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PubMed2002

A Pearson-type goodness-of-fit test for stationary and time-continuous Markov regression models.

Markov regression models describe the way in which a categorical response variable changes over time for subjects with different explanatory variables. Frequently it is difficult to measure the response variable on equally spaced discrete time intervals. Here we propose a Pearson-type goodness-of-fit test for stationary Markov regression models fitted to panel data. A parametric bootstrap algorithm is used to study the distribution of the test statistic. The proposed technique is applied to examine the fit of a Markov regression model used to identify markers for disease progression in psoriatic arthritis.

Arthritis, Psoriatic↗

PubMed2002

The origin of DNA replication and Fieller's problem.

The paper considers the statistical problem of estimating the origin of DNA replication within the human ribosomal DNA (rDNA) locus and the issue of assessing the standard error of the estimate. Based on mapping the cumulative replication index (CRI), two different modelling schemes are suggested and investigated. The statistical problem of constructing a confidence interval for the origin of DNA replication is related to Fieller's problem of obtaining a confidence interval for the ratio of two normal means. Standard normal theory, the delta and bootstrap methods are used to estimate the standard error of the estimate of the origin of DNA replication, as well as the variation of the replication rate.

Chromosomes, Human↗

PubMed2002

Comparison of tests for categorical data from a stratified cluster randomized trial.

Two features commonly exhibited by randomized trials of health promotion interventions are cluster randomization and stratification. Ignoring correlations between individuals within clusters can lead to an inflated type I error rate and hence a P-value which overstates the significance of the result. This paper compares several methods for analysing categorical data from a stratified cluster randomized trial. We propose an extension of a method from survey sampling that uses the design effect to reduce the effective sample size. We compare this with three methods from Zhang and Boos that extend the standard Cochran-Mantel-Haenszel (CMH) statistic by using appropriate covariance matrices, and with a bootstrap method. The comparison is based on empirical type I error rates from a simulation study, in which the number of clusters randomized is small, as in most public health intervention studies. The method that performs consistently well is one of the Zhang and Boos extensions of the standard CMH statistic.

Alcohol Drinking↗

PubMed2002

Binary partitioning for continuous longitudinal data: categorizing a prognostic variable.

We investigate a binary partitioning algorithm in the case of a continuous repeated measures outcome. The procedure is based on the use of the likelihood ratio statistic to evaluate the performance of individual splits. The procedure partitions a set of longitudinal data into two mutually exclusive groups based on an optimal split of a continuous prognostic variable. A permutation test is used to assess the level of significance associated with the optimal split, and a bootstrap confidence interval is obtained for the optimal split.

Adolescent↗

PubMed2002

Two approaches to mutation detection based on functional data.

A new technique, denaturing high-performance liquid chromatography (dHPLC), allows for detection of any heterozygous sequence variation in a gene without prior knowledge of the precise location of the sequence change. The results of a dHPLC analysis are recorded in real-time in the form of a chromatogram that is sequence-specific. In this paper we present methods to classify an individual, based on the observed chromatogram, as a homozygous wild-type or a carrier of a specific variant for the given DNA segment by comparison to representative chromatograms that are obtained from the training set of individuals with known variant status. The first approach consists of finding a parsimonious parametric model and then classifying each newly observed curve based on comparing the most discriminating characteristic, the main mode, to the main mode of the training curves. The second approach consists of finding empirical estimates of the modes of each chromatogram and using a bootstrap test for equality with the corresponding estimates of the training curves. We apply both methods to data on the breast cancer susceptibility gene BRCA1 and test the performance of the methods on independent samples.

Algorithms↗

PubMed2002

Local likelihood analysis of the latency distribution with interval censored intermediate events.

The distribution of time between an intermediate event and a terminal event is frequently of interest both in studying the behaviour of populations and in predicting outcomes for individuals. Current methods for estimating this latency distribution have either imposed assumptions on the hazard for the terminal event following the occurrence of the intermediate event or on the parametric form of the hazards. Here, local likelihood estimation is applied to the underlying hazard functions of a three-state process in which the time of the intermediate event may be interval censored and the time of the terminal event is either observed or right censored. Smooth non-parametric estimates of the latency distribution, along with bootstrap confidence intervals, are calculated, and tests for the comparison of two latency distributions are presented. The method is applied to two studies: a cohort of haemophiliacs who were infected with HIV by contaminated blood factor and followed for AIDS onset, and an AIDS clinical trial in which the intermediate event is the time to 50 per cent drop in CD4 count and the terminal event is AIDS or death. Simulations are presented to assess the performance of the estimation procedure.

