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PubMed1992

Adjustments to the Mantel-Haenszel test for data from stratified multistage surveys.

The usual form of the Mantel-Haenszel test statistic assumes independent observations. This is inappropriate for data from a stratified multistage survey. Two alternative adjustments to the test statistic are developed to deal with this: (a) a modification of the effective sample size for each row of each table, using the design effects, extending a method proposed by Donald and Donner for familial aggregation studies; (b) a Taylor series approximation to the variance of the square root of the numerator of the Mantel-Haenszel statistic. Both methods are evaluated by application to both simulated and real data. The two methods perform equally well, and offer a considerable improvement over the unadjusted test statistic when observations from the same cluster are highly correlated. A simplified adjustment is also considered, as is the need for correction to the variance of the odds ratio estimator.

Chi-Square Distribution↗
PubMed1992

Analysis of aberrations in public health surveillance data: estimating variances on correlated samples.

The detection of unusual patterns in health data presents an important challenge to health workers interested in early identification of epidemics or important risk factors. A useful procedure for detection of aberrations is the ratio of a current report to some historic baseline. This work addresses the problem of finding the variance of such a ratio when the surveillance reports are correlated. Results show that, when estimating this variance or the variance of the sample mean from a series of observations with an estimated correlation structure, bootstrap and jackknife estimates may be overly optimistic. The delta method or a classical method may be more useful when such model dependence is inappropriate.

Analysis of Variance↗
PubMed1992

Effects of mid-point imputation on the analysis of doubly censored data.

Doubly censored data arise in some cohort studies of the AIDS incubation period because the time of infection may be known only up to an interval defined by two successive screening tests for HIV antibody. A simple analytic approach is to impute the infection time by the mid-point of the interval and then apply standard survival techniques for right censored data. The objective of this paper is to investigate the statistical properties of such a mid-point imputation approach. We investigated the asymptotic bias of the Kaplan-Meier estimate, coverage probabilities of associated confidence intervals, bias in hazard ratio, and the size of the logrank test. We show that the statistical properties of mid-point imputation depend strongly on the underlying distributions of infection times and the incubation periods, and the width of the interval between screening tests. In the absence of treatment, the median incubation period of HIV infection is approximately 10 years, and we conclude that, for this situation, mid-point imputation is a reasonable procedure for interval widths of 2 years or less.

Bias↗
PubMed1993

The effect of matching on the power of randomized community intervention studies.

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.

Bias↗
PubMed1993

A modelling approach to the analysis of menstrual diary data.

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.

Bias↗
PubMed1993

A case for Bayesianism in clinical trials.

This paper describes a Bayesian approach to the design and analysis of clinical trials, and compares it with the frequentist approach. Both approaches address learning under uncertainty. But they are different in a variety of ways. The Bayesian approach is more flexible. For example, accumulating data from a clinical trial can be used to update Bayesian measures, independent of the design of the trial. Frequentist measures are tied to the design, and interim analyses must be planned for frequentist measures to have meaning. Its flexibility makes the Bayesian approach ideal for analysing data from clinical trials. In carrying out a Bayesian analysis for inferring treatment effect, information from the clinical trial and other sources can be combined and used explicitly in drawing conclusions. Bayesians and frequentists address making decisions very differently. For example, when choosing or modifying the design of a clinical trial, Bayesians use all available information, including that which comes from the trial itself. The ability to calculate predictive probabilities for future observations is a distinct advantage of the Bayesian approach to designing clinical trials and other decisions. An important difference between Bayesian and frequentist thinking is the role of randomization.

Bayes Theorem↗
PubMed1993

The role of p-values in analysing trial results.

The current widespread practice of using p-values as the main means of assessing and reporting the results of clinical trials cannot be defended. Reasons for grave concern over the present situation range from the unsatisfactory nature of p-values themselves, their very common misunderstanding by statisticians as well as by clinicians and their serious distorting influence on our perception of the very nature of clinical trials. It is argued, however, that only by fully understanding the reasons why they have become so universally popular can we hope to change opinion and introduce more sensible ways of summarizing and reporting results. Some of the ways in which this might happen are discussed.

