bluuebunny/crossref_metadata_2025 huggingface dataset:
Interim analyses in clinical trials: Classical vs. bayesian approaches
Authors: Berry Donald A.
Published: April 2007

This paper concerns interim analysis in clinical trials involving two treatments from the points of view of both classical and Bayesian inference. I criticize classical hypothesis testing in this setting and describe and recommend a Bayesian approach in which sampling stops when the probability that one treatment is the better exceeds a specified value. I consider application to normal sampling analysed in stages and evaluate the gain in average sample number as a function of the number of interim analyses.
On tests for equality of predictive values fortdiagnostic procedures
Authors: Bennett B. M.
Published: April 2007

This paper concerns comparisons of the efficiency of several diagnostic tests, as characterized by the measures of sensitivity (ξ), specificity (η) and predictive value (ρ). We show that hypotheses concerning the equality of predictive values relate only to hypotheses concerning ξ and η and that we can test these by approximate χ2statistics. Data for the cases of t = 2 or 3 diagnostic tests illustrate the method.
Measures of explained variation for survival data
Authors: Korn Edward L. , Simon Richard
Published: April 2007

The predictive power of a set of prognostic variables in a survival time model is a concept distinct from the statistical significance of the variables or the adequacy of the model fit. In this paper we discuss the importance of quantifying the predictive power of a prognostic model, and suggest measures of explained variation as a possible quantification. The important features of our approach are that (1) the measures are completely model‐based; (2) a specification of the time range of interest is easily incorporated; and (3) the null models used for comparison are derived as mixtures of the predicted distributions.
Further studies in the variability of pock counts
Authors: Breslow Norman
Published: April 2007

The problem of estimating viral activity from pock counts that exhibit a substantial degree of overdispersion is revisited from the viewpoint of quasilikelihood with unknown parameters in the variance function. Score statistics are developed for tests and interval estimates of both mean and variance parameters. These yield somewhat different conclusions than do methods based exclusively on point estimates and standard errors, especially for the variance parameters. A Monte Carlo study confirms that, in the absence of strong prior information about the shape of the error distribution, inferences on variances are highly unstable in small to moderate samples.
Repeated measurements: What is measured and what repeats?
Authors: Finney David J.
Published: April 2007

This paper expresses a personal view of experiments involving repeated measurements; it attempts to classify types of experiment and approaches to statistical analysis: no novel procedures are proposed, only a systematic outlook on objectives and methods.
Estimation issues in clinical trials and overviews
Authors: Pocock Stuart J. , Hughes Michael D.
Published: April 2007

There is a general move towards greater emphasis on point and interval estimates of treatment effect in reporting of clinical trials, so that significance testing plays a lesser role. In this article we examine a number of issues which affect the use and interpretation of conventional estimation methods. Should we accept or avoid the stereotypes of 95 per cent confidence? Should the abstract of a trial report include confidence intervals for major endpoints? Are frequentist confidence intervals being interpreted correctly, and should Bayesian probability intervals be more widely used in trial reports? Does the timing of publication, such as early stopping because of a large observed treatment difference, lead to exaggerated point and interval estimates? How can we produce realistic estimates from subgroup analyses? Is publication bias seriously affecting our ability to obtain unbiased estimates? Is the emphasis on estimation methods a powerful tool for encouraging larger sample sizes? Can we resolve the controversy concerning fixed or random effects models for estimation in overviews of related trials? Our arguments are illustrated by results from recent trials in cardiovascular disease.
The design of case‐control studies: The effect of confounding on sample size requirements
Authors: Drescher Karsten , Timm Jürgen , Jöckel Karl‐Heinz
Published: April 2007

This paper considers the extent to which confounding effects of covariates, which are not controlled for by matching in the design, may influence the sample size necessary for case‐control studies. The quantitative calculations are performed for an age‐matched case‐control study on lung cancer and air pollution, and are based on different evaluation methods. For illustrative purposes attention is confined to a dichotomous risk factor and a single dichotomous covariate. By using the numerical values of a pilot study investigating lung cancer and air pollution, it turns out that the sample size required for detecting a relative risk as close as 1.15 to 1 is only slightly influenced by the strength of the association between confounder and risk factor for reasonable variations around our empirical values. On the other hand, sample size considerably increases with increasing relative risk of a confounder even when the association remains small. The sample size required for an individually matched analysis practically equals that for an age‐stratified analysis when the relative risk of the covariate is one. With a relative risk greater than one, however, the size for a matched analysis exceeds that for a stratified analysis and the ratio between them increases with increasing relative risk.
Efficient evaluation of treatment effects in the presence of missing covariate values
Authors: Schemper Michael , Smith Terry L.
Published: April 2007

