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PubMed2005

Multiple comparisons between two groups on multiple Bernoulli outcomes while accounting for covariates.

The problem of adjusting for multiplicity when one has multiple outcome variables can be handled quite nicely by step-down permutation tests. More difficult is the problem when one wants an analysis of each outcome variable to be adjusted for some covariates and the outcome variables are Bernoulli. Special permutations can be used where the outcome vectors are permuted within each strata of the data defined by the levels of the (made discrete) covariates. This method is described and shown to control the familywise error rate at any prespecified level. The method is compared through simulation to a vector bootstrap approach, also using a step-down testing procedure. It is seen that the method using permutations within strata is superior to the vector bootstrap in terms of error control and power. The method is illustrated on a data set of 55 minor malformations of babies of diabetic and non-diabetic mothers.

Analysis of Variance↗

PubMed2006

Tests of equivalence and non-inferiority for diagnostic accuracy based on the paired areas under ROC curves.

Assessment of equivalence or non-inferiority in accuracy between two diagnostic procedures often involves comparisons of paired areas under the receiver operating characteristic (ROC) curves. With some pre-specified clinically meaningful limits, the current approach to evaluating equivalence is to perform the two one-sided tests (TOST) based on the difference in paired areas under ROC curves estimated by the non-parametric method. We propose to use the standardized difference for assessing equivalence or non-inferiority in diagnostic accuracy based on paired areas under ROC curves between two diagnostic procedures. The bootstrap technique is also suggested for both non-parametric method and the standardized difference approach. A simulation study was conducted empirically to investigate the size and power of the four methods for various combinations of distributions, data types, sample sizes, and different correlations. Simulation results demonstrate that the bootstrap procedure of the standardized difference approach not only can adequately control the type I error rate at the nominal level but also provides equivalent power under both symmetrical and skewed distributions. A numerical example using published data illustrates the proposed methods.

Computer Simulation↗

PubMed2006

Comparison of variance estimation approaches in a two-state Markov model for longitudinal data with misclassification.

We examine the behaviour of the variance-covariance parameter estimates in an alternating binary Markov model with misclassification. Transition probabilities specify the state transitions for a process that is not directly observable. The state of an observable process, which may not correctly classify the state of the unobservable process, is obtained at discrete time points. Misclassification probabilities capture the two types of classification errors. Variance components of the estimated transition parameters are calculated with three estimation procedures: observed information, jackknife, and bootstrap techniques. Simulation studies are used to compare variance estimates and reveal the effect of misclassification on transition parameter estimation. The three approaches generally provide similar variance estimates for large samples and moderate misclassification. In these situations, the resampling methods are reasonable alternatives when programming partial derivatives is not appealing. With smaller chains or higher misclassification probabilities, the bootstrap method appears to be the best choice.

Analysis of Variance↗

PubMed2007

Estimating the response rate in the presence of measurement error.

In clinical research, it is often of interest to estimate the response rate (i.e. the proportion of subjects who achieve a clinically meaningful threshold) for a particular variable. The standard estimator of the response rate is generally biased in the presence of measurement error. The estimation accounting for the measurement error utilizing fully nonparametric (NP) methods is complicated and may not be efficient. Therefore, we propose a model-based approach assuming a parametric model for the true value and only the first few moments for the measurement error. The estimator for the true response rate and the variance for the estimator are derived. An innovative method using bootstrap simulation is proposed to check the model assumption. Simulations show that the proposed estimator outperforms a fully NP estimator if the model assumption for X holds. This method is applied to address a commonly occurring question in osteoporosis regarding response to treatment in terms of longitudinal changes in bone mineral density (BMD). Bootstrap simulations showed that the model utilized is appropriate. The proposed method can also be applied in other fields of clinical research.

Absorptiometry, Photon↗

PubMed2007

A combined superiority and non-inferiority approach to multiple endpoints in clinical trials.

Treatment comparisons in clinical trials often involve multiple endpoints. By making use of bootstrap tests, we develop a new non-parametric approach to multiple-endpoint testing that can be used to demonstrate non-inferiority of a new treatment for all endpoints and superiority for some endpoint when it is compared to an active control. It is shown that this approach does not incur a large multiplicity cost in sample size to achieve reasonable power and that it can incorporate complex dependencies in the multivariate distributions of all outcome variables for the two treatments via bootstrap resampling.

