D. R. Cox

Regression Models and Life-Tables

The analysis of censored failure times is considered. It is assumed that on each individual arc available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations are outlined.

Design and analysis of randomized clinical trials requiring prolonged observation of each patient. II. analysis and examples.

Part I of this report appeared in the previous issue (Br. J. Cancer (1976) 34,585), and discussed the design of randomized clinical trials. Part II now describes efficient methods of analysis of randomized clinical trials in which we wish to compare the duration of survival (or the time until some other untoward event first occurs) among different groups of patients. It is intended to enable physicians without statistical training either to analyse such data themselves using life tables, the logrank test and retrospective stratification, or, when such analyses are presented, to appreciate them more critically, but the discussion may also be of interest to statisticians who have not yet specialized in clinical trial analyses.

The Analysis of binary data

Binary response variables special logistical analyses some complications some related approaches more complex responses. Appendices: Theoretical background Choice of explanatory variables in multiple regression Review of computational aspects Further results and exercises.

Design and analysis of randomized clinical trials requiring prolonged observation of each patient. I. Introduction and design.

The Medical Research Council has for some years encouraged collaborative clinical trials in leukaemia and other cancers, reporting the results in the medical literature. One unreported result which deserves such publication is the development of the expertise to design and analyse such trials. This report was prepared by a group of British and American statisticians, but it is intended for people without any statistical expertise. Part I, which appears in this issue, discusses the design of such trials; Part II, which will appear separately in the January 1977 issue of the Journal, gives full instructions for the statistical analysis of such trials by means of life tables and the logrank test, including a worked example, and discusses the interpretation of trial results, including brief reports of 2 particular trials. Both parts of this report are relevant to all clinical trials which study time to death, and wound be equally relevant to clinical trials which study time to other particular classes of untoward event: first stroke, perhaps, or first relapse, metastasis, disease recurrence, thrombosis, transplant rejection, or death from a particular cause. Part I, in this issue, collects together ideas that have mostly already appeared in the medical literature, but Part II, next month, is the first simple account yet published for non-statistical physicians of how to analyse efficiently data from clinical trials of survival duration. Such trials include the majority of all clinical trials of cancer therapy; in cancer trials,however, it may be preferable to use these statistical methods to study time to local recurrence of tumour, or to study time to detectable metastatic spread, in addition to studying total survival. Solid tumours can be staged at diagnosis; if this, or any other available information in some other disease is an important determinant of outcome, it can be used to make the overall logrank test for the whole heterogeneous trial population more sensitive, and more intuitively satisfactory, for it will then only be necessary to compare like with like, and not, by chance, Stage I with Stage III.

A Common Allele on Chromosome 9 Associated with Coronary Heart Disease

Coronary heart disease (CHD) is a major cause of death in Western countries. We used genome-wide association scanning to identify a 58-kilobase interval on chromosome 9p21 that was consistently associated with CHD in six independent samples (more than 23,000 participants) from four Caucasian populations. This interval, which is located near the CDKN2A and CDKN2B genes, contains no annotated genes and is not associated with established CHD risk factors such as plasma lipoproteins, hypertension, or diabetes. Homozygotes for the risk allele make up 20 to 25% of Caucasians and have a ∼30 to 40% increased risk of CHD.

Genetic variation in PNPLA3 confers susceptibility to nonalcoholic fatty liver disease

Nonalcoholic fatty liver disease (NAFLD) is a burgeoning health problem of unknown etiology that varies in prevalence among ancestry groups. To identify genetic variants contributing to differences in hepatic fat content, we carried out a genome-wide association scan of nonsynonymous sequence variations (n = 9,229) in a population comprising Hispanic, African American and European American individuals. An allele in PNPLA3 (rs738409[G], encoding I148M) was strongly associated with increased hepatic fat levels (P = 5.9 × 10−10) and with hepatic inflammation (P = 3.7 × 10−4). The allele was most common in Hispanics, the group most susceptible to NAFLD; hepatic fat content was more than twofold higher in PNPLA3 rs738409[G] homozygotes than in noncarriers. Resequencing revealed another allele of PNPLA3 (rs6006460[T], encoding S453I) that was associated with lower hepatic fat content in African Americans, the group at lowest risk of NAFLD. Thus, variation in PNPLA3 contributes to ancestry-related and inter-individual differences in hepatic fat content and susceptibility to NAFLD.

Quality of life measures in health care. I: Applications and issues in assessment

Many clinicians remain unsure of the relevance of measuring quality of life to their clinical practice. In health economics quality of life measures have become the standard means of assessing the results of health care interventions and, more controversially, the means of prioritising funding; but they have many other applications. This article--the first of three on measuring quality of life--reviews the instruments available and their application in screening programmes, audit, health care research, and clinical trials. Using the appropriate instrument is essential if outcome measures are to be valid and clinically meaningful.

Linear Amplification with Nonlinear Components

A technique for producing bandpass linear amplification with nonlinear components (LINC) is described. The bandpass signal first is separated into two constant envelope component signals. All of the amplitude and phase information of the original bandpass signal is contained in phase modulation on the component signals. These constant envelope signals can be amplified or translated in frequency by amplifiers or mixers which have nonlinear input-output amplitude transfer characteristics. Passive linear combining of the amplified and/or translated component signals produces an amplified and/or translated replica of the original signal.

Some Models for Rainfall Based on Stochastic Point Processes

Stochastic models are discussed for the variation of rainfall intensity at a fixed point in space. First, models are analysed in which storm events arise in a Poisson process, each such event being associated with a period of rainfall of random duration and constant but random intensity. Total rainfall intensity is formed by adding the contributions from all storm events. Then similar but more complex models are studied in which storms arise in a Poisson process, each storm giving rise to a cluster of rain cells and each cell being associated with a random period of rain. The main properties of these models are determined analytically. Analysis of some hourly rainfall data from Denver, Colorado shows the clustered models to be much the more satisfactory.

A use of complex probabilities in the theory of stochastic processes

The exponential distribution is very important in the theory of stochastic processes with discrete states in continuous time. A. K. Erlang suggested a method of extending to other distributions methods that apply in the first instance only to exponential distributions. His idea is generalized to cover all distributions with rational Laplace transforms; this involves the formal use of complex transition probabilities. Properties of the method are considered.