In clinical trials, treatment comparisons are often performed by models that incorporate important prognostic factors. Since these models require complete covariate information on all patients, statisticians frequently resort to complete case analysis or to omission of an important covariate. A probability imputation technique (PIT) is proposed that involves substituting conditional probabilities for missing covariate values when the covariate is qualitative. Simulation results are presented which demonstrate that the method neither violates the size of the treatment test nor introduces additional bias for the estimation of the treatment effect. It allows use of standard software. A clinical trial of breast cancer treatment, in which an important covariate was partly missing, was analysed by Cox's model. The use of PIT resulted in smaller observed error probability compared with case deletion, and sensitivity analysis supported these results.
A Markovian model for comparing incidences of side effects
Authors: Bristol David R. , Patel H. I.
Published: April 2007

For clinical trials that entail observations at successive visits for the occurrence of a side effect, this paper considers a likelihood‐based method to compare side effect incidence rates. The method, which employs the assumption of a Markov chain of order one for the vectors of binary responses, handles missing data due to premature withdrawals. An actual numerical example and a simulated example illustrate the technique.
More powerful procedures for multiple significance testing
Authors: Hochberg Yosef , Benjamini Yoav
Published: April 2007

The problem of multiple comparisons is discussed in the context of medical research. The need for more powerful procedures than classical multiple comparison procedures is indicated. To this end some new, general and simple procedures are discussed and demonstrated by two examples from the medical literature: the neuropsychologic effects of unidentified childhood exposure to lead, and the sleep patterns of sober chronic alcoholics.
Early methodological developments for clinical trials at the national heart, lung and blood institute
Authors: Halperin Max , Demets David L. , Ware James H.
Published: April 2007

The National Heart Institute, now known as the National Heart, Lung and Blood Institute (NHLBI), initiated its first multicentre randomized clinical trials of rheumatic fever and rheumatic heart disease in 1951. The modern era of multicentre trials began, however, when the Coronary Drug Project was initiated in the 1960s. This trial and subsequent NHLBI trials stimulated a wide variety of research on clinical trial methodology. This paper reviews early methodologic developments in four areas. First, an organizational structure for multicentre clinical trials was developed and codified in the ‘Greenberg Report’ in 1967. Second, design considerations related to patient risk, non‐compliance, a lag in treatment effect, and changing risk were explored. The ‘intention‐to‐treat’; principle was implicit in these investigations. Thirdly, the concept of periodic review of accumulating data, recommended in the Greenberg report, stimulated research on methods for sequential analysis. Three statistical approaches were developed and investigation of their statistical properties continues today. These approaches are usually described as group sequential, stochastic curtailment, and Bayesian methods. Finally, comparison of treatments in longitudinal studies has been an increasing part of NHLBI research and methods have been developed for design and analysis of longitudinal studies.
Estimating benefits of screening from observational cohort studies
Authors: Flanders W. Dana , Longini Ira M.
Published: April 2007

Analysis and interpretation of observational studies of screening effectiveness is difficult because several biases threaten validity, including the structural healthy screenee bias, length bias, and effects of lead time. Although methods for the analysis of observational studies of screening effectiveness have been proposed, most have limitations such as incomplete control of length bias, or a heavy reliance on distributional assumptions. In this report we present a method for the analysis of observational cohort studies of screening effectiveness. Although developed independently and formulated specifically for estimating benefits of screening, our approach is implied by a more general approach developed previously by Robins. Our approach, in contrast to other available methods, avoids the healthy screenee bias, and length and lead time bias, and allows an empirical approach to analysis that need not depend highly on distributional assumptions. We illustrate application of the approach with analysis of published data from a study of breast cancer screening.
The use of logit models to investigate social and biological factors in infant mortality. V: A multilogit analysis of stillbirths, neonatal and post‐neonatal mortality
Authors: Murrells T. J. , Smith T. M. F. , Machin D.
Published: April 2007

Infant mortality data for England and Wales, cross classified by mother's age, parity and social class were published for 1949/50 and 1975. Previous analyses of these data have been based on graphical, tabular and logit models of stillbirths, neonatal and post‐neonatal deaths separately. This paper summarizes the overall changes in infant mortality using a multilogit model. The model selected is illustrated by appropriate graphical presentations.
Proportion cured and mean log survival time as functions of tumour size
Authors: Gamel John W. , McLean Ian W. , Rosenberg Saul H.
Published: April 2007