Acquired Immunodeficiency Syndrome↗

PubMed2002

Alternatives to the hazard ratio in summarizing efficacy in time-to-event studies: an example from influenza trials.

Estimates of the efficacy of new medicines are key to the investigation of their clinical effectiveness. The most widely recommended approach to summarizing time-to-event data from clinical trials is to use a hazard ratio. When the proportional hazards assumption is questionable, a hazard ratio depends on the length of patient follow-up. Hazard ratios do not directly translate into differences in times to events and therefore can present difficulties in interpretation. This paper describes an area where summary by hazard ratio would seem unsuitable and explores alternative estimates of efficacy. In particular, the difference in median time to event between treatments can provide a useful and consistent measure of efficacy. Methods of calculating confidence intervals for differences in medians for censored time-to-event will be described. Accelerated failure time models provide a useful alternative approach to proportional hazards modelling. Estimates of the ratio of the median time to event between treatments are directly available from these models. One of the reasons given for summarizing time-to-event studies by a hazard ratio is to facilitate meta-analyses. The bootstrap estimate of standard error for difference in median in each trial can provide a method for combining results based on summary statistics.

Antiviral Agents↗

PubMed2003

Tumour grading from magnetic resonance spectroscopy: a comparison of feature extraction with variable selection.

Magnetic resonance spectroscopy (MRS) provides a non-invasive measurement of the biochemistry of living tissue. However, signal variation due to tissue heterogeneity causes considerable mixing between different disease categories, making accurate class assignments difficult. This paper compares a systematic methodology for classifier design using multivariate bayesian variable selection (MBVS), with one based on feature extraction using independent component analysis (ICA). We illustrate the methodology and assess the classification performance using a data set comprising 41 magnetic resonance spectra acquired in vivo from two grades of brain tumour, namely low- and medium-grade astrocytic tumours, labelled astrocytomas (AST), and high-grade gliomas and glioblastomas labelled glioblastomas (GL). The aim of this study is threefold. First, to describe the application of the alternative methodologies to MRS, then to benchmark their classification performance, and finally to interpret the classification models in terms of biologically relevant signals derived from the spectra. The classification performance is assessed using the bootstrap method and by application to a test sample in a retrospective study.

Astrocytoma↗

PubMed2003

Estimating the probability of toxicity at the target dose following an up-and-down design.

One of the most important aspects of a phase I trial or other acute toxicity study is estimating accurately the probability of toxicity that is associated with the recommended dose. We use the biased coin up-and-down design to allocate and isotonic regression to estimate toxicity probabilities and determine the recommended dose. We then derive, using bootstrap methods, an estimate of the probability of toxicity at the recommended dose. Small sample properties of this estimator are also evaluated. Published in 2003 by John Wiley & Sons, Ltd.

Bias↗

PubMed2002

Multicollinearity in prognostic factor analyses using the EORTC QLQ-C30: identification and impact on model selection.

Clinical and quality of life (QL) variables from an EORTC clinical trial of first line chemotherapy in advanced breast cancer were used in a prognostic factor analysis of survival and response to chemotherapy. For response, different final multivariate models were obtained from forward and backward selection methods, suggesting a disconcerting instability. Quality of life was measured using the EORTC QLQ-C30 questionnaire completed by patients. Subscales on the questionnaire are known to be highly correlated, and therefore it was hypothesized that multicollinearity contributed to model instability. A correlation matrix indicated that global QL was highly correlated with 7 out of 11 variables. In a first attempt to explore multicollinearity, we used global QL as dependent variable in a regression model with other QL subscales as predictors. Afterwards, standard diagnostic tests for multicollinearity were performed. An exploratory principal components analysis and factor analysis of the QL subscales identified at most three important components and indicated that inclusion of global QL made minimal difference to the loadings on each component, suggesting that it is redundant in the model. In a second approach, we advocate a bootstrap technique to assess the stability of the models. Based on these analyses and since global QL exacerbates problems of multicollinearity, we therefore recommend that global QL be excluded from prognostic factor analyses using the QLQ-C30. The prognostic factor analysis was rerun without global QL in the model, and selected the same significant prognostic factors as before.

Antineoplastic Agents↗

PubMed2003

Confidence intervals for the 50 per cent response dose.

