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PubMed2006

Using nonlinear models in fMRI data analysis: model selection and activation detection.

There is an increasing interest in using physiologically plausible models in fMRI analysis. These models do raise new mathematical problems in terms of parameter estimation and interpretation of the measured data. In this paper, we show how to use physiological models to map and analyze brain activity from fMRI data. We describe a maximum likelihood parameter estimation algorithm and a statistical test that allow the following two actions: selecting the most statistically significant hemodynamic model for the measured data and deriving activation maps based on such model. Furthermore, as parameter estimation may leave much incertitude on the exact values of parameters, model identifiability characterization is a particular focus of our work. We applied these methods to different variations of the Balloon Model (Buxton, R.B., Wang, E.C., and Frank, L.R. 1998. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn. Reson. Med. 39: 855-864; Buxton, R.B., Uludağ, K., Dubowitz, D.J., and Liu, T.T. 2004. Modelling the hemodynamic response to brain activation. NeuroImage 23: 220-233; Friston, K. J., Mechelli, A., Turner, R., and Price, C. J. 2000. Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics. NeuroImage 12: 466-477) in a visual perception checkerboard experiment. Our model selection proved that hemodynamic models better explain the BOLD response than linear convolution, in particular because they are able to capture some features like poststimulus undershoot or nonlinear effects. On the other hand, nonlinear and linear models are comparable when signals get noisier, which explains that activation maps obtained in both frameworks are comparable. The tools we have developed prove that statistical inference methods used in the framework of the General Linear Model might be generalized to nonlinear models.

Adult↗
PubMed2006

Multivariable modeling of radiotherapy outcomes, including dose-volume and clinical factors.

PURPOSE: The probability of a specific radiotherapy outcome is typically a complex, unknown function of dosimetric and clinical factors. Current models are usually oversimplified. We describe alternative methods for building multivariable dose-response models. METHODS: Representative data sets of esophagitis and xerostomia are used. We use a logistic regression framework to approximate the treatment-response function. Bootstrap replications are performed to explore variable selection stability. To guard against under/overfitting, we compare several analytical and data-driven methods for model-order estimation. Spearman's coefficient is used to evaluate performance robustness. Novel graphical displays of variable cross correlations and bootstrap selection are demonstrated. RESULTS: Bootstrap variable selection techniques improve model building by reducing sample size effects and unveiling variable cross correlations. Inference by resampling and Bayesian approaches produced generally consistent guidance for model order estimation. The optimal esophagitis model consisted of 5 dosimetric/clinical variables. Although the xerostomia model could be improved by combining clinical and dose-volume factors, the improvement would be small. CONCLUSIONS: Prediction of treatment response can be improved by mixing clinical and dose-volume factors. Graphical tools can mitigate the inherent complexity of multivariable modeling. Bootstrap-based variable selection analysis increases the reliability of reported models. Statistical inference methods combined with Spearman's coefficient provide an efficient approach to estimating optimal model order.

Carcinoma, Non-Small-Cell Lung↗
PubMed2006

Polynomial spline estimation and inference of proportional hazards regression models with flexible relative risk form.

The Cox proportional hazards model usually assumes an exponential form for the dependence of the hazard function on covariate variables. However, in practice this assumption may be violated and other relative risk forms may be more appropriate. In this article, we consider the proportional hazards model with an unknown relative risk form. Issues in model interpretation are addressed. We propose a method to estimate the relative risk form and the regression parameters simultaneously by first approximating the logarithm of the relative risk form by a spline, and then employing the maximum partial likelihood estimation. An iterative alternating optimization procedure is developed for efficient implementation. Statistical inference of the regression coefficients and of the relative risk form based on parametric asymptotic theory is discussed. The proposed methods are illustrated using simulation and an application to the Veteran's Administration lung cancer data.

Algorithms↗
PubMed2000

Causal effects in clinical and epidemiological studies via potential outcomes: concepts and analytical approaches.

A central problem in public health studies is how to make inferences about the causal effects of treatments or agents. In this article we review an approach to making such inferences via potential outcomes. In this approach, the causal effect is defined as a comparison of results from two or more alternative treatments, with only one of the results actually observed. We discuss the application of this approach to a number of data collection designs and associated problems commonly encountered in clinical research and epidemiology. Topics considered include the fundamental role of the assignment mechanism, in particular the importance of randomization as an unconfounded method of assignment; randomization-based and model-based methods of statistical inference for causal effects; methods for handling noncompliance and missing data; and methods for limiting bias in the analysis of observational data, including propensity score matching and sensitivity analysis.

Analysis of Variance↗
PubMed1997

Analysis of dynamic radioligand displacement or "activation" studies.

