Methods to evaluate risks for composite end points and their individual components

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Abstract

Objective

Both randomized and observational studies commonly examine composite end points, but the literature on model development and criticism in this setting is limited.

Study Design and Setting

We examined approaches for evaluating heterogeneity in the effects of risk factors for different components of the end point, and determining the impact of heterogeneity on the ability to predict the composite end point. A specific example considered the composite cardiovascular disease end point in the Physicians' Health Study that occurred in 1,542 (myocardial infarction, n = 716; stroke, n = 557; cardiovascular death, n = 269) of 16,688 participants with complete information on baseline covariates. The strategy compared alternative polytomous logistic regression models assuming different effects of risk factors on components of the end point and a comparable logistic model assuming common effects.

Results

Likelihood ratio tests identified heterogeneity in the effects of age, alcohol consumption, and diabetes across components of the outcome, but comparability in the effects of other risk factors. However, a model assuming uniform effects explained over 90% of the log-likelihood change in the best polytomous model, and the two models also performed similarly based on a comparison of ROC curves.

Conclusion

The overall strategy may be helpful for evaluating the validity of a composite end point analysis and identifying heterogeneity in risk factors.

Introduction

Both clinical trials and observational studies commonly examine end points that are composed of several related, but distinct, diseases. For example, the randomized, double-blind, placebo-controlled Physicians' Health Study evaluated 325 mg aspirin every other day for the primary prevention of cardiovascular disease including a first myocardial infarction, stroke, or cardiovascular death with no prior myocardial infarction or stroke, as well as the effect of 50 mg beta carotene on alternate days for prevention of cancer, including cancer at any site other than nonmelanoma skin cancer [1], [2]. Use of a composite end point can substantially enhance statistical power if an exposure of interest has a fairly uniform effect on each component of the end point. Furthermore, consideration of a composite end point gives a broad evaluation of the benefits or risks of an intervention. However, use of a composite end point can also obscure differences between the relationships of an exposure with the different components. Consideration of these differences can help to clarify disease mechanisms and also aid in generalizing study findings to other populations where the distributions of both exposures and outcomes may differ. For example, if a risk factor has a different effect on stroke than on myocardial infarction, then the association of this factor with the composite end point will differ across populations with differing relative numbers of strokes vs. myocardial infarctions.

In this article we compare alternative approaches to evaluate the relationship of risk factors with a composite end point and to identify heterogeneity in the effects of factors across the individual disease components. We illustrate the methods with data on risk factors for cardiovascular end points in the Physicians' Health Study. Previous work, notably from the Framingham Heart Study, has developed separate risk prediction models for separate components of cardiovascular disease [3], [4], [5], [6], and noted some similarities as well as differences in the coefficients in these models [7], [8].

Approaches used in the applied cardiovascular disease literature to evaluate heterogeneity in the effects of risk factors for different disease components have included comparisons of standardized regression coefficients or magnitudes of statistical significance [7], [9], [10]. Limitations of these strategies include the dependence of levels of statistical significance on numbers of events for each component of the outcome, the dependence of standardized regression coefficients on study-specific variability in risk factors [11], [12], and the correlations among relative risk estimates for different components arising from the common reference group of persons remaining disease free. Thus, formal comparisons of the coefficients from these alternative models are limited. Also unclear is the relative predictive ability of a model for the composite end point compared to prediction from disease-specific models. Thus, we suggest comparisons of ROC curves and measures of explained variation as more appropriate approaches to compare models assuming uniform and heterogeneous effects of risk factors on different disease components.

Section snippets

Materials and methods

The subjects and methods of the Physicians' Health Study, a 2×2 factorial trial of aspirin and β-carotene for the primary prevention of cardiovascular disease or cancer, have been described previously [1], [2]. Briefly, the trial randomized 22,071 U.S. male physicians, aged 40 to 84 years in 1982, who had no history of myocardial infarction, stroke, transient cerebral ischemia, cancer (except nonmelanoma skin cancer), current renal or liver disease, peptic ulcer, or gout. At baseline,

Results

At baseline, the 16,688 participants in this study had a mean age of 53.5 years, a mean systolic (diastolic) blood pressure of 126.1 (78.8) mmHg, and a mean body mass index of 24.9 kg/m2; 10.9% of subjects were current smokers and 2.6% had previously diagnosed diabetes mellitus. Consistent with previous studies in this and other populations, all variables were significantly associated with the development of the composite end point, except for former cigarette smoking (Table 1). Inclusion of a

Discussion

A variety of approaches are used in the applied literature to evaluate the relationship of risk factors with a composite end point and compare the effects of a risk factor on different components of the end point. Perhaps the most commonly used strategy, applicable to both retrospective and prospective studies, is to fit separate models comparing each component of the disease to the common reference group of persons remaining disease free. Advantages of this approach include the accessibility

Acknowledgements

This work was supported by grants R01-EY08103 from the National Eye Institute and P01-CA87969 from the National Cancer Institute, Bethesda, MD.

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