NEAREST NEIGHBOUR ANALYSIS OF UNEQUALLY REPLICATED TRIALS

There has been much work on the use of neighbouring plots to control environmental variation in the analysis of agricultural field experiments. In particular, the Residual Maximum Likelihood Neighbour (REMLN) analysis of Gleeson&Cullis (1987) appears very promising. The application of the REMLN analysis to an unequally replicated field trial augmented with an additional variety planted every six plots in a grid system is here compared with a covariance (COV) analysis using the neighbouring grid or check plot values as the covariate. The results indicate that the REMLN analysis gives more accurate estimates of treatment contrasts than the COV analyses, but that the estimate of treatment means can be biased. The bias depends on the mean of the check plot. This bias can be removed by adjusting the estimates of the treatment means such that their average equals the average of the raw means rather than that of the raw data.     

A COMPARISON OF TESTS OF UNIFORMITY FOR SPHERICAL DATA

A comparison is made af three tests of uniformity for spherical vector data, and of the corresponding tests of uniformity for spherical axial data.     

NEIGHBOUR ANALYSIS WITH ADJUSTMENT FOR INTERPLOT COMPETITION

In field experiments involving a large number of experimental plots, a neighbour analysis can be used to control environmental variation by estimating the trend within blocks. The effect of interplot competition is another important source of variation which has an influence on the estimation of treatment contrasts. To reduce the effect of the variation from these sources and to improve the precision of comparison between treatments, a spatial model is proposed for incorporating both trend effect and interplot competition. It is a modification to the residual maximum likelihood neighbour analysis of Gleeson & Cullis (1987) using the two neighbouring treatment effects to estimate interplot competition. A real example is used to illustrate this methodology. The results indicate that the extended model gives no appreciable difference in standard error of mean differences compared with the model taking into account the trend effect only. However, the rankings of estimated treatment means do differ. More research using both real and simulated data is required before such models that incorporate trend and competition effects can be confidently recommended.     

FACTORIAL ANALYSIS OF RECIDIVIST DATA

This paper presents a method of fitting factorial models to recidivism data consisting of the (possibly censored) time to ‘fail’ of individuals, in order to test for differences between groups. Here ‘failure’ means rearrest, reconviction or reincarceration, etc. A proportion P of the sample is assumed to be ‘susceptible’ to failure, i.e. to fail eventually, while the remaining 1-P are ‘immune’, and never fail. Thus failure may be described in two ways: by the probability P that an individual ever fails again (‘probability of recidivism’), and by the rate of failure Λ for the susceptibles. Related analyses have been proposed previously: this paper argues that a factorial approach, as opposed to regression approaches advocated previously, offers simplified analysis and interpretation of these kinds of data. The methods proposed, which are also applicable in medical statistics and reliability analyses, are demonstrated on data sets in which the factors are Parole Type (released to freedom or on parole), Age group (≤ 20 years, 20–40 years, > 40 years), and Marital Status. The outcome (failure) is a return to prison following first or second release.     

VALID RANDOMISATION FOR THE FIRST-DIFFERENCE ANALYSIS

A general method is presented for randomising a block design while preserving the neighbour relationships between treatments. The randomisation possesses validity properties for the first-difference analysis introduced by Besag & Kempton (1986). The estimators of treatment differences are unbiased, and the paper shows how to calculate quadratic estimators of their variance, which are unbiased if treatment effects and plot effects are additive. Simplifications, which appear when the design is neighbour-balanced, are described and illustrated.     

A SEMIPARAMETRIC MIXTURE MODEL FOR THE ANALYSIS OF COMPETING RISKS DATA

This paper deals with the regression analysis of failure time data when there are censoring and multiple types of failures. We propose a semiparametric generalization of a parametric mixture model of Larson & Dinse (1985), for which the marginal probabilities of the various failure types are logistic functions of the covariates. Given the type of failure, the conditional distribution of the time to failure follows a proportional hazards model. A marginal like lihood approach to estimating regression parameters is suggested, whereby the baseline hazard functions are eliminated as nuisance parameters. The Monte Carlo method is used to approximate the marginal likelihood; the resulting function is maximized easily using existing software. Some guidelines for choosing the number of Monte Carlo replications are given. Fixing the regression parameters at their estimated values, the full likelihood is maximized via an EM algorithm to estimate the baseline survivor functions. The methods suggested are illustrated using the Stanford heart transplant data.     

THE REDUCED-RANK GROWTH CURVE MODEL FOR DISCRIMINANT ANALYSIS OF LONGITUDINAL DATA

This paper presents a method of discriminant analysis especially suited to longitudinal data. The approach is in the spirit of canonical variate analysis (CVA) and is similarly intended to reduce the dimensionality of multivariate data while retaining information about group differences. A drawback of CVA is that it does not take advantage of special structures that may be anticipated in certain types of data. For longitudinal data, it is often appropriate to specify a growth curve structure (as given, for example, in the model of Potthoff & Roy, 1964). The present paper focuses on this growth curve structure, utilizing it in a model-based approach to discriminant analysis. For this purpose the paper presents an extension of the reduced-rank regression model, referred to as the reduced-rank growth curve (RRGC) model. It estimates discriminant functions via maximum likelihood and gives a procedure for determining dimensionality. This methodology is exploratory only, and is illustrated by a well-known dataset from Grizzle & Allen (1969).     