Confidence intervals for the 50 per cent response dose are usually computed using either the Delta method or Fieller's procedure. Recently, confidence intervals computed by inverting the asymptotic likelihood ratio test have also been recommended. There is some controversy as to which of these methods should be used. By means of an extensive simulation study we examine these methods as well as confidence intervals obtained by the approximate bootstrap confidence (ABC) procedure and an adjusted form of the likelihood ratio based confidence intervals.

Animals↗

PubMed2003

A probability model for the meiosis I non-disjunction fraction in numerical chromosomal anomalies.

Numerical chromosome abnormalities (aneuploidies) are among the most common known causes of mental retardation and the leading cause of pregnancy loss in humans. They primarily arise by the process of meiotic non-disjunction. We still know very little about the contribution of genetic and environmental causes for non-disjunction in humans. In order to increase our understanding of the epidemiology of human trisomies, it is necessary to establish the proportion of cases occurring in the first or second division of meiosis. Trisomic patients will display, in study of microsatellite typed by the polymerase chain reaction (PCR), three fragment peaks of equal intensity, two fragments at an average 2:1 dosage or one individual fragment. In this work we describe a statistical approach for estimation of the fraction of meiosis I non-disjunctions (F) in the absence of the parental information. First we determine a probability model for the number of peaks in a polymorphic microsatellite locus, which is a function of F. Based on this model, we obtain a maximum likelihood estimator for F, using the observed proportion of one, two and three allele patterns in trisomic individuals. Relying on the properties of maximum likelihood theory, we also calculate the asymptotic variance and confidence intervals for F. Owing to the fact that the samples of trisomic patients are limited in number, the use of asymptotic theory may be compromised. Thus, we employ the bootstrap technique to build confidence intervals for F and compare the results with those obtained from the normal theory. This estimator that dispenses the need to study parents opens the possibility of using archival material for comparative epidemiological studies of Down's syndrome and other aneuploidies. In this paper we propose a probability model to estimate the fraction of meiosis I non-disjunction, F, by only using the proportion of allele patterns of trisomy individuals, while traditional methods require typing pericentromeric markers from those affected and their parents.

Brazil↗

PubMed2003

The use of regression models for medians when observed outcomes may be modified by interventions.

Some outcomes used in epidemiological studies and clinical trials are prone to modification by interventions, for example, individuals with high blood pressure are likely to receive antihypertensive medication. Often the scientific interest is in the relationship of covariates (exposures or randomized treatment) to the outcomes that would have been observed in the absence of intervention. We compare three approaches to the analysis of such data: ignoring the intervention; excluding individuals who receive the intervention, and assuming that individuals who receive the intervention have underlying outcomes above the median. The latter approach requires comparison of median outcomes between groups. In many situations it is plausible that neither the probability of intervention nor the effect of intervention depend on the covariates. In this case we show that analysis of medians is unbiased in general, that the other approaches are biased towards the null but that ignoring the intervention typically has the greatest power for detecting an effect. In other situations, ignoring the intervention and excluding individuals who receive the intervention may be biased towards or away from the null, and we recommend analysis of medians. We illustrate practical analysis of medians in a study of the association between adult blood pressure and birth weight. Adjustment for confounders is performed by median regression. We show that the significance levels are comparable to those derived from logistic regression. We also discuss the effect of grouping of blood pressure and the need for bootstrap standard errors.

Antihypertensive Agents↗

PubMed2003

Novel designs for multi-arm clinical trials with survival outcomes with an application in ovarian cancer.

With the increasing pace of drug development, it is not unusual for several promising treatment regimens to be ready simultaneously for testing in a randomized phase III setting. Various limiting factors, including the time needed to transfer research results to clinical practice and a narrow 'window of opportunity', may make it unfeasible to perform trials to test such regimens sequentially against a control treatment in a traditional two-arm parallel group design. We present an approach to trial design based on eliminating inferior contenders at an early stage, allowing through to a second stage only treatments that show a predefined degree of advantage against a control treatment. The first stage of testing utilizes a marker known to be a valid intermediate outcome measure or surrogate for the definitive outcome. The experimental arms are compared pairwise with control according to this intermediate outcome measure. Arms that survive the comparison enter a second stage of patient accrual culminating in comparisons against control on the outcome measure of primary interest. We show how the design may be realized in practice by considering hypothetically distinct trials at stages 1 and 2, each with their own operating characteristics. The overall operating characteristics are computed from the stage 1 and 2 size and power and the correlation between the treatment effects on the intermediate and primary outcome measures according to a bivariate Normal approximation. The correlation is estimated by bootstrapping individual patient data from previous trials. We illustrate the general approach in a design of a real trial of four new chemotherapy regimens for advanced ovarian cancer. The intermediate outcome measure is progression-free survival. An international randomized controlled trial using the new design is already under way.

