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PubMed2003

Tests for individual and population bioequivalence based on generalized p-values.

The U.S. Food and Drug Administration (FDA) has proposed new regulations that address the 'prescribability' and 'switchability' of new formulations of already-approved drugs. These new criteria are known, respectively, as population and individual bioequivalence. Two methods have been proposed in the bioequivalence literature for assessing population and individual bioequivalence that calculate an upper 95 per cent confidence bound for the bioequivalence criterion in question, and then test bio-equivalence by comparing this bound to the limit established by the FDA. In this paper we propose applying the generalized test function (GTF) methodology of Tsui and Weerahandi (Journal of the American Statistical Association 1989; 602-607) to this problem to produce tests based on a generalized p-value (GPV). This methodology allows us to construct hypothesis tests in the presence of nuisance parameters. Using simulation we show that these tests perform well in comparison to the confidence interval methods and have superior power for assessing population bioequivalence.

Adrenergic Agents↗

PubMed2004

GEE approaches to marginal regression models for medical diagnostic tests.

The evaluation of a new medical diagnostic test may focus on two different scientific questions: (1). The new test may replace an existing one because of lower cost or higher validity. A related question would be the selection of the 'best' test(s) from a bundle of new or established measurements. (2). The new test may be used supplementary to other new or established procedures. In a recent publication, Leisenring and co-workers (Stat Med 1997; 16:1263-1281) developed a general marginal regression model for comparisons of diagnostic tests focussing on question (1). i.e. on the selection of the 'best' procedure. They applied the GEE approach of Liang and Zeger (Biometrika 1987; 73:13-22) to adjust for the correlation of data as a nuisance parameter. Using the general framework provided by Leisenring et al., we extend their approach and apply the GEE methodology to question (2). i.e. to the investigation of which of several diagnostic tests should be used supplementary to each other. We analyse data from a longitudinal study concerning pathogenesis, diagnosis and long-term course of the eye disease glaucoma. We find a dependence of the correlation structure of several diagnostic measurements on the severity of the disease. This result may be useful in clinical applications as regards the selection of subsets of diagnostic measurements in individual diagnostic processes but also in investigations concerning the relationship of the pathogenic process and the rationales of the different diagnostic procedures.

Biometry↗

PubMed2006

Adaptive, group sequential and decision theoretic approaches to sample size determination.

This paper presents two adaptive methods for sample size re-estimation within a unified group sequential framework. The conceptual and practical distinction between these adaptive modifications and more traditional sample size changes due to revised estimates of nuisance parameters is highlighted. The motivation for the adaptive designs is discussed. Having established that adaptive sample size modifications can be made without inflating the type 1 error, the paper concludes with a novel decision theoretic approach for determining the magnitude of the sample size modification.

Clinical Trials as Topic↗

PubMed2007

Analysis of matched case-control data with multiple ordered disease states: possible choices and comparisons.

In an individually matched case-control study, effects of potential risk factors are ascertained through conditional logistic regression (CLR). Extension of CLR to situations with multiple disease or reference categories has been made through polychotomous CLR and is shown to be more efficient than carrying out separate CLRs for each subgroup. In this paper, we consider matched case-control studies where there is one control group, but there are multiple disease states with a natural ordering among themselves. This scenario can be observed when the cases can be further classified in terms of the seriousness or progression of the disease, for example, according to different stages of cancer. We explore several popular models for ordered categorical data in this context. We first adopt a cumulative logit or equivalently, a proportional-odds model to account for the ordinal nature of the data. The important distinction of this model from a stratified dichotomous and polychotomous logistic regression model is that the stratum-specific nuisance parameters cannot be eliminated in this model via the conditional-likelihood approach. We discuss a Mantel-Haenszel approach for analysing such data. We point out possible difficulties with standard likelihood-based approaches with the cumulative logit model when applied to case-control data. We then consider an alternative conditional adjacent-category logit model. We illustrate the methods by analysing data from a matched case-control study on low birthweight in newborns where infants are classified according to low and very low birthweight and a child with normal birthweight serves as a control. A simulation study compares the different ordinal methods with methods ignoring sub-classification of the ordered disease states.

Case-Control Studies↗

PubMed1991

The analysis of categorical data from cross-over trials using a latent variable model.