CANONICAL VARIATE ANALYSIS WITH SPATIALLY-CORRELATED DATA

A general canonical variate model is derived when the observations are spatially correlated. For spatial covariance structures resulting from dependence of a pixel on its nearest neighbours, the solution reduces to an analysis of neighbour-corrected values. The usual analysis, in which spatial correlation is ignored, gives similar canonical vectors but over-estimates the canonical roots. A formula for approximating the reduction in the canonical roots to adjust for the spatial correlation is given.     

ON THE DESIGN OF FIELD EXPERIMENTS UNDER A ONE-DIMENSIONAL NEIGHBOUR MODEL

This paper examines the effect of randomisation restrictions, either to satisfy conditions for a balanced incomplete block design or to attain a higher level of partial neighbour balance, on the average variance of pair-wise treatment contrasts under a neighbour model discussed by Gleeson & Cullis (1987). Results suggest that smaller average pairwise variances can be obtained by ignoring requirements for incomplete block designs and concentrating on achieving a higher level of partial neighbour balance. Field layout of the design, although often determined by practical constraints, e.g. size, shape of site, minimum plot size and experimental husbandry, may markedly affect average pairwise variance. For the one-dimensional (row-wise) neighbour model considered here, investigation of three different layouts suggests that for a rectangular array of plots, smaller average pairwise variances can generally be obtained from layouts with fewer rows and more plots per row.     

ANALYSIS OF MASKED DATA IN A DEPENDENT COMPETING RISKS MODEL UNDER UNKNOWN ENVIRONMENT

ABSTRACT

System failure data is often analyzed to estimate component reliabilities. Due to cost and time constraints, the exact component causing the failure of the system cannot be identified in some cases. This phenomenon is called masking. Further, it is sometimes necessary for us to take account of the influence of the operating environment. Here we consider a series system, operating under unknown environment, of two components whose failure times follow the Marshall-Olkin bivariate exponential distribution. We present a maximum likelihood approach for obtaining estimators from the masked data for this system. From a simulation study, we found that the relative errors of the estimates are almost well behaved even for small or moderate expected number of systems whose cause of failure is identified.     

MULTIVARLYTE ANALYSIS OF CLUSTERED SURVEY DATA: TESTING EQUALITY OF COVARLANCE MATRICES

The problem of testing the hypothesis of equality of covariance matrices in the presence of two-stage sampling is considered. Asymptotic test procedures based on linearization, grouping and jackknifing with or without transformation are proposed. The finite sample properties of these procedures are investigated in sampling experiments both from simulated known distributions and from a natural population.     

ACCOUNTING FOR NON-COMPLIANCE IN THE ANALYSIS OF RANDOMIZED RESPONSE DATA

The randomized response model is a misclassification design that is used to protect the privacy of respondents with respect to sensitive questions. Conditional misclassification probabilities are specified by the researcher and are therefore considered to be known. It is to be expected that some of the respondents do not comply with respect to the misclassification design. These respondents induce extra perturbation, which is not accounted for in the standard randomized response model. An extension of the randomized response model is presented that takes into account assumptions with respect to non-compliance under simple random sampling. The extended model is investigated using Bayesian inference. The research is motivated by randomized response data concerning violations of regulations for social benefit.     

ON THE ROBUST ANALYSIS OF VARIANCE COMPONENTS MODELS FOR PEDIGREE DATA

Quantitative traits measured over pedigrees of individuals may be analysed using maximum likelihood estimation, assuming that the trait has a multivariate normal distribution. This approach is often used in the analysis of mixed linear models. In this paper a robust version of the log likelihood for multivariate normal data is used to construct M-estimators which are resistant to contamination by outliers. The robust estimators are found using a minimisation routine which retains the flexible parameterisations of the multivariate normal approach. Asymptotic properties of the estimators are derived, computation of the estimates and their use in outlier detection tests are discussed, and a small simulation study is conducted.     

GRAPHICAL SENSITIVITY ANALYSIS WITH DIFFERENT METHODS OF IMPUTATION FOR A TRIAL WITH PROBABLE NON‐IGNORABLE MISSING DATA

Graphical sensitivity analyses have recently been recommended for clinical trials with non‐ignorable missing outcome. We demonstrate an adaptation of this methodology for a continuous outcome of a trial of three cognitive‐behavioural therapies for mild depression in primary care, in which one arm had unexpectedly high levels of missing data. Fixed‐value and multiple imputations from a normal distribution (assuming either varying mean and fixed standard deviation, or fixed mean and varying standard deviation) were used to obtain contour plots of the contrast estimates with their P‐values superimposed, their confidence intervals, and the root mean square errors. Imputation was based either on the outcome value alone, or on change from baseline. The plots showed fixed‐value imputation to be more sensitive than imputing from a normal distribution, but the normally distributed imputations were subject to sampling noise. The contours of the sensitivity plots were close to linear in appearance, with the slope approximately equal to the ratio of the proportions of subjects with missing data in each trial arm.     