We present a simple way of assessing dynamic or time-dependent changes in displacement during single-subject radioligand positron emission tomography (PET) activation studies. The approach is designed to facilitate dynamic activation studies using selective radioligands. These studies are, in principle, capable of characterising functional neurochemistry by analogy with the study of functional neuroanatomy using rCBF activation studies. The proposed approach combines time-dependent compartmental models of tracer kinetics and the general linear model used in statistical parametric mapping. This provides for a comprehensive, voxel-based and data-led assessment of regionally specific effects. The statistical model proposed in this paper is predicated on a single-compartment model extended to allow for time-dependent changes in kinetics. We have addressed the sensitivity and specificity of the analysis, as it would be used operationally, by applying the analysis to 11C-Flumazenil dynamic displacement studies. The activation used in this demonstration study was a pharmacological (i.v. midazolam) challenge, 30 min after administration of the tracer. We were able to demonstrate, and make statistical inferences about, regional increases in k2 (or decreases in the volume of distribution) in prefrontal and other cortical areas.

Activation Analysis↗
PubMed1999

Multinomial processing tree models: an implementation.

Multinomial processing tree (MPT) models have been widely used by researchers in cognitive psychology. This paper introduces MBT.EXE, a computer program that makes MPT easy to use for researchers. MBT.EXE implements the statistical theory developed by Hu and Batchelder (1994). This user-friendly software can be used to construct MPT models and conduct statistical inferences, including point and interval estimation, hypothesis testing, and goodness of fit. Furthermore, this program can be used to examine the robustness of MPT models. Algorithms for parameter estimation, hypothesis testing, and Monte Carlo simulation are presented.

Algorithms↗
PubMed2004

Prior convictions: Bayesian approaches to the analysis and interpretation of clinical megatrials.

Large, randomized clinical trials ("megatrials") are key drivers of modern cardiovascular practice, since they are cited frequently as the authoritative foundation for evidence-based management policies. Nevertheless, fundamental limitations in the conventional approach to statistical hypothesis testing undermine the scientific basis of the conclusions drawn from these trials. This review describes the conventional approach to statistical inference, highlights its limitations, and proposes an alternative approach based on Bayes' theorem. Despite its inherent subjectivity, the Bayesian approach possesses a number of practical advantages over the conventional approach: 1). it allows the explicit integration of previous knowledge with new empirical data; 2). it avoids the inevitable misinterpretations of p values derived from megatrial populations; and 3). it replaces the misleading p value with a summary statistic having a natural, clinically relevant interpretation-the probability that the study hypothesis is true given the observations. This posterior probability thereby quantifies the likelihood of various magnitudes of therapeutic benefit rather than the single null magnitude to which the p value refers, and it lends itself to graphical sensitivity analyses with respect to its underlying assumptions. Accordingly, the Bayesian approach should be employed more widely in the design, analysis, and interpretation of clinical megatrials.

Bayes Theorem↗
PubMed2004

Nonstationary cluster-size inference with random field and permutation methods.

Because of their increased sensitivity to spatially extended signals, cluster-size tests are widely used to detect changes and activations in brain images. However, when images are nonstationary, the cluster-size distribution varies depending on local smoothness. Clusters tend to be large in smooth regions, resulting in increased false positives, while in rough regions, clusters tend to be small, resulting in decreased sensitivity. Worsley et al. proposed a random field theory (RFT) method that adjusts cluster sizes according to local roughness of images [Worsley, K.J., 2002. Nonstationary FWHM and its effect on statistical inference of fMRI data. Presented at the 8th International Conference on Functional Mapping of the Human Brain, June 2-6, 2002, Sendai, Japan. Available on CD-ROM in NeuroImage 16 (2) 779-780; Hum. Brain Mapp. 8 (1999) 98]. In this paper, we implement this method in a permutation test framework, which requires very few assumptions, is known to be exact [J. Cereb. Blood Flow Metab. 16 (1996) 7] and is robust [NeuroImage 20 (2003) 2343]. We compared our method to stationary permutation, stationary RFT, and nonstationary RFT methods. Using simulated data, we found that our permutation test performs well under any setting examined, whereas the nonstationary RFT test performs well only for smooth images under high df. We also found that the stationary RFT test becomes anticonservative under nonstationarity, while both nonstationary RFT and permutation tests remain valid under nonstationarity. On a real PET data set we found that, though the nonstationary tests have reduced sensitivity due to smoothness estimation variability, these tests have better sensitivity for clusters in rough regions compared to stationary cluster-size tests. We include a detailed and consolidated description of Worsley nonstationary RFT cluster-size test.

Brain↗
PubMed1990

The summarizing of clinical experiments by significance levels.

For a controlled clinical experiment in which two alternative treatments are compared, the statistical report often culminates in a significance test of the null hypothesis of no difference between the treatments, and significance at the 5 per cent level is taken as positive evidence of difference. It is argued that such an experiment serves primarily an inferential purpose; it is not a simple decision procedure, although its effect on practice may be considered in relation to ethical issues. Statistical inference should not be identified with testing this null hypothesis, despite the emphasis on such tests by R. A. Fisher in his work on design of experiments. This null hypothesis often has no interest or credibility.