A latent variable model for categorical data is described. The nuisance parameters in the model can be eliminated from the analysis through the use of a conditional likelihood and this leads to an analysis based on a log-linear model. It is shown how the structure of a cross-over trial allows considerable simplification in the formulation of this model and routine application of well-known statistical packages. The method is illustrated by data from a three-period cross-over trial on the relief of primary dysmenorrhea using the GLIM and SAS packages.

Analysis of Variance↗

PubMed1992

Exact unconditional tables for significance testing in the 2 x 2 multinomial trial.

This paper presents tables analogous to T-tables for use in the 2 x 2 multinomial trial, where the continuity corrected Z-statistic is used to make exact unconditional inference. This is the first solution of a discrete exact unconditional inference problem involving a multivariate nuisance parameter for which no ancillary statistic exists.

Bias↗

PubMedDate not supplied

Sample size recalculation using conditional power.

The sample size required to achieve a given power at a prespecified absolute difference in mean response may depend on one or more nuisance parameters, which are usually unknown. Proposed methods for using an internal pilot to recalculate the sample size using estimates of these parameters have been well studied. Most of these methods ignore the fact that data on the parameter of interest from within this internal pilot will contribute towards the value of the final test statistic. We propose a method which involves recalculating the target sample size by computing the number of further observations required to maintain the probability of rejecting the null hypothesis at the end of the study under the prespecified absolute difference in mean response conditional on the data observed so far. We do this within the framework of a two-group error-spending sequential test, modified so as to prevent inflation of the type I error rate.

Breast Neoplasms↗

PubMed2004

Time-domain quantitation of 1H short echo-time signals: background accommodation.

Quantitation of 1H short echo-time signals is often hampered by a background signal originating mainly from macromolecules and lipids. While the model function of the metabolite signal is known, that of the macromolecules is only partially known. We present time-domain semi-parametric estimation approaches based on the QUEST quantitation algorithm (QUantitation based on QUantum ESTimation) and encompassing Cramér-Rao bounds that handle the influence of 'nuisance' parameters related to the background. Three novel methods for background accommodation are presented. They are based on the fast decay of the background signal in the time domain. After automatic estimation, the background signal can be automatically (1) subtracted from the raw data, (2) included in the basis set as multiple components, or (3) included in the basis set as a single entity. The performances of these methods combined with QUEST are evaluated through extensive Monte Carlo studies. They are compared in terms of bias-variance trade-off. Because error bars on the amplitudes are of paramount importance for diagnostic reliability, Cramér-Rao bounds accounting for the uncertainty caused by the background are proposed. Quantitation with QUEST of in vivo short echo-time (1)H human brain with estimation of the background is demonstrated.

Brain↗

PubMed1995

The estimation of event related potentials affected by random shifts and scalings.

There is considerable evidence for trial to trial variability of the event related potentials (ERPs) within a given subject's recording. This variability influences the outcome of usual procedures in ERP analysis. Better results may be obtained if the sources of variability are explicitly taken into account in an appropriate model. This paper considers a probabilistic model, the random shift and scaling (RSS) model, where the response is modified by a random time shift and a random scale factor. In addition to this, an additional random scale factor which affects both the response and the background noise is taken into account. This time shift and these scale factors are handled as nuisance parameters. Maximum likelihood and least squares estimators of these parameters and the waveform of response are derived for the RSS model. It is shown that the Woody estimate of the ERP reported in earlier work can be derived by restricting the assumptions for the RSS model. Test statistics for hypotheses on means are obtained for the RSS model and a new type of discriminant function. The usefulness of the method is illustrated by means of simulation studies. Receiver operating characteristic (ROC) curves are used to demonstrate that the new type of discriminant performs better than the usual Fisher's Linear Discriminant.

Artifacts↗

PubMed2004

Epidemiological factors that influence time-to-treatment of trypanosomosis in Orma Boran cattle raised at Galana Ranch, Kenya.