Bayes Theorem↗
PubMed1993

Comparison of two tests useful in situations where treatment is expected to increase variability relative to controls.

The type I error and power characteristics of the modified t test were compared with those of the generalized t test. Results suggested that, in contrast to the generalized t test, the modified t test can be seriously non-robust to departures from population normality, with such departures often producing anti-conservative results. Neither test held an absolute power advantage over the other when responses were from normal distributions, but the modified t test was generally more powerful for these conditions. In comparison with the pooled samples t test, both tests were usually much more efficient when treatment caused increases both in mean response and between-subject variance, and suffered only small disadvantages when between-subject variance was unchanged by treatment. Given these results and other considerations, recommendations for use of these recently devised tests are given.

Bias↗
PubMed1994

A comparative study of several antibiotic formulations using a design based on a combination of balanced incomplete blocks and Latin squares.

A practical application of an experimental design, suitable for the comparison of several treatments, and based on combining balanced incomplete blocks and Latin squares balanced for carryover effects, is presented in the context of comparing a number of paediatric antibiotic formulations for taste, smell and colour. The recommended designs originally suggested by Patterson, have the advantage of balanced incomplete blocks, in that a single trial may be used to compare a larger number of treatments than may reasonably be given to any individual subject. In addition, the incorporation of suitably chosen Latin squares allows for assessment of any effect of order of presentation of the treatments and for any simple first-order carryover effect of one treatment into the following treatment period. Inclusion of such effects in the overall analysis could result in the reduction of bias in the comparisons of the treatments.

Analysis of Variance↗
PubMed1994

A geometric approach to the analysis of physiological flow data.

Physiological flow data are common in various medical fields. Examples include urinary, blood and expiratory flows. They are widely used in assessing functions in the urinary, circulatory, or pulmonary systems, respectively. Current statistical methods for analysing these flow data in clinical trials are either univariate analyses, which do not utilize all the information together, or some conventional multivariate methods (such as regression analyses) which yield results that do not render clear medical interpretations. This paper presents a new approach to analysing the flow data, using urinary flow as the primary focus. The basic idea and technical steps are applicable to other flow data as well. The proposed method aims to transform the flow measurements back to the shape of the flow graphs. Since the whole geometric pattern of the flow graph provides more information about the patient's flow condition than any individual flow parameter alone, the method is a meaningful way of combining and analysing the flow data in both statistical and clinical senses. The method is a three-stage procedure. Patients are classified into three classes in the first stage and then ranked in sequence in the second stage, according to the geometry of the shape pattern and some clinical criteria. The classification procedure is shown to be very reliable when compared with the clinician's visual evaluation, and hence can be implemented by computer programming to aid clinical trials involving many patients. The whole ranking score is then readily analysed at the third stage for comparing treatment effects by the analysis of covariance method based on ranks, with the post-treatment score as the response variable and the baseline score as the covariate. An example of a urinary flow data set is provided to illustrate the use of the procedure.

Analysis of Variance↗
PubMed1995

Model inconsistency, illustrated by the Cox proportional hazards model.

We consider problems involving the comparison of two or more treatments where we have the opportunity to adjust for relevant covariates either conditionally in a regression model or implicitly in repeated measures data, for example, in crossover trials. It is seen that for data arising from non-Normal distributions there is the possibility that models adjusting for covariates and those not adjusting for covariates will be inconsistent, that is, at most one of the models can be valid. Alternatively, even if conditional and unconditional models are valid, parameters in each model may have different interpretations. We note that this presents difficulties for the specification and interpretation of the analysis. It is also clear that model validation is critical. Specific attention is paid to survival data analysed by the Cox proportional hazards model.

Analysis of Variance↗
PubMed1995

Longitudinal data analysis for linear Gaussian models with random disturbed-highest-derivative-polynomial subject effects.