We obtained maximum likelihood estimates (MLEs) of the proportion cured πcand mean log survival time μtfor a sample of 4355 patients with intraocular melanoma whose survival times subsequent to treatment were assumed to follow a log‐normal distribution. Following stratification by tumour size, MLEs of πcand μtderived for each stratum correlate inversely with tumour size. We then expressed πcand μtas continuous functions of tumour size and calculated MLEs for the parameters of these functions from the entire sample. This investigation documents for ocular melanoma a significant relationship of tumour size to both cured fraction and mean log survival time.
Practical bayesian analysis of a simple logistic regression: Predicting corneal transplants
Authors: O'Hagan A. , Woodward E. G. , Moodaley L. C.
Published: April 2007

The Bayesian analysis of a logistic regression model is described using an example of predicting the need for a corneal transplant in keratoconus. Controversy over the use of subjective prior information in Bayesian methods is avoided by a formulation representing negligible prior information. Simple computational procedures are described, and it is argued that the results are more accurate, clearer and make fuller use of the information contained in the data. Analysis of more complex models is considered. In particular, it is argued that classical methods as implemented in the computer package GLIM can be used as approximations to Bayesian methods, particularly at the initial stage of model selection.
Estimation of the design effect in community intervention studies
Authors: Mickey Ruth M. , Goodwin Gregory D. , Costanza Michael C.
Published: April 2007

This paper considers the estimation of the variance of a mortality rate in community intervention studies with little or no replication of intervention regimens. Our approach in estimation of this cluster sampling variance is to determine the variance for simple random sampling and multiply it by a design effect which we calculate with use of information obtained from other sources. When the county is the unit of randomization and the outcome is mortality, we calculate the design effect as the ratio of the age adjusted mortality rates for single stage cluster sampling relative to simple random sampling; we use information from all counties in a state in the calculations. We apply this approach empirically for breast cancer mortality. We found that these design effects were dependent on length of time for accumulation of deaths (1.1 for one year up to 3.5 for eight years) and were quite consistent for the three states and nine years considered in the investigation. We present a model that accounts for the time dependence of the design effect and we show it provides a good representation of the observed relationship.
The effect of variable infectivity on the risk of HIV infection
Authors: Eisenberg Bennett
Published: April 2007

This paper analyses the risk that an individual contracts the AIDS virus in terms of the number of sexual contacts and the number of different partners. It considers the effect of the variability of susceptibility and infectiousness on the evaluation of this risk. In particular, it shows why this variability leads to a greater risk from multiple partners than previously thought.
Some methods of combining class information in multivariate normal discrimination for the classification of human chromosomes
Authors: Kirby S. P. J. , Theobald C. M. , Piper J. , Carothers A. D.
Published: April 2007

We consider the use of discriminant analysis based on an assumption of multivariate Normality for allocating human chromosomes in an automated system. In this context, the assumptions which might be made about the covariance matrices for the different chromosome classes have important implications for the error rate of the system and the time required to allocate a chromosome. Linear discriminant functions based on the assumption of a common covariance matrix for all classes are fast but sometimes give bigger error rates than the assumption of a separate covariance matrix for each class. The latter assumption requires many more calculations to evaluate the associated quadratic discriminant functions. However, it is possible to assume that the covariance matrices for the different classes are, in various senses, similar to one another in order to derive other methods of combining class information on variability. These methods are here incorporated in the estimative maximum‐likelihood approach to discrimination. The methods considered lead to machine classification times of human chromosomes intermediate between those for the assumptions of a common or unrelated covariance matrices. They also require the simultaneous estimation of fewer parameters than the use of a separate covariance matrix for each chromosome class. The methods are illustrated by three data sets of very different quality. Graphs of estimated error rate against classification time show that some of these ways of combining class information can be useful in the trade‐off of error rate against time.
Statistical methods to adjust for date and age misreporting to improve estimates of vital rates in Pakistan
Authors: Pullum Thomas W.
Published: April 2007

Misreporting of dates and ages poses serious difficulties for the estimation of the age distribution and birth and death rates in many developing countries. The pervasiveness of these problems is illustrated with data from a well‐designed on‐going survey in Pakistan, the Pakistan Demographic Survey. Methods for reconciling discrepancies, based on the assumptions of constant misreporting and survivorship patterns, are presented. The reasoning behind these methods could be applied much more generally. Research into the cultural interpretations of age and dates, and the nature of possible biases, is called for.
Coping with extra poisson variability in the analysis of factors influencing vaginal ring expulsions
Authors: Campbell M. J. , Machin D. , D'Arcangues C.
Published: April 2007