Algorithms↗

PubMed2007

Comparing the small sample performance of several variance estimators under competing risks.

We examine several variance estimators for cumulative incidence estimators that have been proposed over time, some of which are derived from asymptotic martingale or counting process theory, and some of which are developed from the moments of the multinomial distribution. There is little published work comparing these variance estimators, largely because the variance estimators are algebraically complex and difficult to interpret and all but one have yet to be programmed for a standard statistical package. Through simulation and application to real data, we compare the performance of six variance estimators in relation to each other and the bootstrap in order to confirm earlier reports of their performance and to provide future direction toward their application. We find that the multinomial-moment-based estimators have performance close to that of the bootstrap, and are quite accurate for estimating the variance, even in samples of 20 subjects. All but one of the martingale theory-based estimators tend to perform poorly in small samples, tending to either overestimate or underestimate the empirical variance in samples of fewer than 100 subjects.

Analysis of Variance↗

PubMed1993

A method to test for a recent increase in HIV-1 seroconversion incidence: results from the Multicenter AIDS Cohort Study (MACS).

We have formulated the problem of determining whether there has been an upturn in HIV-1 seroconversion incidence over the first five years of follow-up in the Multicenter AIDS Cohort Study (MACS) as that of locating the minimum of a quadratic regression or examination of two-knot piecewise spline models. Under a quadratic model, we propose a method to obtain a direct estimate and a bootstrap estimate for the location of the temporal turning point (local minimum) for HIV-1 seroconversion incidence and three methods to estimate confidence intervals for the location of the turning point for HIV seroconversion incidence: (1) Wald confidence interval estimate with or without log transformation assuming the asymptotic normality and applying the Delta method; (2) asymmetric confidence intervals using Fieller's Theorem and its modification; and (3) bootstrapping confidence intervals. Inferences for the temporal turning point based on Wald tests for a single regression term in a non-linear regression model were not reliable compared to inferences based on confidence intervals placed on calendar time. We present results using these different methods applied to the MACS data and we obtain power estimates to illustrate the performances of different methods.

Cohort Studies↗

PubMedDate not supplied

Advances in statistical methodology for the evaluation of diagnostic and laboratory tests.

The ROC plot is a useful tool in the evaluation of the performance of medical tests for separating two populations. For a two-state decision rule based on such a test, the ROC plot is the graph of all observed (1-specificity, sensitivity) pairs. Each point on this empirical plot can be represented by a 2 x 2 contingency table. The non-parametric statistics of Mann-Whitney and Kolmogorov-Smirnov can be immediately identified on this plot. Local non-parametric confidence interval procedures related to the theoretical ROC curve are briefly reviewed. For continuous data, two new simultaneous confidence regions associated with the ROC curve are presented, one based on Kolmogorov-Smirnov confidence bands for distribution functions and the other based on bootstrapping. Two different tests on the same patients can be compared on the ROC scale. For continuous data, one important problem concerns the comparison of two ROC plots (as would arise from two correlated diagnostic tests on each patient) using a sup norm (this metric can detect differences that the ROC area cannot). The distribution of a statistic based on this norm is studied, using the bootstrap. A biomedical example illustrates the methodologies.

Clinical Laboratory Techniques↗

PubMedDate not supplied

Empirical Bayes estimation and inference for the random effects model with binary response.

Waclawiw and Liang introduced an estimating function-based approach for estimating the parameters of the classical two-stage random effects model for longitudinal data. In the present paper, the authors conduct a case study of the general approach for the binary response setting, where the fully specified parametric two-stage model with fixed and univariate random effects has an analytically intractable likelihood. With successful convergence of the algorithm, the authors propose a fully parametric bootstrapping method for deriving empirical Bayes confidence intervals for all model parameters. The bootstrapping approach is a blend of the estimating function technique with the developments of Laird and Louis. The estimating function approach to estimation and inference provides a general framework for the analysis of a wide variety of medical data, including the setting of small and varying numbers of discrete repeated observations. An application of the methodology to the analysis of binary responses in a crossover clinical trial is presented.

