bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of empirical bayes inference to estimation of rate of change in the presence of informative right censoring
Authors: Mori Motomi , Woodworth George G. , Woolson Robert F.
Published: April 2007

We apply parametric empirical Bayes inference of Morris7 to the estimation of rate of change from incomplete longitudinal studies where the right censoring process is considered informative, that is, the length of time the subjects participate in the study is associated with level of the study variable. Ignoring such an association can result in a biased estimate of rate of change. The proposed method provides estimates of rate of change for individual subjects as well as for the entire group, adjusted for informative right censoring. The method is considered more robust than those based on a specific parametric model for the censoring distribution. Under non‐informative right censoring these estimators of slopes are equivalent to the Bayes estimators derived by Fearn.11 We illustrate the method with an example involving renal transplant data. We evaluate the method's performance through a simulation study.
Sample size requirement for repeated measurements in continuous data
Authors: Lui Kung‐Jong , Cumberland William G.
Published: April 2007

In this paper we extend Bloch's discussion on the usefulness and the limitations in the application of repeated measurements per subject in study designs. We derive general sample size formulae for any finite number of comparison groups to calculate the required number of subjects with repeated measurements, that do not have to be conditionally independent. For fixed total cost, we discuss the optimal sample allocation for repeated measurements needed to maximize the power and the underestimation when using Bloch's sample size formula if in the hypothesis testing procedure the variance parameters are unknown. We have also included a quantitative investigation of the effectiveness of taking repeated measurements per subject to reduced the required number of subjects for a given power at a given α‐level.
Monitoring clinical trials with a conditional probability stopping rule
Authors: Snapinn Steven M.
Published: April 2007

Conditional probability procedures offer a flexible means of performing sequential analysis of clinical trials. Since these procedures are not based on repeated significance tests, the number and schedule of the interim analyses is less important than with group sequential procedures. Their main disadvantage is that the magnitude of their effect on the significance level is difficult to assess. This paper describes a conditional probability procedure which attempts to maintain the overall significance level by balancing the probabilities of false early rejection and false early acceptance. Monte Carlo sampling results suggest that this procedure can achieve a large reduction in expected sample size without greatly affecting either the significance level or power of the trial.
A decision‐theoretic evaluation of early stopping rules
Authors: Heitjan Daniel F. , Houts Peter S. , Harvey Harold A.
Published: April 2007

We consider the decision‐theoretic evaluation of early stopping rules for clinical trials. We describe a hypothetical phase III, two‐arm trial with interim analysis, modelling it as a decision problem. We present methods for constructing a group‐sequential test that is optimal for a given utility and prior distribution, and for determining a utility and prior under which a given test is optimal. Using our methods, we construct optimal tests for utilities and priors representing a variety of perspectives: a view that seeks to maximize the long‐run response rate, a view that seeks to maximize the chance of a correct decision, and a personal view elicited from a medical oncologist. Characteristics of the optimal rules are sensitive to the input utilities and priors, and their critical values and sampling properties can differ markedly from those of group‐sequential tests. We also compute utility functions and priors under which some standard group‐sequential stopping rules are optimal. Our results suggest that the group‐sequential tests, considered as decision procedures, imply a symmetry in the decision problem that is inconsistent with the response‐rate perspective. We conclude that decision theory is a useful device for illuminating the sometimes conflicting goals of clinical research, and that the use of decision theory in designing clinical trials could lead to marked changes in statistical criteria for early termination.
Regression toward the mean in 2 × 2 crossover designs with baseline measurements
Authors: Grender Julie Myers , Johnson William D. , Elston Robert C.
Published: April 2007

Clinical trials often involve the study of patients whose values for some quantitative characteristic are in the extreme of the distribution for the normal population. Subsequent observation of the characteristic of interest will ordinarily tend to regress toward the mean of the distribution even in the absence of a treatment effect. We consider the impact of regression toward the mean in the analysis of data arising in 2 × 2 crossover trials with two baseline measurements. The usual summary statistics can be especially misleading in the presence of regression toward the mean.
Sample size requirements for stratified cluster randomization designs
Authors: Donner Allan
Published: April 2007

Sample size requirements are provided for designs of studies in which clusters are randomized within each of several strata, where cluster size itself may be a stratifying factor. The approach generalizes a formula derived by Woolson et al., which provides sample size requirements for the Cochran‐Mantel‐Haenszel statistic. Issues of data analysis are also discussed.
Designs and analysis of two‐stage studies
Authors: Zhao L. P. , Lipsitz S.
Published: April 2007