The vaginal ring is one method of contraception currently under investigation and development by the Human Reproduction Programme of WHO. One factor that reduces its acceptability is that some women experience involuntary expulsions of the ring. WHO have collected prospective data on 1005 women from 19 centres worldwide to investigate various aspects of ring use including factors that might affect expulsions. For each subject the data include number of expulsions, age, parity, ponderal index, number of days of ring use and health care centre. To model the factors influencing expulsion, the number of expulsions was first considered as a Poisson variate with mean directly proportional to the log of the duration of ring use. Such a model gave a poor description of the data and it appeared that the number of expulsions was considerably over‐dispersed for an assumed Poisson variate. This paper examines a variety of strategies for coping with the resulting lack of fit of the model. It turns out that a truncated Poisson model gives a better description of the expulsion data and that health care centre and parity influence the rates.
A note on the analysis of titration studies
Authors: Chuang‐Stein Christy , Shih Weichung Joseph
Published: April 2007

We propose a method to incorporate all types of dropouts in the evaluation of an intervention based on binary data from a titration study. The proposed procedure does not require that the dropouts occur randomly, but instead examines each outcome individually. Our procedure has a built‐in penalty factor in the estimation process that determines the amount of penalty on efficacy parameters due to efficacy‐related dropouts. We also propose a method to estimate the variances associated with the estimates. The results have use in exploration of a potential dose‐response relationship or to answer questions pertinent for phase III studies. We use data from a phase III antihypertension study to illustrate the procedure.
Alternative parameterization of polychotomous models: Theory and application to matched case‐ontrol studies
Authors: Becher Heiko
Published: April 2007

A method is proposed for transforming a class of models having an outcome variable with more than two levels into an equivalent binary model. The polychotomous logistic model is used to demonstrate the method. The equivalency to a simple logistic regression model after some data transformation (augmentation) is shown. The method is applied to the data from two case‐ontrol studies each with two control groups, and further applications are indicated.
Are ordinal models useful for classification?
Authors: Campbell M. Karen , Donner Allan , Webster Karen M.
Published: April 2007

There is recent interest in classification procedures intended for use only when the response is ordinal. Ordinal response, however, is evident in the parameters estimated by either multinomial logistic or normal discriminant analyses, both of which classify either ordinal or non‐ordinal responses. Further, there may be harm in applying ordinal models inappropriately and ample opportunity to assume mistakenly ordinality in real data sets. Therefore, it becomes important to ascertain whether there is benefit obtained in the appropriate application of ordinal models. This paper presents the results of a simulation study designed to compare classification accuracy of various models. We show that ordinal models classify less accurately than the multinomial logistic and normal discriminant procedures under a variety of circumstances. Until further studies become available, we presently conclude that ordinal models confer no advantage when the main purpose of the analysis is classification.
Modelling length bias in a longitudinally‐linked record system of HIV cases
Authors: Nedelman Jerry , Burns Alice , Cleary Joan , Gordon Dan , Vernon Philip , Lawrence Charles E.
Published: April 2007

We compare numbers of hospital admissions for intravenous drug using (IVDU) HIV patients and other HIV patients in acute‐are facilities in New York State. Data consist of routinely collected hospital‐discharge reports from New York's Statewide Planning and Research Cooperative System, linked into longitudinal case histories. Because recognition of an IVDU depends on an opioid diagnosis on any record in the case history, the observed distribution of the number of admissions per case for recognized IVDU's is biased towards greater numbers of admissions. We develop and apply a model to overcome this biasing. Our findings reveal that the mean numbers of admissions for the two groups differ significantly, but less so than without recognition of the length biasing.
The problem of therapeutic equivalence with paired qualitative data: An example from a clinical trial using haemophiliacs with an inhibitor to factor VIII
Authors: Lee Martin L. , Lusher Jeanne M.
Published: April 2007

The problem of demonstrating the equivalence of two treatments or drugs occurs fairly frequently in medicine, but is quite often misformulated. The common error is to assume equivalence is demonstrated if the usual null hypothesis of no difference is not rejected, which ignores the potential of a substantial β‐error. We describe here two procedures for testing equivalence when the data are paired and dichotomous, and provide sample size formulas. We give an example based on a clinical trial of haemophiliacs with inhibitor to Factor VIII.
Confidence intervals for weighted sums of poisson parameters
Authors: Dobson Annette J. , Kuulasmaa Kari , Eberle Ernst , Scherer Josef
Published: April 2007

Directly standardized mortality rates are examples of weighted sums of Poisson rate parameters. If the numbers of events are large then normal approximations can be used to calculate confidence intervals, but these are inadequate if the numbers are small. We present a method for obtaining approximate confidence limits for the weighted sum of Poisson parameters as linear functions of the confidence limits for a single Poisson parameter, the unweighted sum. The location and length of the proposed interval depend on the method used to obtain confidence limits for the single parameter. Therefore several methods for obtaining confidence intervals for a single Poisson parameter are compared. For single parameters and for weighted sums of parameters, simulation suggests that the coverage of the proposed intervals is close to the nominal confidence levels. The method is illustrated using data on rates of myocardial infarction obtained as part of the WHO MONICA Project in Augsburg, Federal Republic of Germany.
Practice databases and their uses in clinical research
Authors: Tierney William M. , McDonald Clement J.
Published: April 2007

