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Visualizing and analyzing time to event data: Lifting the veil of censoring

By Patrick Royston

Abstract

Most survival data are analyzed by using the Cox proportional hazards model (in Stata: the stcox command). Almost by definition, a proportion of the observations will be right-censored. Analysis of covariate effects in the Cox model is couched in terms of (log) hazard ratios, and the distribution of time itself is essentially ignored. This practice is totally different from standard analysis of a continuous outcome variable, where multiple (linear) regression is the technique most often used. Hazard ratios are difficult to interpret and give little insight into how a covariate affects the time to an event. Furthermore, the assumption of proportional hazards is strong, and when there is long-term follow-up, is often breached. I will illustrate how the censored lognormal model can be used to good effect to remedy some of these deficiencies and give better insight into the data. Multiple imputation of the censored observations may be followed by use of familiar exploratory graphical tools, such as dotplots, scatterplots, and scatterplot smoothers. Analyses using standard linear regression methods may be done on the log time scale, leading to simple interpretations and informative graphs of effect size. I will explore these ideas in the context of a familiar breast cancer dataset and will show how a treatment/covariate interaction is easily conveyed graphically.

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