This paper concerns the design and analysis of two‐stage studies, where, at the first stage, the response and the exposure variables are available among a large group of subjects. The other covariables, however, are available in only a subset of the large group, obtained in a second‐stage sample. This paper introduces a class of twelve such two‐stage designs, including two‐stage case‐control and case‐cohort designs as special cases. In analysing such two‐stage data, one objective is to extract information about the relationship between the exposure variable and the response after controlling for other covariables. We discuss three statistical methods to analyse the data and report results of Monte Carlo simulation to study the efficiency of the three methods.
Analysing the relationship between change in a risk factor and risk of disease
Authors: Cain Kevin C. , Kronmal Richard A. , Kosinski Andrzej S.
Published: April 2007

There are numerous examples in the epidemiologic literature of analyses that relate the change in a risk factor, such as serum cholesterol, to the risk of an adverse outcome, such as heart disease. Many of these analyses fit some type of regression model (such as logistic regression or the Cox model for survival time data) that includes both the change in the risk factor and the baseline value as covariates. We show that this method of adjusting for the baseline level can produce misleading results. The problem occurs when the true value of the risk factor relates to the outcome, and the measured value differs from the true value due to measurement error. We may find the observed change in the risk factor significantly related to the outcome when there is in fact no relationship between the true change and the outcome. If the question of interest is whether a person who lowers his level of the risk factor by means of drugs or lifestyle changes will thereby reduce his risk of disease, then we should consider an association due solely to measurement error as spurious. We present a method that adjusts for the measurement error in a linear regression analysis and show that an analogous adjustment applies asymptotically to logistic regression. As in other errors‐in‐variables problems, this analysis depends on knowledge of the relative variances of the random variation, the true baseline value, and the true change. Since the magnitudes of these variances are usually unknown and sometimes unknowable (the distinction between true change and measurement error being ambiguous), we recommend a sensitivity analysis that examines how the analysis results depend on the assumptions concerning the variances. The commonly used analysis method corresponds to the extreme case in which there is no measurement error. We use data from the Framingham Study and simulations to illustrate these points.
Estimating the stage‐specific numbers of HIV infection using a markov model and back‐calculation
Authors: Longini Ira M. , Byers Robert H. , Hessol Nancy A. , Tan Wai Y.
Published: April 2007

The back‐calculation method has been used to estimate the number of HIV infections from AIDS incidence data in a particular population. We present an extension of back calculation that provides estimates of the numbers of HIV infectives in different stages of infection. We model the staging process with a timedependent Markov process that partitions the HIV infectious period into the following progressive stages and/or substages: stage 1, infected but antibody negative; substages 2–3; antibody positive but asymptomatic; substages 4–6, pre‐AIDS symptoms and/or abnormal haematologic indicator; stage 7, clinical AIDS. We also model an eighth stage, deceased due to AIDS. The model allows for time‐dependent treatment effects that slow the rate of progression in substages 4–7. We use the estimated AIDS incubation period distribution from the Markov model in back calculation from AIDS incidence data to estimate the total number of HIV infections and the parameters of the infection probability distribution. We then use these estimates in the Markov model to estimate the stage‐specific numbers of HIV infections over the course of the epidemic in the population under study. Example calculations employ data for the HIV epidemic in San Francisco City Clinic Cohort.
Estimation of direct formulation effect under log‐normal distribution in bioavailability/bioequivalence studies
Authors: Liu Jen‐Pei , Weng Chung‐Sing
Published: April 2007

This paper considers estimation of a measure of relative bioavailability of a test formulation to a reference formulation, on the original scale, under the assumption of a log‐normal distribution for the data from a 2 × 2 crossover bioavailability/bioequivalence study. We propose the minimum variance unbiased estimator which is equal to the maximum likelihood estimator adjusted for bias by a correction factor. We also derive the variance of the minimum variance unbiased estimator and its unbiased estimator. We derive the biases and mean square errors of the maximum likelihood estimator, the ratio of the least squares means, and the least squares mean of individual subject ratios, with respect to this measure, and compare them in a simulation study. Both theoretical and empirical results strongly suggest that one always consider the minimum variance unbiased estimator. A numerical example illustrates the proposed estimation procedure.
On the computation of likelihood ratio and score test based confidence intervals in generalized linear models
Authors: Alho Juha M.
Published: April 2007

Numerical procedures for calculating likelihood ratio test and score test based confidence intervals in generalized linear models are considered. Newton's method appears to have better convergence properties than the secant method in the likelihood ratio test case. However, the secant method may be easier to program for models with link functions that are not natural. Similarly, the secant method is easier to implement for the computation of score test based intervals. The practical implementation of the procedures in GLIM is illustrated.
Empirical bayes versus fully bayesian analysis of geographical variation in disease risk
Authors: Bernardinelli Luisa , Montomoli Cristina
Published: April 2007