A few large clinical information databases have been established within larger medical information systems. Although they are smaller than claims databases, these clinical databases offer several advantages: accurate and timely data, rich clinical detail, and continuous parameters (for example, vital signs and laboratory results). However, the nature of the data vary considerably, which affects the kinds of secondary analyses that can be performed. These databases have been used to investigate clinical epidemiology, risk assessment, post‐marketing surveillance of drugs, practice variation, resource use, quality assurance, and decision analysis. In addition, practice databases can be used to identify subjects for prospective studies. Further methodologic developments are necessary to deal with the prevalent problems of missing data and various forms of bias if such databases are to grow and contribute valuable clinical information.
Using a claims database to investigate drug‐induced Stevens‐Johnson syndrome
Authors: Strom Brian L. , Carson Jeffrey L. , Halpern Allan C. , Schinnar Rita , Snyder Ellen Sim , Stolley Paul D. , Shaw Michele , Tilson Hugh H. , Joseph Michael , Dai Wanju S. , Chen Diane , Stern Robert S. , Bergman Ulf , Lundin Frank
Published: April 2007

In order to explore a priori hypotheses about drug‐induced Stevens‐Johnson Syndrome (SJS), a case‐ontrol study was initiated using data from COMPASSR, a computerized data base consisting of Medicaid claims data. The records of 3.8 million patients in five U.S. states were searched to identify patients with an inpatient diagnosis of ICD‐9‐M code 695.1 (erythema multiforme‐EM). Out of the total of 367 cases that were identified, primary medical records for 249 were sought and 128 (51.4 per cent) of these were obtained. The remainder could not be obtained because: in 36 (29.8 per cent) the hospital refused to provide medical records; in 33 (27.3 per cent) there were transcription errors; in 20 (16.5 per cent) the state could not translate the identification number, primarily because the patients lost Medicaid eligibility too long before our request; in 27 (22.3 per cent) the hospital could not locate the patient's record; and in 5 (4.1 per cent) there were other reasons. Of those with a medical record, 121 (94.5 per cent) had a skin diagnosis and 109 (85.2 per cent) had a diagnosis compatible with ICD‐9‐CM code 695.1 specified on their discharge summary. However, in 35 (27.3 per cent) an expert reviewer felt that the discharge diagnosis was incorrect. In 50 (39 per cent) the computer diagnosis was incorrect. Only 19 (14.8 per cent) were judged by the expert reviewer to truly have Stevens‐Johnson Syndrome, and an additional 37 (28.9 per cent) were judged to have erythema multiforme minor. Thus, the computerized diagnosis agreed very well with the diagnoses specified on the discharge summary. However, EM is frequently misdiagnosed, ICD‐9‐CM code 695.1 contains multiple other diagnoses which are not EM, and much of hospitalized EM is EM minor. Thus, studies of SJS cannot be performed except in patients whose medical records are available.
Channeling bias in the interpretation of drug effects
Authors: Petri H. , Urquhart J.
Published: April 2007

Channeling is a form of allocation bias, where drugs with similar therapeutic indications are prescribed to groups of patients with prognostic differences. Claimed advantages of a new drug may channel it to patients with special pre‐existing morbidity, with the consequence that disease states can be incorrectly attributed to use of the drug. For the study of adverse drug reactions, large databases supply information on comedication and morbidity of patients. For diseases with a stepped‐are approach, the drug history of patients, as available from some databases, can show channeling of drugs to patients with markers of relatively severe disease.
Multiple imputation in health‐are databases: An overview and some applications
Authors: Rubin Donald B. , Schenker Nathaniel
Published: April 2007

Multiple imputation for non‐response replaces each missing value by two or more plausible values. The values can be chosen to represent both uncertainty about the reasons for non‐response and uncertainty about which values to impute assuming the reasons for non‐response are known. This paper provides an overview of methods for creating and analysing multiply‐imputed data sets, and illustrates the dramatic improvements possible when using multiple rather than single imputation. A major application of multiple imputation to public‐use files from the 1970 census is discussed, and several exploratory studies related to health care that have used multiple imputation are described.
Variance components and their implications for statistical information in medical data
Authors: Orav E. J. , Louis T. A. , Palmer R. H. , Wright E. A.
Published: April 2007