Bayes Theorem↗

PubMedDate not supplied

Analysis of pseudo-profiles in organ pharmacokinetics and toxicokinetics.

In general, the pharmacokinetic model parameters, like rate constants, area under the curve (AUC) etc. are estimated via a two-stage procedure, where the values obtained from concentration-time relationships within one subject (experimental unit) are considered to be functionally related to the drug concentrations measured. In many cases 'mean' estimators and their respective standard errors are calculated afterwards. The determination of drug concentrations in organs as well as in the serum of small animals (mice, rats) in dependence of the time after administration often does not permit the establishment of reasonable profiles within one subject suited for conventional pharmacokinetic analyses and tolerability studies. Frequently, only one experimental value per organ or animal is recorded. The consequence is that most pharmacokinetic parameters are to be estimated on the basis of the mean concentrations rather than via the mean of individual parameter estimates. In all cases of a non-linear relationship between a target item and the concentration, the mean-concentration based estimators and the two-stage profile based estimators need not coincide. In addition, in the former case variance estimators may be either difficult to obtain or not deducible. In order to get variance estimators as well as to enable comparisons between different treatment regimens, in addition to bioequivalence testing as a step towards human dose finding studies, various resampling techniques (parametric and non-parametric bootstrap) were applied to generate pseudo-profiles from independent measurements and compared to their more conventional counterparts where applicable. Simulation studies based on different predefined pharmacokinetic models (first-order elimination after i.v. bolus, first-order elimination after first-order absorption, simple capacity-limited kinetics) revealed that even the non-parametric pseudo-profile stratified 'bootstrap' (resampling with replacement per time point) performs quite satisfactorily.

Administration, Oral↗

PubMedDate not supplied

The effect of outliers on confidence interval procedures for cost-effectiveness ratios.

Cost-effectiveness ratio (CER) is defined as the ratio of the difference in cost between a test and standard health care programme to the difference in benefit, respectively. Methods to obtain confidence intervals for CERs are either variants of Fieller's method (1954), or bootstrap methods. We study the effect of outliers in cost measures on the precision of confidence interval procedures for CERs. In particular the performance of the procedures under single and multiple case influential deletion diagnostics, respectively, are evaluated. Simulation studies suggest that the bias-corrected percentile bootstrap procedure gives better precision and coverage under either diagnostic.

Computer Simulation↗

PubMed1998

The calculation of a confidence interval on the absolute estimated benefit for an individual patient.

Physicians need a method to predict the individualized absolute therapeutic benefit before deciding which therapy to prescribe to a given patient and the confidence intervals around this estimate. We have derived a method to predict the absolute individual therapeutic benefit in a previous work. In this paper, we present a Monte Carlo simulation to estimate the bias of prediction for an individual with certain characteristics and use a bootstrap method to compute its confidence intervals. Because the bootstrap approach does not depend upon the parametric assumption for the distribution of the prediction, it can be applied to situations where the parametric distribution is unknown. Over 35,000 cases of subjects at risk of cardiovascular events were available for analysis. Our results show the 95% confidence intervals for each individual. In a clinical setting, the use of this approach makes it possible to predict the absolute therapeutic benefit for each patient (the quantity of individual benefit) with sufficient precision.

Cardiovascular Diseases↗

PubMed1993

Molecular phylogeny of the New World monkeys (Platyrrhini, primates).