This paper reviews methods for mapping geographical variation in disease incidence and mortality. Recent results in Bayesian hierarchical modelling of relative risk are discussed. Two approaches to relative risk estimation, along with the related computational procedures, are described and compared. The first is an empirical Bayes approach that uses a technique of penalized log‐likelihood maximization; the second approach is fully Bayesian, and uses an innovative stochastic simulation technique called the Gibbs sampler. We chose to map geographical variation in breast cancer and Hodgkin's disease mortality as observed in all the health care districts of Sardinia, to illustrate relevant problems, methods and techniques.
Analysis strategies for serial multivariate ultrasonographic data that are incomplete
Authors: Espeland Mark A. , Byington Robert P. , Hire Donald , Davis Vicki G. , Hartwell Tyler , Probstfield Jeffrey
Published: April 2007

Ultrasonographic measurement of intima‐media thicknesses in the carotid artery has emerged as an important non‐invasive means of assessing atherosclerosis, and has served to define primary outcome measures related to progression of arterial lesions in several large clinical trials and epidemiologic studies. It is characteristic that measurements often cannot be obtained from all sites during repeated examinations. This leads to incomplete multivariate serial data, for which the set and number of visualized sites may vary across time. We have contrasted several conditional and unconditional maximum likelihood analytical approaches, and have evaluated these with a simulation experiment based on characteristics of ultrasound measurements collected during the course of the Asymptomatic Carotid Artery Plaque Study. We examined analyses based on unweighted and generalized least squares regression in which we estimated cross‐sectional summary statistics using raw means, unconditional maximum likelihood estimates and full maximum likelihood estimates. Since the genesis of missing data is not fully clear, and since the approaches we examined are based, to some degree, on the assumption that data are missing at random, we also examined the relative impact of deviations from such an assumption on each of the approaches considered. We found that maximum likelihood based approaches increased the expected efficiency of the analysis of serial ultrasound data over ignoring missing data by up to 21 per cent.
Organization and analysis of safety data using a multivariate approach
Authors: Chuang‐Stein Christy , Mohberg Noel R. , Musselman David M.
Published: April 2007

The collection of safety data is an important part of clinical trials. These safety data are often described and reported in great detail with expenditure of substantial effort and energy. Because of the wide variety of data that require scrutiny from the safety perspective, however, statistical comparisons of the safety profiles of different treatments often lack focus and structure and result in situations where the comparisons for each individual item lack power and thus are inconclusive. In this paper, we propose to organize the safety data into a more manageable form by consolidating them into a number ofKclasses characterized by body systems and determined in conjunction with the underlying disease as well as the treatments involved. Within each class, we propose assignment to each patient of an overall intensity grade based on all relevant information. The consolidation of the safety data as proposed provides an informative summary for the safety profile of each treatment. The analysis of such organized data concentrates on comparison of the mean intensity grades for different treatments within theKclasses simultaneously with use of scores that reflect the acceptability of the various intensity levels to an individual. Furthermore, we demonstrate that the proposed multivariate comparison has much higher power than the univariate one to detect differences in certain cases. We provide examples to illustrate the proposed procedure.
Sixteen S‐squared over D‐squared: A relation for crude sample size estimates
Authors: Lehr Robert
Published: April 2007

I suggest for memorization an equation for calculating approximate sample size requirements intended only for a specific set of values (80 per cent power for a two‐tailed alpha = 0.05 test) which seems to occur often in biopharmaceutical research. After presenting the formula in terms of variance estimate s2 and effect size d, I derive a few alternative forms and then discuss the accuracy of the approximation and other properties as well as examples of its use.
Sample sizes for proportional hazards survival studies with arbitrary patient entry and loss to follow‐up distributions
Authors: Yateman Nigel A. , Skene Allan M.
Published: April 2007

In proportional hazards survival studies, power depends on the observed number of deaths,d*. For a given choice of survival, loss, and patient entry distributions, sample sizes can be determined by equatingd* to the expected number of deaths. Approximating the survival and loss distributions with piecewise exponential distributions, and patient entry with a piecewise linear distribution, significantly reduces the computational overhead, and the expected number of deaths can be evaluated routinely. The merits of this approach are illustrated by a clinical trial of chemotherapy for large bowel cancer.
Some large‐sample distribution‐free estimators and tests for multivariate partially incomplete data from two populations
Authors: Lachin John M.
Published: April 2007

