International Biometric Society
British Region

In his justifiably long-lived book on "Planning of Experiments", David Cox wrote "It is frequently not good enough to randomize just at one stage of the experimental procedure". I will describe several ways of incorporating randomization at two or more stages, and comment on the implications both for understanding the experimental structure and for analysing the eventual data.

The association between phylogenetic traits is usually assessed using comparative analyses of independent contrasts (CAIC). Differences (contrasts) are calculated between trait values for each pair of species (or higher nodes) within a phylogeny sharing an immediate common ancestor, providing observations independent of both the position of the nodes within the phylogeny, and any evolutionary events prior to that common ancestor. Null hypotheses of independent evolution are conventionally tested for each pair-wise combination of traits, using these phylogenetically independent contrasts, by applying simple linear regression through the origin, with a slope significantly different than zero indicating an association between the two traits.

However, with multiple traits it would be interesting to simultaneously consider the associations between all traits. We propose an approach using PCA, the interpretation of the associations between traits being based on the angles between the loadings vectors on the first few principal components, the remaining components being assumed to describe only "noise". As the CAIC procedure considers the true phylogeny to bifurcate, splitting daughter taxa of multiple nodes into two groups according to the trait value, each trait may define a different phylogeny and set of contrasts. Separate analyses are therefore required with each trait in turn as the independent (defining) variable (with all contrast values positive) for the phylogeny. Mean correlations between each pair of traits are calculated from the mean angles across the set of principal component analyses. A key decision is the choice of the number of components to include in the "signal".

The emergence of Severe Acute Respiratory Syndrome (SARS) and its rapid worldwide spread provided a major challenge to public health workers. The relatively high case fatality rate, coupled with travel restrictions imposed to control its spread, resulted in high levels of anxiety, not only in SARS-affected countries but also more widely. For epidemiologists and biostatisticians, SARS posed considerable challenges in understanding the factors determining its spread and in devising appropriate control strategies. Data on SARS cases from Hong Kong are analysed to obtain estimates of key epidemiological parameters (including the reproductive number R0) of the Hong Kong epidemic.

The proportional hazards regression model of Cox (1972) has had an enormous impact on both statistical and clinical/epidemiological research. Thus, a large number of scientific papers have appeared both dealing with methodological aspects of survival and event history data analysis and with results from analysis of follow-up data in medical studies.

I will focus on situations from event history analysis where the model or modifications of it have been applied. These include both models for transition intensities in multi-state processes and models for state probabilities in such processes (including the competing risks model and models for the survival probability at a given fixed point in time). In particular, I will review how pseudo-observations (e.g., Andersen, Klein and Rosthøj, Biometrika, 2003) may prove useful when analysing such extensions of the basic Cox model.

Attendance at mammography screening by women aged 50-70 years old has been shown to be associated with a 35% reduction in breast cancer mortality. The NHS breast screening programme in the UK currently invites women aged 50-70 for mammographic screening once every three years. The question of whether to extend this screening programme to women younger than age 50 is frequently raised, in particular for women thought to be at a higher than average risk of the disease, such as those with a family history of breast cancer. However, the reduction in mortality associated with mammographic screening for women younger than age 50 is currently uncertain, but is likely to be less than at older ages. Also, the radiation exposure from mammography X-rays involves a risk of radiation-induced breast cancer and this risk has been found to be greater the younger women are exposed. Radiation risk models were used to estimate the excess risk of radiation-induced breast cancer mortality associated with a decade of mammographic screening from ages 20-30 up to 60-70 years. The estimated number of radiation-induced breast cancer deaths was then compared with the estimated number of deaths that would be prevented by mammographic screening. Estimates are presented for women with and without first-degree relatives with breast cancer and the sensitivity of the results to various assumptions investigated.

Causal inference for treatment efficacy is often of interest in randomised trials with departures from randomised allocation. Methods for time-dependent departures are less well established than for all-or-nothing departures. In particular, there is no extension of the proportional hazards model to the case of time-dependent departures.

I propose a causal model in which the parameter of interest is the hazard ratio at time t between randomised groups, restricted to those who would still be following their allocated treatment at time t regardless of their allocation. This causal hazard ratio may be approximately estimated from the intention-to-treat hazard ratio and the distribution of actual treatment among those who have events at time t. I will discuss the practical application of this method to a trial in HIV infection, and the possibilities for an exact analysis.

In this talk I shall discuss aspects of the development of statistical inference since 1950, with particular reference to those topics strongly influenced by work of David Cox.