We discuss general issues concerning the design and analysis of medical experiments involving repeated measures or hierarchical groupings of subjects within larger study units. Depending on the types of questions being investigated, the correlations induced by clustering can have dramatic impact on the effective sample size. The unique aspects of such experiments must be accounted for during analysis and during interpretation of the results. We illustrate these issues by using a variance components model to investigate the role of leadership in medical practice.
The effects of transformations and preliminary tests for non‐linearity in regression
Authors: Grambsch Patricia M. , O'Brien Peter C.
Published: April 2007

Non‐linear relationships between two variables are often detected as a result of a preliminary statistical test for linearity. Common approaches to dealing with non‐linearity are to (a) make a linearizing transformation in the independent variable or (b) fit a relationship that is non‐linear in the independent variable, such as including a quadratic term. With either approach, the resulting test for association between the two variables can have an inflated type I error. We consider testing the significance of the quadratic term in a quadratic model as a preliminary test for non‐linearity. Using simulation experiments and asymptotic arguments, we quantify the type I error inflation and suggest simple modifications of standard practice to protect the size of the type I error. In the case of quadratic regression, the type I error will be increased by roughly 50 per cent. The simple strategy of appropriately correcting the α‐level is shown to have minimal loss of power if the relationship is truly linear. In the case of a linearizing transformation, the impact on the type I error will depend on the values of the independent variable and on the set of potential linearizing transformations considered. Simulation results suggest that a procedure which adjusts the test statistic according to the results of the preliminary test may offer adequate protection.
Comparison of different maximum likelihood estimators in a small sample logistic regression with two independent binary variables
Authors: Whaley Fredrick S.
Published: April 2007

In order to examine the bias of the estimate of the log odds ratio in a 2 × 2 contingency table, Walter computed the entire distribution of the estimated log odds ratio using various small sample sizes. This is equivalent to computing the distribution of the estimated parameter b1 in a logistic regression with one independent binary variable. In this paper, the distributions of the estimated parameters b1 and b2 for two independent binary variables are computed for some small sample logistic regressions using six different estimation methods based on maximum likelihood. These estimates are then compared to the true parameter values. The best estimation method depends on the frequency of the outcome of interest and on whether the bias or mean square error is considered more important.
A comparison of two simple hazard ratio estimators based on the logrank test
Authors: Berry G. , Kitchin R. M. , Mock P. A.
Published: April 2007

Two hazard ratio estimators based on the logrank test are investigated using a simulation study. The Pike estimator (ratio of relative death rates) was shown to be consistently less biased than the Peto (1‐step) estimator. The latter has recently been advocated as the method of choice for point and interval estimation.8Both estimators exhibited bias with increasing hazard ratios, although the bias was minimal for effects less than 3. The confidence intervals also did not achieve the nominal coverage with increasing hazard ratios, but again the Pike estimator was superior. The coverage could be improved by recalculation of the variance incorporating the point estimate. For a hazard ratio of less than 3 we recommend the use of the Pike estimator, otherwise it is necessary to use a more complex method of estimation.
Misclassification among methods used for multiple group discrimination‐the effects of distributional properties
Authors: Barön Anna E.
Published: April 2007

Methods of multiple group discriminant analysis have not been fully studied with respect to classification into more than two populations when the covariate distributions are normal or non‐normal. The present study examines the classification performance of several multiple discrimination methods under a variety of simulated continuous normal and non‐normal covariate distributions. The methods include polychotomous logistic regression, multiple group linear discriminant analysis, kernel density estimation, and rank transformations of the data as input into the linear function. The parameters of interest were distance among populations, configuration of population mean vectors (collinear or forming the vertices of a regular simplex), skewness, kurtosis and bimodality. Simulation of the last three parameters was by log‐normal, sinh−1normal and a two‐component mixture of normal distributions, respectively. Results with three trivariate populations show that for all distributions, logistic discrimination classifies close to the optimal under Neyman‐Pearson allocation. These results suggest that logistic discrimination is preferable to other widely‐used methods for multiple group classification with non‐normal data, and is comparable to classification by multiple linear discrimination with normal data.
The standard error of Cohen's Kappa
Authors: Garner J. Barry
Published: April 2007

This paper gives a standard error for Cohen's Kappa, conditional on the margins of the observed r × r table. An explicit formula is given for the 2 × 2 table, and a procedure for the more general situation. A parsimonious log‐linear model is suggested for the general case and an approximate confidence interval for kappa is based on that model. Numerical illustrations are given comparing the standard results with exact conditional results and those of the present paper. The conclusions are, first, that the standard error of kappa under the null hypothesis (that kappa is zero) should not be used except when the null is plausible; secondly, that the usual formula for the standard error appears appropriate except in the unusual circumstance of kappa taking large negative values; and, thirdly, in small samples the distribution of the estimate of kappa appears very non‐symmetric, and it is preferable to base confidence intervals on transformations of kappa. A PC program with source code implementing the suggested procedures is available from the author.
Planning controlled clinical trials on the basis of descriptive data analysis
Authors: Abt Klaus
Published: April 2007