The most common instance of multivariate observations is the case of repeated measures over time. The two most widely used methods for the analysis ofKrepeated measures for two groups are theKdegrees of freedom (d.f.)T2MANOVAF‐test and the within‐subjects 1 degree of freedom ANOVAF‐test. Both require complete samples from normally distributed populations. In this paper, I describe alternativeKand 1 d.f. distribution‐free procedures which allow for randomly missing observations. These include a large‐sample analysis of means, the Wei and Lachin multivariate Wilcoxon test with estimates of the Mann‐Whitney parameter, and a multivariate Hodges‐Lehmann location shift estimator based on the multivariateU‐statistic of Wei and Johnson. Each of these methods provides a distribution‐freeK‐variate estimate of the magnitude of group differences which can be used as the basis for an overall test of group differences. These tests include theKd.f. omnibusT2‐like test, 1 d.f. tests of restricted hypotheses, such as the Wei‐Lachin multivariate one‐sided test of stochastic ordering, and the test of general association based on a minimum variance generalized least squares (GLS) estimate of the average group difference. I then describe covariate stratified‐adjusted GLS estimates and tests of group differences. This approach also provides tests of homogeneity (interaction) for within‐subjects and between‐subjects effects. I illustrate these analyses with an analysis of repeated cholesterol measurements in two groups of patients, stratified by sex. Such analyses provide an overall distribution‐free summary estimate and test of the treatment effect obtained by combining the group differences over both time (repeated measures) and strata.
Using follow‐up data to avoid omitted variable bias: An application to cardiovascular epidemiology
Authors: Rehm J. , Arminger G. , Kohlmeier L.
Published: April 2007

Omitted variable bias is discussed in the context of linear models. It is shown that the effect of omitted variables can be controlled in linear models for metric dependent variables by using data from follow‐up studies. Two different models for analysing such data are proposed. In the first model the omitted variables are assumed to be uncorrelated with the explanatory variables in the model and to be constant over time. These assumptions lead to a special structure of the covariance matrix of the errors over time. Efficient estimation of the parameters in the linear model has to take this special covariance matrix of the errors into account by using appropriate generalized least squares or maximum likelihood methods. In the second model the omitted variables are assumed to be time constant. Additionally, they are allowed to be correlated with the explanatory variables, that is these variables are omitted confounders in the usual epidemiological sense. It is shown that even in this case the parameters of the linear model can be estimated consistently with ordinary least squares if a follow‐up study is available. The differences between the parameter estimates under the first and the second model may be used to construct a Hausman test for misspecification. The models, the estimation methods and the Hausman test are illustrated by the example that explores the determinants of serum cholesterol in German adoloscents of both sexes.
Using the virus challenge dose in the analysis of virus neutralization assays
Authors: Parker R. A. , Pallansch M. A.
Published: April 2007

We propose a new basis for adjusting the results of virus neutralization assays. These assays consist of two separate experiments performed in parallel: a virus titration experiment and a serum dilution assay. In the virus titration experiment, one estimates the amount of virus used in the assay (the virus challenge dose). In a typical virus neutralization assay, the virus challenge dose may range over an order of magnitude. In the serial dilution assay, one measures the serum neutralizing activity against a particular virus. Most standard methods use the virus titration results only to ensure that the overall experiment is acceptable; the specific results of the virus titration experiment are not used to adjust the estimate of serum neutralizing activity. Although adjustment based on calibration with reference sera could be done, this seldom occurs in practice. We use results from recent studies of the kinetics and stoichiometry of polio virus neutralization with monoclonal antibodies to develop a method to use results from the virus titration experiment to adjust the serum neutralizing activity directly. Our results also indicate that a simple ad hoc procedure can improve the accuracy of the estimated serum neutralizing activity.
Discussion of session 1: Clinical trials, survival analysis
Authors: Fisher Lloyd D.
Published: April 2007

The paper contains discussion of session 1 of the 1991 American Statistical Association meeting on longitudinal data analysis and subsequently submitted papers. Koch and colleagues present an application of weighted least squares to 24 hour manual blood pressure measurements. Wei reviews linear rank methods for censored survival data using the accelerated failure time model; newer testing methods are presented. The use of these approaches may depend upon the value over currently used methods; the answer is not clear. Schluchter presents a method for evaluating informatively censored longitudinal data. The approach may well be an improvement over currently published approaches; the problems addressed may be important in a minority of situations. Finally, the discussant emphasizes the need for progress in three more mundane but very important areas: (1) data base systems with syntax appropriate for longitudinal data analyses; (2) graphical methods; and (3) software, well documented and supported, to exploit the progress in longitudinal data analytic methods.
Multivariate methods for binary longitudinal data with heterogeneous correlation over time
Authors: Rosner B.
Published: April 2007

