experimental and biological errors) when both biological and experimental replicates are available. Our HEM inference is based on Markov chain Monte Carlo to estimate a large number of parameters from a single-likelihood function for all genes. An F-like summary statistic is proposed to identify differentially expressed genes under multiple conditions based on the HEM estimation. The performance of HEM and its F-like statistic was examined with simulated data and two published microarray datasets-primate brain data and mouse B-cell development data. HEM was also compared with ANOVA using simulated data. AVAILABILITY: The software for the HEM is available from the authors upon request.

Algorithms↗