Clinical Trials as Topic↗
PubMed2005

PAGE: parametric analysis of gene set enrichment.

BACKGROUND: Gene set enrichment analysis (GSEA) is a microarray data analysis method that uses predefined gene sets and ranks of genes to identify significant biological changes in microarray data sets. GSEA is especially useful when gene expression changes in a given microarray data set is minimal or moderate. RESULTS: We developed a modified gene set enrichment analysis method based on a parametric statistical analysis model. Compared with GSEA, the parametric analysis of gene set enrichment (PAGE) detected a larger number of significantly altered gene sets and their p-values were lower than the corresponding p-values calculated by GSEA. Because PAGE uses normal distribution for statistical inference, it requires less computation than GSEA, which needs repeated computation of the permutated data set. PAGE was able to detect significantly changed gene sets from microarray data irrespective of different Affymetrix probe level analysis methods or different microarray platforms. Comparison of two aged muscle microarray data sets at gene set level using PAGE revealed common biological themes better than comparison at individual gene level. CONCLUSION: PAGE was statistically more sensitive and required much less computational effort than GSEA, it could identify significantly changed biological themes from microarray data irrespective of analysis methods or microarray platforms, and it was useful in comparison of multiple microarray data sets. We offer PAGE as a useful microarray analysis method.

Computational Biology↗
PubMedDate not supplied

[Neuroendocrine surgery in Parkinson's disease: comparative analytical evaluation of approaches to microsurgical adrenalectomy. Experimental studies].

In this experimental contribution to the study of neurobiological interactions between adrenal medullary graft and CNS, is presented a model to estimate the approaches to rat adrenalectomy using statistical inference techniques. Eighteen rats were divided into three samples. The members of every sample were left adrenalectomized using lombotomic, anterior transperitoneal and posterior approaches respectively. A score was attributed to every experimentally meaningful parameter, according a previously well established plan. Scores were tested by analysis of variance and by previously planned orthogonal comparisons. Mean, standard deviation of every sample score and confidence interval for mean difference were computed. Statistical analysis results show that, objectively, there is a meaningful difference between anterior approach and posterior or lateral approach, anterior approach being more difficult then posterior or lateral approach, while there is not meaningful difference between posterior and lateral approach. Subjectively, on the contrary, there are not meaningful differences between three approaches to left adrenalectomy statistically.

Adrenalectomy↗
PubMed1996

Does license disqualification reduce reoffence rates?

A review was conducted of the subsequent driving records of over 25,000 Queensland drivers cited for a drink driving offence in 1988 who received at least one subsequent license restriction. The interval of follow-up was at least 3 years, average 3.9 years. Periods of driving disqualification were identified and, for each driver, the total amount of time during restricted and unrestricted driving was computed; the numbers of events, i.e. crashes and traffic offences, recorded during these periods were counted. Rates under disqualification and during legal driving, expressed per thousand person-years were derived by dividing total numbers of events by total time during which they could occur. Three categories of traffic violation were considered: drink driving offences; traffic offences unassociated with drink driving, and any offence involving driving. Since only 12% of the offenders and 9% of the reoffenders were female, detailed analyses are presented for men only; results for women were little different. Statistical inference assumed a Poisson model for crashes and a negative binomial model for offences, and analyses were performed after stratification by number of drink driving offences. Calculated rates during periods of disqualification were about one third of the rates during legal driving for crashes and all three categories of traffic offence, ranging from 25% in the case of unassociated offences to 35% for any driving offence. There were differences, some statistically significant, by age and between metropolitan, provincial city and rural regions of the State, but most were relatively minor. Drivers were apprehended more frequently earlier in the disqualification period than later. It is impossible from these data to distinguish between reduced driving levels and more cautious traffic behaviour during periods of license restriction. It is nonetheless clear that while such penalties are in operation, they substantially reduce the negative impact of convicted drink-drivers on the road. Unfortunately the data do not permit one to say whether or for how long the effect persists.

Accidents, Traffic↗
PubMed2004

Bayes without priors.

BACKGROUND AND OBJECTIVES: Classical statistical inference has attained a dominant position in the expression and interpretation of empirical results in biomedicine. Although there have been critics of the methods of hypothesis testing, significance testing (P-values), and confidence intervals, these methods are used to the exclusion of all others. METHODS: An alternative metaphor and inferential computation based on credibility is offered here. RESULTS: It is illustrated in three datasets involving incidence rates, and its advantages over both classical frequentist inference and Bayesian inference, are detailed. CONCLUSION: The message is that for those who are unsatisfied with classical methods but cannot make the transition to Bayesianism, there is an alternative path.