Clustered binary data occur frequently in biostatistical work. One particular application is in binary longitudinal data, where several visits are available for the same individual. Several approaches have been proposed for the analysis of clustered binary data. In Rosner, a polychotomous logistic regression model was proposed which is a generalization of the beta‐binomial distribution and allows for person‐ and visit‐specific covariates, while controlling for clustering effects. One assumption of this model is that all pairs of visits within an individual are equally correlated, which may be inappropriate if several visits are available over a long follow‐up period. In this paper, this approach is extended to allow for heterogeneous correlation over time. The total time period is divided into subintervals and a beta‐binomial mixture model is introduced to estimate odds ratios relating outcomes for pairs of visits both within a subinterval as well as in different subintervals. To include covariates, an extension of the polychotomous logistic regression model is proposed, which allows one to estimate effects of person‐, subinterval‐, and visit‐specific covariates, while controlling for clustering using the beta‐binomial mixture model. This model is applied to the analysis of respiratory symptom data in children collected over a 14‐year period in East Boston, MA, in relation to maternal and child smoking, where the unit is the child and symptom history is divided into early‐adolescent and late‐adolescent symptom experience.
Non‐linear models for the analysis of longitudinal data
Authors: Vonesh Edward F.
Published: April 2007

Given the importance of longitudinal studies in biomedical research, it is not surprising that considerable attention has been given to linear and generalized linear models for the analysis of longitudinal data. A great deal of attention has also been given to non‐linear models for repeated measurements, particularly in the field of pharmacokinetics. In this article, a brief overview of non‐linear models for the analysis of repeated measures is given. Particular emphasis is placed on mixed‐effects non‐linear models and on various estimation procedures proposed for such models. Several of these estimation procedures are compared via a simulation study. In addition, simulation is used to investigate the effects of model misspecification, particularly with respect to one's choice of random‐effects. A relatively straightforward measure useful in selecting an appropriate set of random effects is investigated and found to perform reasonably well.
Graphs and stochastic relaxation for hierarchical bayes modelling
Authors: Lange Nicholas
Published: April 2007

This expository paper describes two useful tools for the statistical analysis of processes that generate repeated measures and longitudinal data. The first tool is a graph for a visual description of dependency structures. The second tool is a stochastic relaxation method (‘Gibbs sampling’) for fitting hierarchical Bayes models. Graphs are concise and accessible summaries of stochastic models. Graphs aid communications between statistical and subject‐matter scientists, during which formulations of scientific questions are modified. An uncluttered picture of the dependency structure of a model augments effectively its corresponding formulaic description. Stochastic relaxation is a computationally intense method that allows experimentation with broader classes of models than were previously thought feasible because of analytic intractability. Stochastic relaxation is intuitive and easily described to non‐statisticians. Several sample graphs show how hierarchical Bayes models can use stochastic relaxation to obtain their fits. An example based on estimating drug shelf‐life demonstrates some uses of graphs and stochastic relaxation compared with several frequentist growth curve analyses that use restricted maximum likelihood and generalized estimating equations approaches.
A bootstrap resampling procedure for model building: Application to the cox regression model
Authors: Sauerbrei Willi , Schumacher Martin
Published: April 2007

A common problem in the statistical analysis of clinical studies is the selection of those variables in the framework of a regression model which might influence the outcome variable. Stepwise methods have been available for a long time, but as with many other possible strategies, there is a lot of criticism of their use. Investigations of the stability of a selected model are often called for, but usually are not carried out in a systematic way. Since analytical approaches are extremely difficult, data‐dependent methods might be an useful alternative. Based on a bootstrap resampling procedure, Chen and George investigated the stability of a stepwise selection procedure in the framework of the Cox proportional hazard regression model. We extend their proposal and develop a bootstrap‐model selection procedure, combining the bootstrap method with existing selection techniques such as stepwise methods. We illustrate the proposed strategy in the process of model building by using data from two cancer clinical trials featuring two different situations commonly arising in clinical research. In a brain tumour study the adjustment for covariates in an overall treatment comparison is of primary interest calling for the selection of even ‘mild’ effects. In a prostate cancer study we concentrate on the analysis of treatment‐covariate interactions demanding that only ‘strong’ effects should be selected. Both variants of the strategy will be demonstrated analysing the clinical trials with a Cox model, but they can be applied in other types of regression with obvious and straightforward modifications.
A comprehensive algorithm for determining whether a run‐in strategy will be a cost‐effective design modification in a randomized clinical trial
Authors: Schechtman Kenneth B. , Gordon Mae E.
Published: April 2007