In controlled clinical trials the problem of multiplicity of desired inferential statements finds attention at an increasing rate. In this paper the previously proposed concept of Descriptive Data Analysis (DDA), situated between Confirmatory and Exploratory Data Analysis, is applied to the planning aspects of controlled trials for which the problem of multiplicity exists. The (non‐Bayesian) DDA planning concept should provide the investigator with tools to draw final conclusions from data of several variables possibly observed at several time points in possibly several groups of subjects by combining his pre‐trial medical experience with descriptive inferential statements (confidence intervals and test results) at nominal significance levels. DDA also provides for confirmatory statements concerning individual null hypotheses and partially global hypotheses.
Determination of optimal designs using linear models in crossover trials
Authors: Lasserre Virginie
Published: April 2007

This study determines the optimal designs for crossover trials with fixed size of population, in order to estimate contrasts between two treatment effects, for various numbers of periods. The problem is approached in the framework of a linear model, taking into consideration the structure of a variance matrix constructed from two random sources: linked‐to‐subject random effect and linked‐to‐measurement random error. Different models, as well as different optimality criteria, are considered. For example, when two periods are planned, for the criterion of the minimization of the variance of the treatment‐effect estimator, in the presence of residual effect, the optimal design corresponds to four groups of sequences, (T1, T2), (T2, T1), (T1, T1), (T2, T2); without residual effect it corresponds to two groups, (T1, T2), (T2, T1). Optimal designs are given for the comparison of two treatments when using three or four periods.
Some extensions to a new approach for interim analysis in clinical trials
Authors: Falissard Bruno , Lellouch Joseph
Published: April 2007

There already exists many methods for group sequential analysis of clinical trials. A new approach1 suggests to preserve the overall type I error α by requiring that a succession of interim analyses be significant at the α level. In this paper, this procedure is extended. A rule for early acceptance of H0 is presented, with an extension for flexible number and times of analyses. A real example is given.
Analysis of phase II clinical trials in haematology and oncology: Comparison of the triangular test to the usual methods
Authors: Benichou Jacques , Bellissant Eric , Chastang Claude
Published: April 2007

Phase II cancer clinical trials are non‐comparative trials which are designed to determine whether the response rate p to the treatment under study is greater than a certain value p0, that is, to test H0, given by p ⩽ p0 against H1 given by p > p0.

By choosing type I error α and the power 1 ‐ β and by specifying H1, (that is, by choosing a clinically relevant improvement p1), one can compute the number of patients N to be included for a fixed‐sample approach. Various other approaches have been proposed such as multistage methods and Wald's continuous sequential probability ratio test (SPRT).

As an alternative approach, we extended the triangular test (TT), proposed by Whitehead for comparative trials, to the situation of non‐comparative trials with a binary outcome. We expressed H0 and H1 in terms of the log odds‐ratio statistics, namely log {p (1 ‐ p0)/p0 (1 ‐ p)}. With this choice, the two statistics of interest, Z and V, have simple expressions: Z is the difference between the observed number of positive outcomes and the expected number under H0 and V is the variance of Z under H0. After every group of n patients, Z is plotted against V, and the trial proceeds until a boundary is crossed.

In our simulations, type I error α and the power 1 ‐ β were close to nominal values with the TT and the average sample size was close to Wald's continuous SPRT and compared favourably with the multistage methods proposed by Herson and Fleming.

Given its statistical properties and its easy use, the TT should be considered for planning and analysing cancer phase II trials.
Floating absolute risk: An alternative to relative risk in survival and case‐control analysis avoiding an arbitrary reference group
Authors: Easton D. F. , Peto J. , Babiker A. G. A. G.
Published: April 2007

We discuss the problem of describing multiple group comparisons in survival analysis using the Cox model, and in matched case‐control studies. The standard method of comparing the risk in each group with a baseline group is unsatisfactory because the standard errors and confidence limits relate to correlated parameters, all dependent on precision within the baseline group. We describe the construction of standard errors for the parameters of all groups, without the need to select a baseline group. These standard errors can be regarded as relating to roughly independent parameters, so that groups can be compared efficiently without knowledge of the covariances. The method should assist in graphical presentation of relative risks, and in the combination of results from published studies. Two examples are presented.
Assessing the influence of reversible disease indicators on survival
Authors: Andersen Per Kragh , Hansen Lars Sommer , Keiding Niels
Published: April 2007

