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- W2099456211 abstract "Background: Clinical trials with time to event outcomes are often designed utilizing the Cox [1] proportional hazard model with a hazard ratio parameter Δ. Purpose: The purpose of this article is to demonstrate that a Cox proportional hazard model with a hazard ratio parameter is equivalent to a Cox proportional hazard model with a parameter equal to the probability that a patient given one treatment will have an event earlier than if the same patient were given a different treatment. This probability will subsequently be referred to as θ. Clinically interesting differences between the treatment arms are easier for researchers to quantify in terms of θ in situations where they have a difficult time with the hazard ratio, allowing better communication between the statistician and the researcher. Methods: The problem and its solution are demonstrated mathematically. The utility of the Cox proportional hazard model in terms of θ is illustrated through a Lymphoma clinical trial example. Results: The Cox proportional hazard model with parameter θ is shown to be equivalent to the Cox proportional hazard model with a hazard ratio parameter Δ. A table of typical hazard ratios Δ is presented with their equivalent θ values. In the appendix the mathematical derivations are developed and an unbiased estimate of θ is provided using Gehan's [2] generalization of the Wilcoxon statistic. Limitations: The equivalence of the Cox proportional hazard model in terms of the probability θ and the hazard ratio Δ is established only for continuous failure times with a single binary covariate. Conditions under which approximate equivalence holds with multiple covariates are discussed in the Appendix. Conclusions: The probability θ provides a natural parameterization for the Cox proportional hazard model, affords a tool to conceptualize treatment differences, and provides a method to improve communication between statisticians and researchers. Clinical Trials 2008; 5: 248—252. http://ctj.sagepub.com" @default.
- W2099456211 created "2016-06-24" @default.
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- W2099456211 date "2008-06-01" @default.
- W2099456211 modified "2023-10-02" @default.
- W2099456211 title "Reformulating the hazard ratio to enhance communication with clinical investigators" @default.
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- W2099456211 doi "https://doi.org/10.1177/1740774508091452" @default.
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