In randomized clinical trials, poor compliance and treatment intolerance lead to reduced between‐group differences, increased sample size requirements, and increased cost. A run‐in strategy is intended to reduce these problems. In this paper, we develop a comprehensive set of measures specifically sensitive to the effect of a run‐in on cost and sample size requirements, both before and after randomization. Using these measures, we describe a step‐by‐step algorithm through which one can estimate the cost‐effectiveness of a potential run‐in. Because the cost‐effectiveness of a run‐in is partly mediated by its effect on sample size, we begin by discussing the likely impact of a planned run‐in on the required number of randomized, eligible, and screened subjects. Run‐in strategies are most likely to be cost‐effective when: (1) per patient costs during the post‐randomization as compared to the screening period are high; (2) poor compliance is associated with a substantial reduction in response to treatment; (3) the number of screened patients needed to identify a single eligible patient is small; (4) the run‐in is inexpensive; (5) for most patients, the run‐in compliance status is maintained following randomization and, most importantly, (6) many subjects excluded by the run‐in are treatment intolerant or non‐compliant to the extent that we expect little or no treatment response. Our analysis suggests that conditions for the cost‐effectiveness of run‐in strategies are stringent. In particular, if the only purpose of a run‐in is to exclude ordinary partial compliers, the run‐in will frequently add to the cost of the trial. Often, the cost‐effectiveness of a run‐in requires that one can identify and exclude a substantial number of treatment intolerant or otherwise unresponsive subjects.
A pocket‐calculator algorithm for the shapiro‐francia test for non‐normality: An application to medicine
Authors: Royston Patrick
Published: April 2007

An easy‐to‐calculate approximation to the Shapiro—Francia W' test and its P‐value is proposed. Its accuracy is sufficient for practical application in samples of size 5 or larger.
An evaluation of sexual behaviour change using statistical and cognitive models
Authors: Schnell Daniel J. , Galavotti Christine , O'reilly Kevin R.
Published: April 2007

We evaluate sexual behaviour change among homosexual men enrolled in the cohorts in four AIDS Community Demonstration Projects. Behaviour change is classified following the stages of behaviour change model and described using a Markov model. Predictors of behaviour change are identified and evaluated using logit models for correlated data. Sexual behaviour change within the cohort could be modelled as a first‐order Markov process. In addition, predictors suggested by models of health behaviour were correlated with particular patterns of sexual behaviour change. Our evaluation revealed a variety of patterns of sexual behaviour change in the cohorts and suggests multi‐faceted interventions for promotion of behaviour change.
Analysis of a measles epidemic
Authors: Allen L. J. , Lewis T. , Martin C. F. , Jones M. A. , Lo C. K. , Stamp M. , Mundel G. , Way A. B.
Published: April 2007

In January, February and March of 1989 an epidemic of rubeola occurred on the campus of Texas Tech University. A vaccination programme was initiated as soon as the epidemic was confirmed. Extensive case histories of all confirmed cases were collected by the Lubbock City Health Department and given an exhaustive statistical analysis by a group from the Department of Mathematics at Texas Tech University. The data and statistical analysis were used to formulate stochastic and deterministic models of the measles epidemic based on the standard SEIR model. The analysis and the simulations indicate that in order to prevent a measles outbreak on a university campus a high rate of immunity may be required (> 98 per cent). The assumptions in the models raise some interesting questions regarding social contacts which require further investigation.
Using autoregressive and random walk models to detect trends and shifts in unequally spaced tumour biomarker data
Authors: Schlain Brian R. , Lavin Philip T. , Hayden Cheryl L.
Published: April 2007

Continuous time autoregressive (CAR(1)) and random walk models of time series data are provided for detecting non‐random shifts and trends of tumour markers in breast cancer patients following resection for cure. The continuous time random walk model with observation error is extended to the case of multiple patient time series. These models can be used to monitor large numbers of patients with time series with few sampling events that are serially correlated and unequally spaced. Further, the methodologies can be used to recommend appropriate testing intervals. A Kalman filter recursive algorithm is used to calculate the likelihood functions arising from the CAR(1) and random walk models and to calculate recursive residuals, which are monitored by Shewhart—cusum schemes.
Improved imputation of non‐responses to mailback questionnaires
Authors: Drane J. Wanzer , Richter Donna , Stoskopf Carleen
Published: April 2007

Poor response rates, perhaps as low as 10 to 30 per cent, certainly bring into question the validity of any survey suffering such a malady. Repeated mailouts are capable of providing information on those persons who are resistant to responding. If one is willing to assume an exponential drop‐off in response rates, then imputation is possible for the entire group of non‐responders. Furthermore, a second exponential drop‐off in favourable (or non‐favourable) responses to particular items within the questionnaire leads to closed form estimates of population parameters and their associated standard errors. Three or more mailouts also provide a test of validity of the model assumed.
The effect of matching on the power of randomized community intervention studies
Authors: Martin Donald C. , Diehr Paula , Perrin Edward B. , Koepsell Thomas D.
Published: April 2007

Currently, there is considerable interest in studies that use the community as the experimental unit. Health promotion programmes are one example. Because such activities are expensive, the number of experimental units (communities) is usually very small. Investigators often match communities on demographic variables in order to improve the power of their studies. Matching is known to improve power in certain circumstances. However, we show here that if the number of communities is small, the matched design will probably have less power than the unmatched design. This is due primarily to the loss of degrees of freedom in the matched design, which outweighs the benefits of matching on any but the strongest correlates of changes in behaviour. In the community intervention situation, even small differences in sample size between the matched and unmatched analyses can have expensive consequences.
Stopping guidelines for clinical trials with multiple treatments
Authors: Hughes Michael D.
Published: April 2007

