Patrick Royston

Analysis of serial measurements in medical research.

In medical research data are often collected serially on subjects. The statistical analysis of such data is often inadequate in two ways: it may fail to settle clinically relevant questions and it may be statistically invalid. A commonly used method which compares groups at a series of time points, possibly with t tests, is flawed on both counts. There may, however, be a remedy, which takes the form of a two stage method that uses summary measures. In the first stage a suitable summary of the response in an individual, such as a rate of change or an area under a curve, is identified and calculated for each subject. In the second stage these summary measures are analysed by simple statistical techniques as though they were raw data. The method is statistically valid and likely to be more relevant to the study questions. If this method is borne in mind when the experiment is being planned it should promote studies with enough subjects and sufficient observations at critical times to enable useful conclusions to be drawn. Use of summary measures to analyse serial measurements, though not new, is potentially a useful and simple tool in medical research.

Multiple imputation for missing data in epidemiological and clinical research: potential and pitfalls

Most studies have some missing data. Jonathan Sterne and colleagues describe the appropriate use and reporting of the multiple imputation approach to dealing with them

Multiple imputation using chained equations: Issues and guidance for practice

Multiple imputation by chained equations is a flexible and practical approach to handling missing data. We describe the principles of the method and show how to impute categorical and quantitative variables, including skewed variables. We give guidance on how to specify the imputation model and how many imputations are needed. We describe the practical analysis of multiply imputed data, including model building and model checking. We stress the limitations of the method and discuss the possible pitfalls. We illustrate the ideas using a data set in mental health, giving Stata code fragments.

Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling

The relationship between a response variable and one or more continuous covariates is often curved. Attempts to represent curvature in singleor multiple-regression models are usually made by means of polynomials of the covariates, typically quadratics. However, low order polynomials offer a limited family of shapes, and high order polynomials may fit poorly at the extreme values of the covariates. We propose an extended family of curves, which we call fractional polynomials, whose power terms are restricted to a small predefined set of integer and non-integer values. The powers are selected so that conventional polynomials are a subset of the family. Regression models using fractional polynomials of the covariates have appeared in the literature in an ad hoc fashion over a long period; we provide a unified description and a degree of formalization for them. They are shown to have considerable flexibility and are straightforward to fit using standard methods. We suggest an iterative algorithm for covariate selection and model fitting when several covariates are available. We give six examples of the use of fractional polynomial models in three types of regression analysis: normal errors, logistic and Cox regression. The examples all relate to medical data: fetal measurements, immunoglobulin concentrations in children, diabetes in children, infertility in women, myelomatosis (a type of leukaemia) and leg ulcers.

What do we mean by validating a prognostic model

Prognostic models are used in medicine for investigating patient outcome in relation to patient and disease characteristics. Such models do not always work well in practice, so it is widely recommended that they need to be validated. The idea of validating a prognostic model is generally taken to mean establishing that it works satisfactorily for patients other than those from whose data it was derived. In this paper we examine what is meant by validation and review why it is necessary. We consider how to validate a model and suggest that it is desirable to consider two rather different aspects - statistical and clinical validity - and examine some general approaches to validation. We illustrate the issues using several case studies.

Maternal serum screening for Down's syndrome in early pregnancy.

The possibility of improving the effectiveness of antenatal screening for Downs syndrome by measuring human chorionic gonadotrophin concentrations in maternal serum during the second trimester to select women for diagnostic amniocentesis was examined. The median maternal serum human chorionic gonadotrophin concentration in 77 pregnancies associated with Downs syndrome was twice the median concentration in 385 unaffected pregnancies matched for maternal age, gestational age, and duration of storage of the serum sample. Measuring human chorionic gonadotrophin in maternal serum was an effective screening test, giving a lower false positive rate (3%) at a 30% detection rate than that for maternal age (5%) and the two existing serum screening tests, unconjugated oestriol (7%) and alpha fetoprotein (11%). The most effective screening results were obtained with all four variables combined; at the same 30% detection rate the false positive rate declined to 0.5%. The new screening method would detect over 60% of affected pregnancies, more than double that achievable with the same amniocentesis rate in existing programmes (5%), and could reduce the number of children born with Downs syndrome in the United Kingdom from about 900 a year to about 350 a year.

Prognosis and prognostic research: validating a prognostic model.

Prognostic models are of little clinical value unless they are shown to work in other samples. Douglas Altman and colleagues describe how to validate models and discuss some of the problems

The cost of dichotomising continuous variables

Measurements of continuous variables are made in all branches of medicine, aiding in the diagnosis and treatment of patients. In clinical practice it is helpful to label individuals as having or not having an attribute, such as being “hypertensive” or “obese” or having “high cholesterol,” depending on the value of a continuous variable. Categorisation of continuous variables is also common in clinical research, but here such simplicity is gained at some cost. Though grouping may help data presentation, notably in tables, categorisation is unnecessary for statistical analysis and it has some serious drawbacks. Here we consider the impact of converting continuous data to two groups (dichotomising), as this is the most common approach in clinical research.1 What are the perceived advantages of forcing all individuals into two groups? A common argument is that it greatly simplifies the statistical analysis and leads to easy interpretation and presentation of results. A …

Prognosis and prognostic research: Developing a prognostic model

In the second article in their series, Patrick Royston and colleagues describe different approaches to building clinical prognostic models

Prognosis and prognostic research: what, why, and how?

Doctors have little specific research to draw on when predicting outcome. In this first article in a series Karel Moons and colleagues explain why research into prognosis is important and how to design such research