Four thousand nine hundred and seventy-one trypanosomosis-surveillance records from an open population of Orma Boran cattle raised under natural trypanosomosis challenge in Galana Ranch, Kenya between the years 1990 and 2000 were analysed. The objective of the analysis was to identify epidemiological factors that influenced time-to-treatment of trypanosomosis cases. Under the surveillance programme, blood was being examined fortnightly for trypanosomosis using buffy coat technique. Infected animals were treated when their packed cell volumes (PCV) fell to 25% or lower. The number of days between the first diagnosis and treatment of trypanosomosis cases was obtained from the difference between diagnosis and treatment dates. Days-to-treatment clustered around the screening periods; therefore, time-to-treatment was represented by a series of time points 0-8 at 14-day intervals. Factors postulated to affect the outcome (time-to-treatment) were age of an animal at time of diagnosis, sex, number of trypanosome infections, trypanosome species and season of the year. Five animal generations were generated from birth dates and treated as nuisance parameters. Conditional logistic regression and Cox proportional hazards models were fitted to the data, the former to analyse factors that influenced treatment after time 0 (outcome dichotomised as time 0 or >0) and the latter to analyse factors that influenced time-to-treatment for cases that were treated after time 0, excluding all cases treated on time 0. The majority of the cases (89.5%) were treated on the same day of diagnosis. Trypanosome infections were more likely to be treated after time 0 in dry than in wet season. Similarly, the rate of treatment was lower in the dry than the wet season. An increase in number of previous trypanosome infections reduced the odds of an animal being treated after time 0. Animals that had been exposed to many infections before had higher rates of treatment than those that had minimal experiences. We offer possible reasons for these observations and conclude that selection of animals for breeding purposes in programmes geared towards improving trypanotolerance should take into consideration the environmental factors that affect classification of an animal as being resistant or susceptible.

Anemia↗

PubMed1998

Estimating stimulus response latency.

Stimulus response latency is the delay in the onset of stimulus-evoked neuronal activity. We develop maximum likelihood and least squares estimators of stimulus response latency and present a comparison of the performance of these methods with estimators commonly used in the neuroscience literature. The formal statistical change-point estimation problem is nontrivial due to the inclusion of a 'nuisance parameter', the end of stationarity in the stimulus-evoked activity. Our results suggest that the automation of the estimation of stimulus response latency will benefit from the use of the maximum likelihood estimator.

Action Potentials↗

PubMed2006

A test of homogeneity of Hardy-Weinberg disequilibrium across strata.

For genotype data being sampled from several strata with different allele frequencies, it is necessary to verify the assumption of homogeneity of Hardy-Weinberg disequilibrium across strata before testing Hardy-Weinberg law across strata. In practice, disequilibrium can be measured via fixation coefficients (ie, ratios of genotypic frequencies) or disequilibrium coefficients (ie, differences of genotypic frequencies). Test for homogeneity of Hardy-Weinberg disequilibrium using data from several populations has been derived according to fixation coefficients. In this article, using the likelihood score theory extended to nuisance parameters, we derive a homogeneity score test for comparing disequilibrium coefficients across several independent strata. Simulation results demonstrate that the homogeneity score test performs satisfactorily in the sense that its empirical size seldom exceeds the pre-chosen nominal level by more than 10% even for small sample sizes. Corresponding power and sample size formulae are provided as well. We illustrate our test with a real glyoxalase genotype data set.

Gene Frequency↗

PubMed2001

Sustaining genetic variation in a small population: evidence from the Mauritius kestrel.

We obtained measures of genetic diversity in 10 kestrel species at a suite of 12 microsatellite loci. We estimated the relative effective size (Ne) of the species using a Markov chain Monte Carlo (MCMC) approach, which jointly estimated the locus specific mutation rates as nuisance parameters. There was surprisingly high genetic diversity found in museum specimens of the Mauritius kestrel. Being an endemic species on a small island, it is known to have a long history of small population size. Conversely, kestrels with a continental distribution had Ne estimates that were only one order of magnitude larger and similar to each other, despite having current population sizes that were between one and three orders of magnitude larger than the Mauritius kestrel. We show how many of the theoretical results describing the effective size of a subdivided population can be captured in terms of three rates which describe the branching pattern of the gene genealogy, and that they are useful in estimating the time to migration-drift and mutation-drift equilibrium. We use this approach to argue that population subdivision has helped retain genetic diversity in the Mauritius kestrel, and that the continental species' genetic diversity has yet to reach equilibrium after the range changes following the last ice age. We draw parallels with Hewitt's observation that genetic variation seems to survive species' range compression and is rather vulnerable to range expansion.

Animals↗

PubMed1985

Survival models for fertility evaluation.