Stopping guidelines are widely used in long‐term clinical trials involving two treatments. These allow planned interim analyses of the accumulating data to be undertaken whilst preserving the type I error rate for the treatment comparison. Their philosophy is extended to the case of trials with multiple treatments so that at any interim analysis, treatments may be considered for dropping from the trial if they are significantly inferior to all treatments that will remain. The proposed guidelines are designed to preserve the error rate in determining that treatment or group of treatments which is, in reality, best. Using simulation studies, stopping guidelines developed for two‐arm trials are shown to be directly usable in multiple‐arm studies when the treatments studied are all experimental and so in direct competition. When one treatment is the standard of care, a modification gives a better ethical perspective by also permitting treatments to be dropped when they are deemed inferior to the standard. Results are presented for normally distributed responses in trials involving three or four treatments and using stopping boundaries of the form proposed by O'Brien and Fleming. In conclusion, I discuss some of the additional considerations that are important in employing stopping guidelines in trials with multiple treatments.
Construction of age‐related reference centiles using absolute residuals
Authors: Altman Douglas G.
Published: April 2007

This paper proposes a simple approach to the parametric derivation of age‐related reference ranges which avoids the creation of arbitrary age groups, copes easily with a non‐linear relation between variability and age, and is computationally simple. After the mean is modelled as a function of age, the age‐specific standard deviation is estimated by regressing the absolute residuals on age. The method assumes that the data are, or can be transformed to be, normal at each age, and uses the properties of the half normal distribution. An example is given using 450 measurements of fetal foot length.
A modelling approach to the analysis of menstrual diary data
Authors: Collett D. , Weerasooriya N.
Published: April 2007

In clinical trials to compare contraceptives, women are usually asked to record whether or not each day is a bleeding day over the duration of the trial. In this paper we describe how parametric models, which include terms corresponding to covariates recorded for each woman, can be used to analyse data on the occurrence of certain adverse events identified from the diary record. Linear logistic models are used to analyse the probability of prolonged bleeding or amenorrhoea, and log‐linear models are used to analyse the lengths of bleeding episodes. In both cases variation between women is allowed for by including a random effect in the model. The application of our methods is illustrated using a data base made available by the World Health Organization.
Cox regression models for quality adjusted survival analysis
Authors: Cole Bernard F. , Gelber Richard D. , Goldhirsch Aron
Published: April 2007

We develop a method for incorporating covariates as regressors in a quality adjusted survival analysis (Q‐TWiST) using Cox's proportional hazards model. The standard Q‐TWiST method assumes that patients progress through a series of health states which differ in quality of life. The Kaplan—Meier product limit method is used to estimate the mean duration of each state by estimating the survival curves for the health state transition times. These estimates provide the basis for quality adjusted survival analysis. In this paper, the survival curves are modelled using Cox's proportional hazards regression. Quality adjusted survival is estimated given sets of covariate values, allowing one to profile patients. The results are useful for investigating how prognostic factors affect treatment benefits in terms of quality of life. We give a brief review of the standard Q‐TWiST method and illustrate the extended methodology with an example from the International Breast Cancer Study Group Trial V comparing short duration versus long duration chemotherapy in the treatment of node‐positive breast cancer.
Robust inference for multivariate survival data
Authors: Segal Mark R. , Neuhaus John M.
Published: April 2007

Multivariate survival data arise when an individual records multiple survival events or when individuals recording single survival events are grouped into clusters. In this paper we propose a new method for the analysis of multivariate survival data. The technique is a synthesis of the Poisson regression formulation for univariate censored survival analysis and the generalized estimating equation approach for obtaining valid variance estimates for generalized linear models in the presence of clustering. When the survival data are clustered, combining the methods provides not only valid estimates for the variances of regression parameters but also estimates of the dependence between survival times. The approach entails specifying parametric models for the marginal hazards and a dependence structure, but does not require specification of the joint multivariate survival distribution. Properties of the methodology are investigated by simulation and through an illustrative example.
Tests for qualitative treatment‐by‐centre interaction using a ‘pushback’ procedure
Authors: Ciminera Joseph L. , Heyse Joseph F. , Nguyen Ha H. , Tukey John W.
Published: April 2007

