arXiv subjects
Publications and source records attributed to D. R. Cox.
Principles for the planning and analysis of observational studies, as suggested by W.G Cochran in 1972, are discussed and compared to additional methodological developments since then.
We describe how graphical Markov models started to emerge in the last 40 years, based on three essential concepts that had been developed independently more than a century ago. Sequences of joint or single regressions and their regression graphs are singled out as being best suited for analyzing longitudinal data and for tracing developmental pathways. Interpretations are illustrated using two sets of data and some of the more recent, important results for sequences of regressions are summarized.
With graphical Markov models, one can investigate complex dependences, summarize some results of statistical analyses with graphs and use these graphs to understand implications of well-fitting models. The models have a rich history and form an area that has been intensively studied and developed in recent years. We give a brief review of the main concepts and describe in more detail a flexible subclass of models, called traceable regressions. These are sequences of joint response regressions for which regression graphs permit one to trace and thereby understand pathways of dependence. We use these methods to reanalyze and interpret data from a prospective study of child development, now known as the Mannheim Study of Children at Risk. The two related primary features concern cognitive and motor development, at the age of 4.5 and 8 years of a child. Deficits in these features form a sequence of joint responses. Several possible risks are assessed at birth of the child and when the child reached age 3 months and 2 years.
Several different types of statistical interaction are defined and distinguished, primarily on the basis of the nature of the factors defining the interaction. Illustrative examples, mostly epidemiological, are given. The emphasis is primarily on interpretation rather than on methods for detecting interactions.
The main phases of applied statistical work are discussed in general terms. The account starts with the clarification of objectives and proceeds through study design, measurement and analysis to interpretation. An attempt is made to extract some general notions.
After some general remarks about the interrelation between philosophical and statistical thinking, the discussion centres largely on significance tests. These are defined as the calculation of $p$-values rather than as formal procedures for ``acceptance'' and ``rejection.'' A number of types of null hypothesis are described and a principle for evidential interpretation set out governing the implications of $p$-values in the specific circumstances of each application, as contrasted with a long-run interpretation. A variety of more complicated situations are discussed in which modification of the simple $p$-value may be essential.