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### The estimation of average hazard ratios by weighted Cox regression

### The estimation of average hazard ratios by weighted Cox regression

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Schemper, M., Wakounig, S. & Heinze, G. (2009): *Statistics in Medicine* 28, 2473 - 2489

Often the effect of at least one of the prognostic factors in a Cox regression model changes over time, which violates the proportional hazards assumption of this model. As a consequence, the average hazard ratio for such a prognostic factor is under- or overestimated. While there are several methods to appropriately cope with non-proportional hazards, in particular by including parameters for time-dependent effects, weighted estimation in Cox regression is a parsimonious alternative without additional parameters. The methodology, which extends the weighted k-sample logrank tests of the Tarone-Ware scheme to models with multiple, binary and continuous covariates, has been introduced in the nineties of the last century and is further developed and reevaluated in this contribution. The notion of an average hazard ratio is defined and its connection to the effect size measure emphasized. The suggested approach accomplishes estimation of intuitively interpretable average hazard ratios and provides tools for inference. A Monte Carlo study confirms satisfactory performance. Advantages of the approach are exemplified by comparing standard and weighted analyses of an international lung cancer study. SAS and R programs facilitate application.

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Schemper, M., Wakounig, S. & Heinze, G. (2009): *Statistics in Medicine* 28, 2473 - 2489

Often the effect of at least one of the prognostic factors in a Cox regression model changes over time, which violates the proportional hazards assumption of this model. As a consequence, the average hazard ratio for such a prognostic factor is under- or overestimated. While there are several methods to appropriately cope with non-proportional hazards, in particular by including parameters for time-dependent effects, weighted estimation in Cox regression is a parsimonious alternative without additional parameters. The methodology, which extends the weighted k-sample logrank tests of the Tarone-Ware scheme to models with multiple, binary and continuous covariates, has been introduced in the nineties of the last century and is further developed and reevaluated in this contribution. The notion of an average hazard ratio is defined and its connection to the effect size measure emphasized. The suggested approach accomplishes estimation of intuitively interpretable average hazard ratios and provides tools for inference. A Monte Carlo study confirms satisfactory performance. Advantages of the approach are exemplified by comparing standard and weighted analyses of an international lung cancer study. SAS and R programs facilitate application

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