In multicentre clinical trials using a common protocol, the centres are usually regarded as being a fixed factor, thus allowing any treatment‐by‐centre interaction to be omitted from the error term for the effect of treatment. However, we feel it necessary to use the treatment‐by‐centre interaction as the error term if there is substantial evidence that the interaction with centres is qualitative instead of quantitative. To make allowance for the estimated uncertainties of the centre means, we propose choosing a reference value (for example, the median of the ordered array of centre means) and converting the individual centre results into standardized deviations from the reference value. The deviations are then reordered, and the results ‘pushed back’ by amounts appropriate for the corresponding order statistics in a sample from the relevant distribution. The pushed‐back standardized deviations are then restored to the original scale. The appearance of opposite signs among the destandardized values for the various centres is then taken as ‘substantial evidence’ of qualitative interaction. Procedures are presented using, in any combination: (i) Gaussian, or Student's t‐distribution; (ii) order‐statistic medians or outward 90 per cent points of the corresponding order statistic distributions; (iii) pooling or grouping and pooling the internally estimated standard deviations of the centre means. The use of the least conservative combination — Student's t, outward 90 per cent points, grouping and pooling — is recommended.
Evaluation of multicentre clinical trial data using adaptations of the mosteller‐tukey procedure
Authors: Ciminera Joseph L. , Heyse Joseph F. , Nguyen Ha H. , Tukey John W.
Published: April 2007

Two procedures, based on proposals discussed by Mosteller and Tukey, are described for obtaining a combined estimate of the difference between two treatment means and its confidence interval from multicentre clinical trial data. Both procedures provide estimates in the possible presence of heteroscedasticity. The first procedure is designated the primary analysis for efficacy assessment. It omits treatment‐by‐centre interaction from the error term for treatment, unless there is substantial evidence of qualitative interaction (Ciminera et al.) or other special circumstances. The second procedure is the primary analysis whenever there is substantial evidence of qualitative interaction, and can be used whenever there are other reasons to make an analysis allowing for interaction.
Visual and statistical assessment of spatial clustering in mapped data
Authors: Walter S. D.
Published: April 2007

Maps have seen increasing use to examine regional variation in health, but there has been little research on the visual perception of spatial patterns in mapped data. Theories of graphical perception suggest that the interpretation of maps is complex relative to other types of graphical material. This paper describes an experiment in which observers assessed a series of maps with respect to their amount of clustering. Maps with various types of spatial pattern were visually distinguishable; comparisons between variants of the same map, however, using different shading and plotting symbols indicated that the method of data representation also had a strong effect on visual perception. There was some evidence for a learning effect in complex maps. The relationship between the visual assessments and a statistical measure of spatial autocorrelation was significant but imperfect.
Combining independent studies of a diagnostic test into a summary roc curve: Data‐analytic approaches and some additional considerations
Authors: Moses Lincoln E. , Shapiro David , Littenberg Benjamin
Published: April 2007

We consider how to combine several independent studies of the same diagnostic test, where each study reports an estimated false positive rate )FPR( and an estimated true positive rate )TPR(. We propose constructing a summary receiver operating characteristic )ROC( curve by the following steps. )i( Convert each FPR to its logistic transform U and each TPR to its logistic transform V after increasing each observed frequency by adding 1/2. )ii( For each study calculate D = V – U, which is the log odds ratio of TPR and FPR, and S = V + U, an implied function of test threshold; then plot each study's point )Si, Di(. )iii( Fit a robust‐resistant regression line to these points )or an equally weighted least‐squares regression line(, with V – U as the dependent variable. )iv( Back‐transform the line to ROC space. To avoid model‐dependent extrapolation from irrelevant regions of ROC space we propose defining a priori a value of FPR so large that the test simply would not be used at that FPR, and a value of TPR so low that the test would not be used at that TPR. Then )a( only data points lying in the thus defined north‐west rectangle of the unit square are used in the data analysis, and )b( the estimated summary ROC is depicted only within that subregion of the unit square. We illustrate the methods using simulated and real data sets, and we point to ways of comparing different tests and of taking into account the effects of covariates.
How to establish equivalence when data are censored: A randomized trial of treatments for B non‐Hodgkin lymphoma
Authors: Com‐Nougue C. , Rodary C. , Patte C.
Published: April 2007

Interest in equivalence trials has been increasing for many years, though the methodology which has been developed for such trials is mainly for uncensored data. In cancer research we are more often concerned with survival. In an efficacy trial, the null hypothesis specifies equality of the two survival distributions, but in an equivalence trial, a null hypothesis of inequivalenceH0has to be tested. The usual logrank test has to be modified to test whether the true valuerof the ratio of hazard rates in two treatment groups is at least equal to a limit valuer0. If prognostic factors have to be taken into account, the Cox model provides tests ofH0, and a useful confidence interval for the adjusted relative risk derived from the regression parameter for the treatment indicator. An equivalence trial of maintenance therapy was carried out in children with B non‐Hodgkin lymphoma, and serves as an illustration.