A Novel Tool for Visualizing Composite Endpoint Associations
Composite end points play a major role in cardiovascular clinical epidemiology, with many studies examining, for example, the time to the first major adverse cardiac event. Beyond the cardiovascular field, progression-free survival is an important outcome in oncology, and even general mortality can be considered a composite of cause-specific mortalities. Although the common application of composite end points supports their popularity and usefulness, disadvantages and caveats also have been pointed out.1 One difficulty in composite end point studies is the transparent reporting of results in an accessible way, most authors suggesting the side-to-side reporting of results pertaining to separate analyses of the composite end point and its individual components.
Composite end point associations depend on the individual component associations in a complex way. Study duration may further complicate this through 2 main mechanisms. First, the association with any of the component outcomes may be time-varying. Second, the relative importance of the component outcomes may change with time.2 Such study duration–dependent issues are likely to affect a substantial proportion of composite end point studies, but current analysis and reporting practices might often fail to reveal this. Thus, a straight-forward graphical summary of composite end point associations was sought, which would readily disclose such time-varying aspects of composite and underlying component associations. The longitudinal β plot here suggested might be used to this end, providing a simple tool for exploration and communication.
The longitudinal β plot is motivated by the so-called time-dependent coefficient plot, which is commonly used to assess the proportional hazards assumption (ie, that the hazard ratio of some predictors is constant throughout follow-up).3 In brief, a time-dependent coefficient plot shows the development of the predictor outcome association over time, giving a straight horizontal line if the association is perfectly constant. By combining the time-dependent association estimate of a composite end point analysis with time-dependent estimates of the underlying component outcomes, the longitudinal β plot reveals how the composite end point association evolves and changes as a result of the underlying component outcome associations. Generally speaking, changes in the composite end point association may be caused by changes in the strength of either or both component associations or by changes in the relative frequency of the component end points, as demonstrated in the toy example provided in the Data Supplement alongside some more technical comments.
To provide an instructive real-life example for the application of the longitudinal β plot, freely available data of the International Stroke Trial were examined (see Data Supplement for further information and funding).4 In brief, and not to be overinterpreted with respect to the subject matter, the age-adjusted association of impaired consciousness (24% prevalence) with all-cause mortality after ischemic stroke was analyzed (analysis data set featuring 13 780 subjects with median follow-up 185 days; 1651 and 1655 cerebrovascular and noncerebrovascular deaths, respectively). Figure (A) shows a standard time-dependent coefficient plot for this model, suggesting a somewhat larger association during the first weeks of follow-up. Figure (B) shows the longitudinal β plot for the same association, treating all-cause mortality as a composite of cerebrovascular and noncerebrovascular mortality. This plot reveals that the stronger association of impaired consciousness with all-cause mortality (shown by the black solid line) during early follow-up was almost exclusively because of a stronger association with cerebrovascular mortality (represented by the red dashed line) during this time period. The association with noncerebrovascular mortality (blue dotted line) was rather constant throughout the study, hardly explaining the stronger association with the composite end point during early follow-up.
Conventional hazard ratio estimates (95% CIs) for these associations would have been 3.8 (3.6–4.1; all-cause mortality), 5.2 (4.7–5.7; cerebrovascular mortality), and 2.8 (2.6–3.1; noncerebrovascular mortality). A significant violation of the proportional hazards assumption was detected for all 3 models using standard testing procedures.3 Often, this would only be briefly mentioned in the methods, results, or limitations section, with an ultimate statement that the reported hazard ratios present some kind of averaged estimates and thus may be interpreted as suggesting an overall much stronger association of impaired consciousness with cerebrovascular than noncerebrovascular or all-cause mortality. The longitudinal β plot, however, suggested that this stronger association was limited to early follow-up, whereas the associations converge later on. Standard reporting practices in such a situation may be insufficient and misleading. They could insightfully be complemented by the graphical approach proposed.
As demonstrated in the above example, the longitudinal β plot has the potential to convey much more information than conventional summaries or tabulations at a glance. It seems rather intuitive even without statistical background and hopefully provides a useful tool for exploratory composite end point analyses and accessible communication of complex longitudinal composite end point patterns. Some open issues remain, for example, alternative choices for estimating the smoothing lines or limited clarity if more than 2 components are to be visualized.
All analyses presented here were done using R 3.3.2 (R Foundation for Statistical Computing 2016, Vienna, Austria) and the extension package survival.3 Figure (A) shows standard output of a function for testing the Cox proportional hazards assumption, whereas Figure (B) was drawn using a simple custom function. Example code for a 2-component composite end point is available as a Data Supplement.
The Data Supplement is available at http://circoutcomes.ahajournals.org/lookup/suppl/doi:10.1161/CIRCOUTCOMES.117.004226/-/DC1.
Circ Cardiovasc Qual Outcomes is available at http://circoutcomes.ahajournals.org.
- © 2018 American Heart Association, Inc.
- Ferreira-González I,
- Permanyer-Miralda G,
- Busse JW,
- Bryant DM,
- Montori VM,
- Alonso-Coello P,
- Walter SD,
- Guyatt GH
- Breitling LP,
- Mons U,
- Hahmann H,
- Koenig W,
- Rothenbacher D,
- Brenner H
- Therneau TM,
- Grambsch PM