Phylogenetic relationships among the 16 extant genera of Ceboidea (the New World monkeys) were examined using aligned epsilon-globin gene sequences from 19 New World monkeys (representing all 16 extant ceboid genera), and seven catarrhines (one Old World monkey and six hominoids) and tarsier as the outgroups. The consensus maximum parsimony tree found for these epsilon-globin sequences and the levels of support from parsimony and bootstrap analyses, for the clades in this tree, provided strong evidence for a cladistic classification with the following clusters. Subtribes Callitrichina (Callithrix, Cebuella), Callimiconina (Callimico), Leontopithecina (Leontopithecus), and Saguina (Saguinus) constitute subfamily Callitrichinae, and subfamilies Callitrichinae, Aotinae (Aotus), Saimiriinae (Saimiri), and Cebinae (Cebus) constitute family Cebidae. In turn, subtribes Chiropotina (Chiropotes, Cacajao) and Pitheciina (Pithecia) constitute tribe Pithecini, tribes Pitheciini and Callicebini (Callicebus) constitute subfamily Pitheciinae, tribes Atelini (Brachyteles, Lagothrix, Ateles) and Alouattini (Alouatta) constitute subfamily Atelinae, and subfamilies Pitheciinae and Atelinae constitute family Atelidae. The two families (Cebidae and Atelidae) constitute the Ceboidea, the only extant superfamily of infraorder Platyrrhini. The sister-group relationships of Brachyteles and Lagothrix, Saguinus and Leontopithecus, and Callimico with a Cebuella/Callithrix clade is not as well supported by the parsimony and bootstrap analyses. Therefore, these relationships are not incorporated in the proposed cladistic classification. On determining branch lengths for the ceboid phylogenetic tree from only the more freely evolving noncoding sequences at the epsilon-globin locus and taking the reference age of 35 million years ago (MYA) for the New World monkey-catarrhine branch point, we estimated the age of the atelid-cebid branch point as about 20 MYA, and the ages of the next branch points, those between the subfamilies in each family, as 19-16 MYA.

Animals↗

PubMed1994

DNA-DNA hybridization-based phylogeny for "higher" nonpasserines: reevaluating a key portion of the avian family tree.

A matrix of delta T mode values for 10 birds, including 9 nonpasserines and a suboscine passerine flycatcher, was generated by DNA-DNA hybridization. Within the most derived lineages, all bootstrapped and jackknifed FITCH trees lend strong support to sister-groupings of the two swift families, of hummingbirds to swifts, and of these to a clade containing both owls and night-hawks. The outgroup duck roots the tree between the woodpecker (Piciformes) and the remaining taxa, indicating that Piciformes are among the earliest branches within nonpasserines. However, the succeeding branches to kingfisher, mousebird, and suboscine passerine flycatcher are based on short internodes that are poorly supported by bootstrapping and that give inconsistent results in jackknifing. Although these 3 orders may have arisen through rapid or near-simultaneous divergence, placement of the "advanced" Passeriformes deep within a more "primitive" radiation indicates that nonpasserines are paraphyletic, echoing the same distinction for reptiles with respect to their advanced descendants. Despite significant rate variation among different taxa, these results largely concur with those obtained with the same technique by Sibley and Ahlquist, who used the delta T50H measure and UPGMA analysis. This agreement lends credence to some of their more controversial claims.

Animals↗

PubMed1994

How many nucleotides are required to resolve a phylogenetic problem? The use of a new statistical method applicable to available sequences.

The evolution of bootstrap proportions (BP) with sequence length was studied using a 28S ribosomal RNA data set. For different sequence lengths, informative sites were jackknifed several times. Bootstrapping was subsequently performed on each of these subsamples. For each node, BPs so obtained were plotted against sequence length, showing the evolution of the robustness with increasing number of informative sites. For robust nodes (BP of 100%), the pattern of BPs is unvarying and is described by a simple function BP = 100 (1-e-b(x-x')), where x is the number of informative sites and b and x' are two parameters estimated using a nonlinear regression procedure. When a node has a BP < 100% and the pattern of BPs fits this function, it is possible to estimate the number of informative sites required to obtain a given average BP. The method also identifies nonrobust nodes (nonascending clusters of BP dots), for which it seems to be more cost effective and fruitful to turn to other species and/or genes rather than to continue sequencing longer gene lengths from the same species to reach a BP of 95%.

Animals↗

PubMed1996

Interordinal mammalian relationships: evidence for paenungulate monophyly is provided by complete mitochondrial 12S rRNA sequences.