For linear regression analysis of longitudinal data with Gaussian response, I propose a new model to generalize the traditional class of random effects models in which the random effects are deterministic polynomials with coefficients randomly distributed over subjects with mean zero. The generalization is accomplished by adding zero mean Gaussian 'disturbances' to the highest derivative of each random coefficient subject polynomial, independently at each observation time. The resulting random effects, which have mean zero at each observation time, are called disturbed highest derivative polynomials (DHDPs). The disturbances induce serial correlation and also allow the subject-specific DHDP time trends to be non-linear. I do not estimate the subject-specific DHDP time trends. Analysis is based on the marginal model, that is, the fixed effects or population model obtained by integrating the random polynomial coefficients and all disturbances out of the joint distribution of themselves and the response vector. This allows a 'population averaged' interpretation. One can select the DHDP order by an information criterion. When the population time trend is not correctly modelled, the optimal DHDP order will be larger than when it is correctly modelled. One can make the covariance matrix of the regression coefficients robust to errors in modelling the within-subject dependence. I describe the relationship of a DHDP to a smoothing polynomial spline, and show how to replace the DHDP model with a smoothing polynomial spline model for the within-subject dependence in the marginal model.

Bias↗
PubMed1995

Smoothing splines for longitudinal data.

In a longitudinal data model with fixed and random effects, polynomials are used to model the fixed effects and smoothing polynomial splines are used to model the within-subject random effect curves. The splines are generated by modelling the data for each subject as observations of an integrated random walk with observational error. The initial conditions for each subject's deviation from the fixed effect curve are assumed to have zero mean and arbitrary covariance matrix which is estimated by maximum likelihood, producing an empirical Bayes estimate. This is in contrast to modelling a single curve using a diffuse prior. An example is presented using unbalanced longitudinal data from a pilot study in breast cancer patients.

Bayes Theorem↗
PubMed1995

The design and analysis of randomized trials with recurrent events.

This paper describes a method for planning the duration of a randomized parallel group study in which the response of interest is a potentially recurrent event. At the design stage we assume patients accrue at a constant rate, we model events via a homogeneous Poisson process, and we utilize an independent exponential censoring mechanism to reflect loss to follow-up. We derive the appropriate study duration to ensure satisfaction of power requirements for the effect size of interest under a Poisson regression model. An application to a kidney transplant study illustrates the potential savings of the Poisson-based design relative to a design based on the time to the first event. Revised design criteria are also derived to accommodate overdispersed Poisson count data. We examine the frequency properties of two non-parametric tests recently proposed by Lawless and Nadeau for trials based on the above design criteria. In simulation studies involving homogeneous and non-homogeneous Poisson processes they performed well with respect to their type I error rate and power. Results from supplementary simulation studies indicate that these tests are also robust to extra-Poisson variation and to clustering in the event times, making these tests attractive in their generality. We illustrate both tests by application to data from a completed kidney transplant study.

Algorithms↗
PubMed1995

Longitudinal models for analysis of respiratory function.

We compare the results of fitting three longitudinal models, two autoregressive models (the serial correlation model and a damped autoregressive model) and a compound symmetry model, to data on a cohort of 1154 adult men in Boston. The serial correlation model assumes that the error terms are autocorrelated with correlation of the form lambda t for visits t years apart while the damped autoregressive assumes that the correlation between error terms of observations t years apart is of the form lambda t theta. The compound symmetry model assumes that the errors are correlated, with the same correlation regardless of how far apart observations are in time. These three models are all related in that the serial correlation and compound symmetry models are particular cases of the damped autoregressive models (that is, theta = 1 corresponds to the serial correlation model and theta = 0 corresponds to the compound symmetry model). For current smokers, the damped autoregressive model provided a significantly better fit than either of the other two models (p < 0.001); for never smokers the damped autoregressive and compound symmetry models were almost identical with both providing a significantly better fit than the serial correlation model (p < 0.001).

Adult↗