In a randomized clinical trial of the effect of prednisone versus placebo on survival in patients with liver cirrhosis, follow‐up visits were scheduled after 3,6 and 12 months of treatment and thereafter once a year. At each follow‐up theprothrombin index, a measure of liver function, was recorded and scored as either low or normal. The interaction between treatment and prothrombin index was analysed using a three‐state illness‐death model with recovery. The continuous‐time Markov process model with constant or piecewise constant intensities suggested by Kay allows inference to proceed even though the status of the disease indicator, here the prothrombin index, is only known at the time of each visit and not between visits. We compare the analysis with the theoretically incorrect, but practically rather common approximation, where the status of the disease indicator is assumed to remain constant from one visit until just before the next. Under this approximation both standard parametric methods and non‐parametric approaches developed by Aalen and Johansen are available.
Generalized Norton‐Simon models of tumour growth
Authors: Heitjan Daniel F.
Published: April 2007

This paper considers the analysis of serial data on the growth of tumours in laboratory rodents. I propose a model ‐ a generalization of the tumour growth model of Norton and Simon ‐ that leads to a rich family of growth and decay curves. The model assumes that unperturbed growth follows the generalized logistic form; it accommodates time‐varying treatment effects through an effective dose function. I fit two such models to data on a human prostate tumour growing in nude mice and compare the fitted curves and dose functions with a non‐parametric curve and dose function estimated from a cubic spline model. All three models account for both random animal effects and autocorrelation. Monte Carlo results suggest that (a) maximum likelihood estimates of growth parameters are biased, although not severely, and (b) standard errors are conservative in small samples but become increasingly accurate in larger samples.
Approximate multinormal probabilities applied to correlated multiple endpoints in clinical trials
Authors: James Susan
Published: April 2007

Clinical trials with multiple endpoints incur increased familywise type I errors. The Bonferroni correction is a common method used to modify the p‐values to account for multiple significance testing. For independent endpoints the Bonferroni method is slightly conservative whereas with high correlation the conservatism is extreme, as demonstrated by Pocock et al. This paper presents a procedure which allows for the correlation present, whilst adjusting the multiple p‐values. The method is based on an approximation derived for multinormal probabilities.
Simple tests of homogeneity of controls in matched studies
Authors: Gart John J.
Published: April 2007

Consider matched case‐control studies with a pair of distinguishable controls, say neighbourhood and hospital, wherein one of the controls may be missing. Liang and Stewart derive an efficient test for the possible difference in controls for the complete data case. They suggest inefficient tests for the situation where some triplets are incomplete. Levin, and Risch and Tibshirani, derive efficient tests for the incomplete triplet case by the methods of maximum likelihood estimator (Wald) tests and likelihood ratio tests, respectively. All these tests require the use of compute algorithms. Using score theory, we derive a simple efficient test for complete triplets which only requires solving a quadratic equation. Furthermore, we show that the usual normal approximation to McNemar's test is equivalent to the score test and is thus fully efficient as well. For incomplete triplets, score theory leads to a fully efficient test which only requires the solution of a cubic equation. We propose a nearly efficient test which is even more simply computed. The example of Liang and Stewart illustrates application of the results.
Three measures for simultaneously evaluating benefits and risks using categorical data from clinical trials
Authors: Chuang‐Stein Christy , Mohberg Noel R. , Sinkula Michaline S.
Published: April 2007

Randomized clinical trials are typically conducted to compare the efficacy (benefits) and side effects (risks) of two or more treatments. One can use results from such trials to decide on a preferable treatment that reflects one's own evaluation of the benefits and risks. To facilitate the necessary decision making, we propose in this paper three measures for simultaneously assessing benefits and risks. All three measures use weights that reflect the relative importance of the various treatment outcomes to an individual. Two of them carry the flavour of benefit/risk ratios, while the third generalizes Hilden's measure which incorporates patients' preferences. The proposed measures and procedures are illustrated using data from a phase III clinical trial of antihypertensive compounds.
A comparison of methods for calculating a stratified kappa
Authors: Barlow William , Lai Mei‐Ying , Azen Stanley P.
Published: April 2007

Investigators use the kappa coefficient to measure chance‐corrected agreement among observers in the classification of subjects into nominal categories. The marginal probability of classification may depend, however, on one or more confounding variables. We consider assessment of interrater agreement with subjects grouped into strata on the basis of these confounders. We assume overall agreement across strata is constant and consider a stratified index of agreement, or ‘stratified kappa’, based on weighted summations of the individual kappas. We use three weighting schemes: (1) equal weighting; (2) weighting by the size of the table; and (3) weighting by the inverse of the variance. In a simulation study we compare these methods under differing probability structures and differing sample sizes for the tables. We find weighting by sample size moderately efficient under most conditions. We illustrate the techniques by assessing agreement between surgeons and graders of fundus photographs with respect to retinal characteristics, with stratification by initial severity of the disease.