Statistical issues in the analysis of outcomes in critical care medicine

Abstract

1.1 The focus of this thesis will be the nexus of statistical methods and clinical practice, as it applies to Critical Care Medicine and is reflected in the literature ( for instance : Anaesthesia and Intensive Care ( Anaesthesia and Intensive Care 2005 ) and Critical Care & Resuscitation ( Critical Care and Resuscitation 2005 ) in Australia ; and internationally : Critical Care Medicine ( Critical Care Medicine 2005 ), Intensive Care Medicine ( Intensive Care Medicine 2005 ), Chest ( Chest 2005 ), American Journal of Respiratory and Critical Care Medicine ( American Journal of Respiratory and Critical Care Medicine 2005 ) and Journal of the American Medical Association ( JAMA 2005 ) ). 1.2 Altman has documented the career of statistics in medical journals over a 20 year period and has lamented the general state of affairs ( Altman 1982 ; Altman 1991b ; Altman 1994 ; Altman 2000 ). The transfer of statistical techniques into medical literature is characterised by a significant lag - time ( Altman et al. 1994b ) and statistical input into medical research and publication, although " widely recommended ... ( is ) ... inconsistently obtained " ( Altman et al. 2002 ), perhaps reflecting an undervaluation of statistical contributions to medicine, as articulated by one of the doyen ' s of biostatistics, Norman Breslow ( Breslow 2003 ). The latter observed that, as opposed to the awarding of a Nobel Prize ( in 2000 ) to econometricians Daniel McFadden and James Heckman for work on discrete choice models and selection bias, similar contributions to medicine by statisticians and epidemiologists have been, as yet, unrecognized. 1.3 Our comparators in statistical " critique " ( Berk 2004 ; BROSS 1960 ) are drawn from analytic approaches, more than thirty years apart. First, the lucid contributions of Jerome Cornfield ( Greenhouse 1982 ) ; in particular : the classic intervention ( in 1959 ) into the tobacco smoking / lung cancer debate " Smoking and lung cancer : recent evidence and a discussion of some questions " ( Cornfield et al. 1959 ) ; and " Further statistical analysis of the mortality findings " of the University Group Diabetes Program ( Cornfield 1971 ), which was an elegant response to the controversy which raged ( for some years ( Kolata 1979 ) ) over the discontinuance of tolbutamide and diet arm in that trial. The textual lucidity to which we refer was presumably a function of the literary background of Cornfield, as documented in the classic review by Salsburg of the rise of the modern statistical paradigm in the twentieth century ( Salsburg 2001 ). Second, the muscular re - examination, or rather, dissection, by Freedman et al ( Freedman et al. 2004 ) of the controversy surrounding breast cancer screening and its efficacy ; being a detailed reading of the meta - analysis by Gotszche and Olsen ( Gotzsche et al. 2000 ), who had questioned the role of mammography in breast cancer screening in terms of potential lives saved. Third, the subtle 1994 reappraisal by Petitti of the mortality treatment effect of patient " compliance " in randomized trials, as it related to both therapy and placebo groups in the Coronary Drug Project ( The Coronary Drug Project Research Group 1981 ) and the Beta - blocker Heart Attack Trial ( Byington 1984 ). The demonstration that the ( cardiovascular ) mortality reduction of compliance with placebo was of the same magnitude as that experienced by users of oestrogen replacement therapy, followed the publication of a quantitative assessment of the of the efficacy of oestrogen on coronary heart disease by Stampfer and Colditz, in which a relative risk of 0.56 ( 95 % CI 0.5 - 0.61 ) was postulated ( Stampfer et al. 1991 ). Petitti ' s review anticipated the null effects ( of replacement oestrogen ) demonstrated in the subsequent randomized trials of the Women ' s Health Initiative ( The Women ' s Health Initiative Study Group 1998 ). These null effects caused extensive debate and some degree of angst in the epidemiological literature and the consequent death of observational epidemiology was rhetorically announced ( Lawlor et al. 2004 ). 1.4 The thesis is divided into two parts: 1.4.1 First, a detailed expository analysis of various questions relating to the interpretation of the results of recent noteworthy trials in the medical and Critical Care literature. Initially we come to terms with the seemingly intractable P - value question which has regularly surfaced in the literature over the years. We also address the thorny but perennial parametric versus non - parametric test controversy. Next we look at the methodology of recent trials in Critical Care and find some problematic areas in terms of interim analyses and the reporting of results. These concerns are expanded into a detailed consideration of the issues surrounding group sequential and equivalence trials. The subsequent section analyses particular aspects of ( i ) effect size ( ii ) prognostic factors and responsiveness ( iii ) sample size, power and interpretation of trials and we conclude ( iv ) with a critique of various aspects of Critical Care practice, as it relates to certain key trials and overviews ( meta - analyses ) of these trials : the PROWESS trial of activated protein C in sepsis ; hypothermia as therapy in cerebral injury ; selective decontamination of the digestive tract ; and nutrition as therapy. 1.4.2 Second, concrete focused analyses are performed on particular datasets and particular statistical techniques are subject to scrutiny. The first encompasses multivariate analysis of phosphate metabolism in ICU patients ; in particular, issues relating to regression to the mean, appropriate estimators ( ordinary least squares or generalized linear models ), model and variable selection, and missing data. The second looks at the analysis of cost data and explores the use of generalized linear models as appropriate estimators. The third introduces time - to - event analysis in and reviews the use of the Cox model and random effects estimators in a data set of patients with malignancies. The fourth is a in depth analysis of three aspects of meta - analysis as it applies in the Critical Care field : heterogeneity, publication bias and metaregression. 1.5 In this endeavour, we are mindful of certain cautions regarding treatment effects : ( i ) it is reasonable to find odds ratio ( s ) below 0.6 " extremely surprising " ( Speigelhalter et al. 2004 ) ( ii ) " If a result appears too good to be true, it probably is " ( Yusuf 1997 ) and ( iii ) we may " require that data indicate an increased relative risk for a characteristic of at least 50 percent, on the assumption that an excess of this magnitude would not arise from extraneous factors alone " ( Mantel et al. 1959 ). The latter proposition was first articulated in 1959 by Mantel and Haenszel, but needed to be reiterated ( by Mantel ) some thirty four years later ( Mantel 1993 ). Finally, we endorse the admonition of Jerome Cornfield that " Any set of hospital or clinical data that is worth analysing at all is worth analysing properly " ( Cornfield 1951). 1.6 The importance of statistical principles in both the interpretation and conduct of analysis would seem to be obvious and we must " grapple " with statistics in the same manner as Appleby urged with respect to health economics ( Appleby 1987 ). To this extent, the evidence - based - medicine movement has mandated " critical appraisal ", which incorporates, to varying degree, statistical methods ( Morris 2002b ) and at least one prominent medical journal has recently welcomed papers " detailing important contributions in the design of studies or analysis of epidemiological data " ( Dominici et al. 2004 ). Thus statistics is increasingly engaged with " front - line science " ( Efron 2005 ) and these recent trends prefigure the overall thrust of the sections below.