A GENEALOGY OF CORRESPONDENCE ANALYSIS

Over the past half a century correspondence analysis has grown from a little known statistical technique designed to graphically depict the association structure of categorical variables that form a contingency table to a very popular tool used in a wide variety of disciplines. Despite this growth, correspondence analysis remains relatively unknown in some parts of the world, including the Australasian statistical community. This paper provides a non‐technical, bibliographic exploration of correspondence analysis. We take a step back to view the development of this statistical technique and provide a brief account of its genealogy with a selection of over 270 key publications that have contributed to its growth. We also look at its maturity over the decades.     

ASYMPTOTIC PROPERTIES OF AN OPTIMAL ESTIMATING FUNCTION APPROACH TO THE ANALYSIS OF MARK RECAPTURE DATA

ABSTRACT

A drawback of non parametric estimators of the size of a closed population in the presence of heterogeneous capture probabilities has been their lack of analytic tractability. Here we show that the martingale estimating function/sample coverage approach to estimating the size of a closed population with heterogeneous capture probabilities is mathematically tractable and develop its large sample properties.     

THE ANALYSIS OF DISCRETE CHOICE EXPERIMENTS WITH CORRELATED ERROR STRUCTURE

In a stated preference discrete choice experiment each subject is typically presented with several choice sets, and each choice set contains a number of alternatives. The alternatives are defined in terms of their name (brand) and their attributes at specified levels. The task for the subject is to choose from each choice set the alternative with highest utility for them. The multinomial is an appropriate distribution for the responses to each choice set since each subject chooses one alternative, and the multinomial logit is a common model. If the responses to the several choice sets are independent, the likelihood function is simply the product of multinomials. The most common and generally preferred method of estimating the parameters of the model is maximum likelihood (that is, selecting as estimates those values that maximize the likelihood function). If the assumption of within-subject independence to successive choice tasks is violated (it is almost surely violated), the likelihood function is incorrect and maximum likelihood estimation is inappropriate. The most serious errors involve the estimation of the variance-covariance matrix of the model parameter estimates, and the corresponding variances of market shares and changes in market shares.

In this paper we present an alternative method of estimation of the model parameter coefficients that incorporates a first-order within-subject covariance structure. The method involves the familiar log-odds transformation and application of the multivariate delta method. Estimation of the model coefficients after the transformation is a straightforward generalized least squares regression, and the corresponding improved estimate of the variance-covariance matrix is in closed form. Estimates of market share (and change in market share) follow from a second application of the multivariate delta method. The method and comparison with maximum likelihood estimation are illustrated with several simulated and actual data examples.

Advantages of the proposed method are: 1) it incorporates the within-subject covariance structure; 2) it is completely data driven; 3) it requires no additional model assumptions; 4) assuming asymptotic normality, it provides a simple procedure for computing confidence regions on market shares and changes in market shares; and 5) it produces results that are asymptotically equivalent to those produced by maximum likelihood when the data are independent.     

NONPARAMETRIC STATISTICAL ANALYSIS OF DISCRETE-TIME QUEUES,WITH APPLICATIONS TO ATM TELETRAFFIC DATA

In this paper nonparametric statistical analysis of a discrete-time queueing system is considered. Estimation of performance measures of the system is studied. The attention is first focused on the estimation of the waiting time probability distribution, as well as of functionals of interest (mean waiting time, variance of the waiting time, etc.). The approach is based on the estimation of the corresponding generating function. Attention is paid to the estimation of the probability of a “long delay”, in view of its importance for applications. Results for possibly unstable models are also obtained. Finally, an application to ATM teletraffic data is provided.     

ANALYSIS OF DOUBLY CENSORED DATA AND THE HIV INCUBATION PERIOD DISTRIBUTION IN WESTERN AUSTRALIA

The paper analyses the distribution of times from HIV seroconversion to the first AIDS defining illness for a subcohort of the Western Australian HIV Cohort Study for whom the seroconversion date is known to fall within a calendar time window. The analysis is based on a generalised gamma model for the incubation times and a piecewise constant distribution for the conditional times of seroconversion given the seroconversion windows. This allows flexible hazard shapes and also allows comparison of goodness of fit of the gamma and Weibull distributions which are often used for modelling incubation times. Computational issues are discussed. In these data, neither age at seroconversion, nor calendar time of seroconversion, nor the identification of a seroconversion illness appears to afFect incubation distributions. The Weibull distribution appears to provide a reasonable fit. The distribution of times from seroconversion to an HIV-related death is also briefly considered.     

USE OF A LOG-LINEAR MODEL TO COMPUTE THE EMPIRICAL SURVIVAL CURVE FROM INTERVAL-CENSORED DATA, WITH APPLICATION TO DATA ON TESTS FOR HIV POSITIVITY

We describe how a log-linear model can be used to compute the nonparametric maximum likelihood estimate of the survival curve from interval-censored data. This permits such computation to be performed with the aid of readily available statistical software such as GLIM or SAS. The method is illustrated with reference to data from a cohort of Danish homosexual men, each of whom was tested for HIV positivity on one or more of six possible follow-up times.