Clinical Trials as Topic↗

PubMed2003

Assessing non-inferiority of a new treatment in a three-arm clinical trial including a placebo.

In non-inferiority trials, where non-inferiority of a new experimental drug compared to an active control has to be shown, it may be advisable to use an additional placebo group for internal validation if ethically justifiable. The focus of this paper is on such designs. Assuming normality and homogeneity of variances we will derive a statistical test procedure which turns out to be equivalent to the assessment based on Fieller's confidence interval. Based on the power function of this test, sample size calculations are carried out to achieve a given power. Additionally, the optimal allocation of the total sample size is derived. As an alternative to this parametric procedure, the bootstrap percentile interval is discussed and finally compared with Fieller's confidence interval in a study on mildly asthmatic patients.

Anti-Asthmatic Agents↗

PubMed2003

An investigation of error sources and their impact in estimating the time to the most recent ancestor of spatially and temporally distributed HIV sequences.

This is an investigation of significant error sources and their impact in estimating the time to the most recent common ancestor (MRCA) of spatially and temporally distributed human immunodeficiency virus (HIV) sequences. We simulate an HIV epidemic under a range of assumptions with known time to the MRCA (tMRCA). We then apply a range of baseline (known) evolutionary models to generate sequence data. We next estimate or assume one of several misspecified models and use the chosen model to estimate the time to the MRCA. Random effects and the extent of model misspecification determine the magnitude of error sources that could include: neglected heterogeneity in substitution rates across lineages and DNA sites; uncertainty in HIV isolation times; uncertain magnitude and type of population subdivision; uncertain impacts of host/viral transmission dynamics, and unavoidable model estimation errors. Our results suggest that confidence intervals will rarely have the nominal coverage probability for tMRCA. Neglected effects lead to errors that are unaccounted for in most analyses, resulting in optimistically narrow confidence intervals (CI). Using real HIV sequences having approximately known isolation times and locations, we present possible confidence intervals for several sets of assumptions. In general, we cannot be certain how much to broaden a stated confidence interval for tMRCA. However, we describe the impact of candidate error sources on CI width. We also determine which error sources have the most impact on CI width and demonstrate that the standard bootstrap method will underestimate the CI width.

Animals↗

PubMed2003

Selecting the best treatment in designed experiments.

A common question in biological experimentation is concerned with finding an optimal level for a treatment using data obtained from a designed experiment. For example, an experiment might concern a group of hyperactive adolescent males that have been grouped into blocks according to some relevant factors. Within each group the subjects are randomly assigned to several treatments for hyperactivity. An important aspect of the study would then be determining which of the treatment options is most effective in reducing hyperactivity in the subjects. Basing such a determination directly on the estimated treatment effects may be unreliable because of the inherent variability associated with the estimates. Other methods, such as multiple comparison procedures and best subset selection procedures can also be applied to this problem. Unfortunately, such procedures are often difficult to interpret and rely on assumptions that may not be appropriate for the experiment under consideration. In this paper we develop a method of assigning a confidence level to each treatment that measures how confident we are that each treatment is optimal. The method for assigning the confidence levels is based on a more general methodology developed for the problem of regions, where one assigns levels of confidence that an unknown parameter is within specified subsets of the parameter space. The actual computation of the confidence levels is based on the bootstrap. The method is applied to an example and is studied empirically.

Adolescent↗

PubMed2004

Bagging survival trees.

Predicted survival probability functions of censored event free survival are improved by bagging survival trees. We suggest a new method to aggregate survival trees in order to obtain better predictions for breast cancer and lymphoma patients. A set of survival trees based on B bootstrap samples is computed. We define the aggregated Kaplan-Meier curve of a new observation by the Kaplan-Meier curve of all observations identified by the B leaves containing the new observation. The integrated Brier score is used for the evaluation of predictive models. We analyse data of a large trial on node positive breast cancer patients conducted by the German Breast Cancer Study Group and a smaller 'pilot' study on diffuse large B-cell lymphoma, where prognostic factors are derived from microarray expression values. In addition, simulation experiments underline the predictive power of our proposal.

Breast Neoplasms↗