The complete mitochondrial 12S rRNA sequences of 5 placental mammals belonging to the 3 orders Sirenia, Proboscidea, and Hyracoidea are reported together with phylogenetic analyses (distance and parsimony) of a total of 51 mammalian orthologues. This 12S rRNA database now includes the 2 extant proboscideans (the African and Asiatic elephants Loxodonta africana and Elephas maximus), 2 of the 3 extant sirenian genera (the sea cow Dugong dugon and the West Indian manatee Trichechus manatus), and 2 of the 3 extant hyracoid genera (the rock and tree hyraxes Procavia capensis and Dendrohyrax dorsalis). The monophyly of the 3 orders Sirenia, Proboscidea, and Hyracoidea is supported by all kinds of analysis. There are 23 and 3 diagnostic subsitutions shared by the 2 proboscideans and the 2 hyracoids, respectively, but none by the 2 sirenians. The 2 proboscideans exhibit the fastest rates of 12S rRNA evolution among the 11 placental orders studied. Based on various taxonomic sampling methods among eutherian orders and marsupial outgroups, the most strongly supported clade in our comparisons clusters together the 3 orders Sirenia, Proboscidea, and Hyracoidea in the superorder Paenungulata. Within paenungulates, the grouping of sirenians and proboscideans within the mirorder Tethytheria is observed. This branching pattern is supported by all analyses by high bootstrap percentages (BPs) and decay indices. When only one species is selected per order or suborder, the taxonomic sampling leads to a relative variation in bootstrap support of 53% for Tethytheria (BPs ranging from 44 to 93%) and 7% for Paernungulata (92-99%). When each order or suborder is represented by two species, this relative variation decreased to 10% for Tethytheria (78-87%) and 3% for Paenungulata (96-99%). Two nearly exclusive synapomorphies for paenungulates are identified in the form of one transitional compensatory change, but none were detected for tethytherians. Such a robust and reliable resolution of the paenungulate node implies a long history of the common ancestors, allowing time for synapomorphies to accumulate. This observation suggests a Late Cretaceous/Early Paleocene origin for the Paenungulata.

Animals↗

PubMed1999

Molecular phylogeny of ateline new world monkeys (Platyrrhini, atelinae) based on gamma-globin gene sequences: evidence that brachyteles is the sister group of lagothrix.

Nucleotide sequences, each spanning approximately 7 kb of the contiguous gamma1 and gamma2 globin genomic loci, were determined for seven species representing all extant genera (Ateles, Lagothrix, Brachyteles, and Alouatta) of the New World monkey subfamily Atelinae. After aligning these seven ateline sequences with outgroup sequences from several other primate (non-ateline) genera, they were analyzed by maximum parsimony, maximum likelihood, and neighbor-joining algorithms. All three analyzes estimated the same phylogenetic relationships: [Alouatta [Ateles (Brachyteles, Lagothrix)]]. Brachyteles and Lagothrix are sister-groups supported by 100% of bootstrap replications in the parsimony analyses. Ateles joins this clade, followed by the basal genus Alouatta; these joinings were strongly supported, again with 100% bootstrap values. This cladistic pattern for the four ateline genera is congruent with that obtained in previous studies utilizing epsilon-globin, IRBP, and G6PD nuclear genomic sequences as well as mitochondrial COII sequences. Because the number of aligned nucleotide positions is much larger in the present datasetoff than in any of these other datasets, much stronger support was obtained for the cladistic classification that divides subfamily Atelinae into tribes Alouattini (Alouatta) and Atelini, while the latter divides into subtribes Atelina (Ateles) and Brachytelina (Brachyteles and Lagothrix).

Animals↗

PubMed2000

Molecular phylogeny of parasitic zygomycota (Dimargaritales, zoopagales) based on nuclear small subunit ribosomal DNA sequences.

We analyzed sequence data of the 18S rDNA gene from representatives of nine mycoparasitic or zooparasitic genera to infer the phylogenetic relationships of these fungi within the Zygomycota. Phylogenetic analyses identified a novel monophyletic clade consisting of the Zoopagales, Kickxellales, Spiromyces, and Harpellales. Analyses also identified a monophyletic mycoparasitic-zooparasitic Zoopagales clade in which Syncephalis, Thamnocephalis, and Rhopalomyces form a sister group to a Piptocephalis-Kuzuhaea clade. Although monophyly of the mycoparasitic Dimargaritales received strong bootstrap and decay index support, phylogenetic relationships of this order could not be resolved because of the unusually high rate of base substitutions within the 18S rDNA gene. Overall, the 18S gene tree topology is weak, as reflected by low bootstrap and decay index support for virtually all internal nodes uniting ordinal and superordinal taxa. Nevertheless, the 18S rDNA phylogeny is mostly consistent with traditional phenotypic-based classification schemes of the Fungi.

Classification↗