Arizona↗
PubMed2000

Total deviation index for measuring individual agreement with applications in laboratory performance and bioequivalence.

In areas of inter-laboratory quality control, method comparisons, assay validation and individual bioequivalence, etc., the agreement between observations and target (reference) values is of interest. The mean of the squared difference between observations and target values (MSD) is a good measure of the total deviation. A new user-friendly statistic, the total deviation index (TDI(1-p)), is introduced that translates the MSD into an index that can be directly compared to a predetermined criterion. The TDI(1-p) describes a boundary such that a majority, 100(1-p) per cent, of the observations are within the boundary (measurement unit and/or per cent) from their target values. Statistical inference using the sample counter part (estimate) is presented. A Monte Carlo experiment with 5000 runs was performed to confirm the estimate's validity. Applications in laboratory performance and validation, as well as individual bioequivalence, are presented.

Analysis of Variance↗
PubMed2007

Methods for the statistical analysis of binary data in split-mouth designs with baseline measurements.

Many split-mouth trials are characterized by the pairing of site-specific outcome and baseline data within each segment of a subject's mouth. However when the response variable of interest is binary, methods of statistical analysis for this design are not well developed. In this paper we present several analytic approaches that may be taken to the resulting data, showing how the efficiency of statistical inferences can be improved by appropriately incorporating the baseline information. The advantages and disadvantages of the different approaches are discussed in the context of an example from the published literature. The results from a limited simulation study are also presented.

Clinical Trials as Topic↗
PubMed2002

In vivo detection of striatal dopamine release during reward: a PET study with [(11)C]raclopride and a single dynamic scan approach.

A new simple method is proposed to detect, using PET and [(11)C]raclopride, changes in striatal extracellular dopamine concentration during a rewarded effortful task. This approach aimed to increase the sensitivity in detection of these effects. It requires a single-dynamic PET study and combines the classic kinetic compartmental model with the general linear model of SPM to provide statistical inference on changes in [(11)C]raclopride time-activity curve due to endogenous dopamine release during two short periods of activation. Kinetic simulations predicted that 100% dopamine increase during two 5-min periods starting at 30 and 60 min after the injection can be detected. Moreover the effects of dopamine release on the [(11)C]raclopride time-activity-curve are different from those induced by CBF increase. These simulated curves were used to construct the statistical linear model and to test voxel-by-voxel in healthy subjects the hypothesis that dopamine is released in the ventral striatum during periods of unexpected monetary gains, but not during periods of unexpected monetary loss. The experimental results are in line with the expected results although the amplitude of the effects due to dopamine release is moderate. The advantages and the limits of this method as well as the relevance of the results for dopamine involvement in reward processing are discussed.

Adult↗
PubMed2006

Progressivity and horizontal equity in health care finance and delivery: what about Africa?

This paper applies concentration curves and indices, that have been previously used to analyze progressivity in health care finance and horizontal equity in health care delivery in developed countries, to a 1998-1999 household survey about health care expenditures and utilization carried out in four francophone West African capitals (Abidjan, Bamako, Conakry and Dakar). The paper also uses statistical inference for testing stochastic dominance relationship between curves, a technique already applied in the literature about equity in taxation, as the criterion for making rigorous inequality comparisons. In all four capitals, the results strongly suggest a regressive pattern of payments for health care, with lower income groups bearing an higher burden of health expenditures as a proportion of their income than do the higher income segments of the population. As soon as dominance between concentrations curves is statistically tested, results appear less conclusive, notably for the groups of population affected by severe morbidity, on the issue of horizontal inequity in health care delivery, which requires that persons with similar medical need be treated equally. Some recommendations are made for the use of equity measurements in access to care for future evaluations of the impact of health care reforms in Africa.

Africa, Western↗
PubMed1994

Bootstrap hypothesis tests for evolutionary trees and other dendrograms.

The bootstrap computer-intensive statistical technique is frequently applied to statistical analyses of phylogenetic trees. The widely used rule that a group is supported significantly if it appears in at least 95% of bootstrap trees is conservative in most situations. This paper describes three ways of using the bootstrap to carry out statistical inference on phylogenies. The first method tests whether there is nonrandom support for a single group or tree. The second method compares the support for two groups or trees. The third method tests whether a single group or tree has better support than the set of all possible alternatives; this may be a replacement for the "95% rule." These tests generally require fewer bootstrap trees to be estimated than do other methods of bootstrapping phylogenies. A simple, sequential statistical method can be used to increase the efficiency further. These methods can be applied to tests of multiple hypotheses about a single phylogeny. Parsimony analyses of 5S rRNA sequences of plants and cluster analyses of randomly amplified polymorphic DNA bands in three pathotypes of the cereal eyespot fungus are used as illustrative examples. The tests can be used to analyze dendrograms in subjects other than taxonomy.

Base Sequence↗