On Testing Equality of Means of Correlated Variates with Incomplete Data

A statistic is proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on one of the variates. Expressions for the second and fourth central moments of the statistic are obtained. These moments are used to approximate the distribution of the statistic by a Student's t distribution under the null hypothesis. The powers of the test are computed and compared with those of the conventional paired t and the other known statistics.     

On Comparing Correlated Means in the Presence of Incomplete Data

Two statistics are proposed for testing the hypothesis of equality of the means of a bivariate normal distribution with unknown common variance and correlation coefficient when observations are missing on both variates. One of the statistics reduces to the one proposed by Bhoj (1978, 1984) when the unpaired observations on the variates are equal. The distributions of the statistics are approximated by well known distributions under the null hypothesis. The empirical powers of the tests are computed and compared with those of some known statistics. The comparison supports the use of one of the statistics proposed in this paper.     

Estimating survival of the shortfin mako Isurus oxyrinchus (Rafinesque) in the north-west Atlantic from tag-recapture data

Survival was estimated for shortfin mako Isurus oxyrinchus in the north-west Atlantic from tag-recapture data. The data used in this study were collected by the National Marine Fisheries Service Cooperative Shark Tagging Programme from 1962 to 2003. In total, 6309 shortfin mako sharks were tagged, of which 730 were recaptured. The high recapture rate of 11·6% for this species provided adequate recapture data to carry out survival analyses. Estimates of survival were generated with the computer software MARK, which provided a means for estimating parameters from tagged animals when they were recaptured. The results of several models are presented with various combinations of constant and time-specific survival and recovery rates. A parametric bootstrap and the median variance inflation factor ( ) approach were used to test the fit of the general model to the data. The estimated indicated a very good model fit. The models with time invariant survival rate had the most support from the data and no group or time period effects were found. Recovery rate ( f ) appeared to increase from 0·043 in the early years to 0·056 in the later years. The nominal survival rate of 0·59 year⁻¹ was adjusted with an estimated tag-shedding rate of 0·26 year⁻¹ to generate a final corrected annual survival estimate of 0·79 with a 95% CI of 0·71–0·87.     

Abalone I: Analyzing Mark-Recapture-Recovery Data Incorporating Growth and Delayed Recovery

Abalone are semimobile marine gastropods that form the basis of Australia's second most valuable fishery. A site off the coast of Port Arthur, Tasmania, was visited on six occasions. On each occasion, any unmarked live abalone found were marked with a unique identification number and were recorded. Any previously marked abalone found had its identification number and whether or not it was still alive recorded. This results in integrated mark-recapture-recovery data, as in Catchpole et al. (1998, Biometrics 54, 33-46). During the study period, abalone grew in size, and we model the survival of individuals as a function of their size, estimated from a fitted growth curve. The shells of dead animals are long lasting, and we extend existing methodology to allow for the possibility that an animal found dead may have been dead but overlooked for several visits.     

Cervical screening in Luxembourg: 1990–1999

For quality assurance purposes, the results of the 1990's obtained by the National Cervical Cancer Screening Programme (NCCSP) launched in 1962 were reviewed. The positive cytodiagnosis, the histologically verified in situ and invasive cervical cancers and the mortality rates were reported.     

Describing Ordinal Odds Ratios for Stratified r × c Tables

For an r × ctable with ordinal responses, odds ratios are commonly used to describe the relationship between the row and column variables. This article shows two types of ordinal odds ratios where local‐global odds ratios are used to compare several groups on a c‐category ordinal response and a global odds ratio is used to measure the global association between a pair of ordinal responses. When there is a stratification factor, we consider Mantel‐Haenszel (MH) type estimators of these odds ratios to summarize the association from several strata. Like the ordinary MH estimator of the common odds ratio for several 2 × 2 contingency tables, the estimators are used when the association is not expected to vary drastically among the strata. Also, the estimators are consistent under the ordinary asymptotic framework in which the number of strata is fixed and also under sparse asymptotics in which the number of strata grows with the sample size. Compared to the maximum likelihood estimators, simulations find that the MH type estimators perform better especially when each stratum has few observations. This article provides variances and covariances formulae for the local‐global odds ratios estimators and applies the bootstrap method to obtain a standard error for the global odds ratio estimator. At the end, we discuss possible ways of testing the homogeneity assumption.     

Introducing the Multivariate Dale Model in Population‐Based Genetic Association Studies

Until recently, the most common parametric approaches to study the combined effects of several genetic polymorphisms located within a gene or in a small genomic region are, at the genotype level, logistic regressions and at the haplotype level, haplotype analyses. An alternative modeling approach, based on the case/control principle, is to regard exposures (e.g., genetic data such as derived from Single Nucleotide Polymorphisms – SNPs) as random and disease status as fixed and to use a marginal multivariate model that accounts for inter‐relationships between exposures. One such model is the multivariate Dale model. This model is based on multiple logistic regressions. That is why the model, applied in a case/control setting, leads to straightforward interpretations that are similar to those drawn in a classical logistic modeling framework. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)