Longitudinal studies, where data are repeatedly collected on subjects over a period, are common in medical research. When estimating the effect of a time-varying treatment or exposure on an outcome of interest measured at a later time, standard methods fail to give consistent estimators in the presence of time-varying confounders if those confounders are themselves affected by the treatment. Robins and colleagues have proposed several alternative methods that, provided certain assumptions hold, avoid the problems associated with standard approaches. They include the g-computation formula, inverse probability weighted estimation of marginal structural models and g-estimation of structural nested models. In this tutorial, we give a description of each of these methods, exploring the links and differences between them and the reasons for choosing one over the others in different settings.

In diverse fields of empirical research—including many in the biological sciences—attempts are made to decompose the effect of an exposure on an outcome into its effects via a number of different pathways. For example, we may wish to separate the effect of heavy alcohol consumption on systolic blood pressure (SBP) into effects via body mass index (BMI), via gamma-glutamyl transpeptidase (GGT), and via other pathways. Much progress has been made, mainly due to contributions from the field of causal inference, in understanding the precise nature of statistical estimands that capture such intuitive effects, the assumptions under which they can be identified, and statistical methods for doing so. These contributions have focused almost entirely on settings with a single mediator, or a set of mediators considered en bloc; in many applications, however, researchers attempt a much more ambitious decomposition into numerous path-specific effects through many mediators. In this article, we give counterfactual definitions of such path-specific estimands in settings with multiple mediators, when earlier mediators may affect later ones, showing that there are many ways in which decomposition can be done. We discuss the strong assumptions under which the effects are identified, suggesting a sensitivity analysis approach when a particular subset of the assumptions cannot be justified. These ideas are illustrated using data on alcohol consumption, SBP, BMI, and GGT from the Izhevsk Family Study. We aim to bridge the gap from “single mediator theory” to “multiple mediator practice,” highlighting the ambitious nature of this endeavor and giving practical suggestions on how to proceed.

Summary Survival analysis has found widespread applications in medicine in the last 10-15 years. However, there has been no published review of the use and presentation of survival analyses. We have carried out a systematic review of the research papers published between October and December 1991 in five clinical oncology journals. A total of 132 papers were reviewed. We looked at several aspects of study design, data handling, analysis and presentation of the results. We found that almost half of the papers did not give any summary of length of follow-up; that in 62% of papers at least one end point was not clearly defined; and that both logrank and multivariate analyses were frequently reported at most only as P-values [63/84 (75%) Survival analysis has found widespread applications in medicine in the last 10-15 years (Andersen, 1991), particularly in clinical oncology, and its correct application and presentation is critically relevant for much of the cancer literature. Although the use of statistical methods in medicine has been subjected to much scrutiny (see Altman, 1982Altman, , 1991, we believe that there has not been any published review of the use of survival analysis methods in medical journals. Hence, we have carried out a systematic review of the appropriateness of the application and presentation of survival analyses in clinical oncology journals. We have focused on the size of the studies being published, the adequacy of the description of the data analysed (with particular interest given to the length and quality of follow-up and the clarity of the end points of interest) and the choice and quality of univariate, multivariate and graphical analyses. In the light of disappointing findings, we discuss existing guidelines and present some new guidelines aimed in particular at presentation. MethodsWe examined all papers published in British Journal of Cancer, European Journal of Cancer, Journal of Clinical Oncology and American Journal of Clinical Oncology between October and December 1991 which included analyses of survival data. There were 132 papers which reported at least one of the following: Kaplan-Meier or actuarial survival curves; logrank or related tests; parametric or semiparametric survival analyses. Those papers with survival data which did not present any of these analyses, and thus were not included, were largely phase I or II clinical trials.The 132 papers were reviewed using a standard form that had been tested in a small pilot study of 20 papers which were read by all four authors. When the form was finalised each paper was read by two of the authors according to a balanced randomisation scheme. Disagreements between reviewers were resolved in paired discussions and by discussion between all four reviewers on the rare occasions when it was necessary.The assessment form included separate sections relating to distinct aspects of each paper. It also included the time taken by each author to extract the information from the paper onto the form as an indication of the clarity of each...

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