"Two proportional hazards models for cohort fertility evaluation are constructed. Time-dependent covariates describe sources of heterogeneity between and within women regarding fertility characteristics. In the first model, U.S. birth rates specific to maternal age, race, parity, and birth cohort are used as underlying hazard rates. Covariate effects are estimated by maximizing the full likelihood. In the second model, covariate effects are estimated via Cox regression with stratified underlying hazard rates regarded as unknown nuisance parameters." The authors illustrate the models "with an evaluation of the fertility histories of the wives of workers at a manufacturing plant with potential for hazardous exposure. Adjustments to the U.S. birth rates for maternal age and parity zero experience are required with the first approach. Then, despite differences in the model-specific estimation procedures, the point estimates of the exposure effect and the estimated standard errors from the two models are practically equivalent."

Americas↗

PubMed1998

Significance levels in complex inheritance.

A LOD score >=3 is necessary but not sufficient to make a linkage test reliable, and this applies to complex inheritance as well as to major loci. Factors that affect this threshold are considered here. A LOD score as small as 2 is suggestive but is unreliable except as confirmation of either a significant linkage or a strong candidate locus. A threshold as great as 4 is unnecessarily conservative if multipoint tests are used sensibly. Marker density is not a major factor, and biases in the evaluation of LOD scores-especially inadequate allowance for estimation of nuisance parameters in multiple models-are paramount. Allelic association increases resolution for oligogenes within a candidate region and remains the only practical method to locate polygenes. The method sketched here combines multipoint linkage and allelic association to test efficiently for a regional candidate locus.

Alleles↗

PubMed2003

How Bayes tests of molecular phylogenies compare with frequentist approaches.

MOTIVATION: The desire to compare molecular phylogenies has stimulated the design of numerous tests. Most of these tests are formulated in a frequentist framework, and it is not known how they compare with Bayes procedures. I propose here two new Bayes tests that either compare pairs of trees (Bayes hypothesis test, BHT), or test each tree against an average of the trees included in the analysis (Bayes significance test, BST). RESULTS: The algorithm, based on a standard Metropolis-Hastings sampler, integrates nuisance parameters out and estimates the probability of the data under each topology. These quantities are used to estimate Bayes factors for composite vs. composite hypotheses. Based on two data sets, the BHT and BST are shown to construct similar confidence sets to the bootstrap and the Shimodaira Hasegawa test, respectively. This suggests that the known difference among previous tests is mainly due to the null hypothesis considered.

Algorithms↗

PubMed2002

Multipoint linkage detection in the presence of heterogeneity.

Linkage heterogeneity is common for complex diseases. It is well known that loss of statistical power for detecting linkage will result if one assumes complete homogeneity in the presence of linkage heterogeneity. To this end, Smith (1963, Annals of Human Genetics 27, 175-182) proposed an admixture model to account for linkage heterogeneity. It is well known that for this model, the conventional chi-squared approximation to the likelihood ratio test for no linkage does not apply even when the sample size is large. By dealing with nuclear families and one marker at a time for genetic diseases with simple modes of inheritance, score-based test statistics (Liang and Rathouz, 1999, Biometrics 55, 65-74) and likelihood-ratio-based test statistics (Lemdani and Pons, 1995, Biometrics 51, 1033-1041) have been proposed which have a simple large-sample distribution under the null hypothesis of linkage. In this paper, we extend their work to more practical situations that include information from multiple markers and multi-generational pedigrees while allowing for a class of general genetic models. Three different approaches are proposed to eliminate the nuisance parameters in these test statistics. We show that all three approaches lead to the same asymptotic distribution under the null hypothesis of no linkage. Simulation results show that the proposed test statistics have adequate power to detect linkage and that the performances of these two classes of test statistics are quite comparable. We have applied the proposed method to a family study of asthma (Barnes et al., 1996), in which the score-based test shows evidence of linkage with p-value <0.0001 in the region of interest on chromosome 12. Additionally, we have implemented this score-based test within the frequently used computer package GENEHUNTER.

Journal Article↗

PubMed2002

Unconditional small-sample confidence intervals for the odds ratio.

The traditional approach to 'exact' small-sample interval estimation of the odds ratio for binomial, Poisson, or multinomial samples uses the conditional distribution to eliminate nuisance parameters. This approach can be very conservative. For two independent binomial samples, we study an unconditional approach with overall confidence level guaranteed to equal at least the nominal level. With small samples this interval tends to be shorter and have coverage probabilities nearer the nominal level.

Journal Article↗