A simulation-based evaluation of the asymptotic power formulas for cox models in small sample cases

Mehmet Kocak, Arzu Onar-Thomas

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Cox proportional hazards (PH) models are commonly used in medical research to investigate the associations between covariates and time-to-event outcomes. It is frequently noted that with less than 10 events per covariate, these models produce spurious results and therefore should not be used. Statistical literature contains asymptotic power formulas for the Cox model which can be used to determine the number of events needed to detect an association. Here, we investigate via simulations the performance of these formulas in small sample settings for Cox models with one or two covariates. Our simulations indicate that when the number of events is small, the power estimate based on the asymptotic formula is often inflated. The discrepancy between the asymptotic and empirical power is larger for the dichotomous covariate especially in cases where allocation of sample size to its levels is unequal. When more than one covariate is included in the same model, the discrepancy between the asymptotic power and the empirical power is even larger, especially when a high positive correlation exists between the two covariates.

Original languageEnglish (US)
Pages (from-to)173-179
Number of pages7
JournalAmerican Statistician
Volume66
Issue number3
DOIs
StatePublished - Nov 2 2012

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Asymptotic Power
Cox Model
Small Sample
Covariates
Evaluation
Simulation
Discrepancy
Cox Proportional Hazards Model
Unequal
Asymptotic Formula
Cox model
Small sample
Sample Size
Model
Estimate

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Cite this

A simulation-based evaluation of the asymptotic power formulas for cox models in small sample cases. / Kocak, Mehmet; Onar-Thomas, Arzu.

In: American Statistician, Vol. 66, No. 3, 02.11.2012, p. 173-179.

Research output: Contribution to journalArticle

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