### 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 language | English (US) |
---|---|

Pages (from-to) | 173-179 |

Number of pages | 7 |

Journal | American Statistician |

Volume | 66 |

Issue number | 3 |

DOIs | |

State | Published - Nov 2 2012 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*American Statistician*,

*66*(3), 173-179. https://doi.org/10.1080/00031305.2012.703873

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

Research output: Contribution to journal › Article

*American Statistician*, vol. 66, no. 3, pp. 173-179. https://doi.org/10.1080/00031305.2012.703873

}

TY - JOUR

T1 - A simulation-based evaluation of the asymptotic power formulas for cox models in small sample cases

AU - Kocak, Mehmet

AU - Onar-Thomas, Arzu

PY - 2012/11/2

Y1 - 2012/11/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84868016596&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868016596&partnerID=8YFLogxK

U2 - 10.1080/00031305.2012.703873

DO - 10.1080/00031305.2012.703873

M3 - Article

VL - 66

SP - 173

EP - 179

JO - American Statistician

JF - American Statistician

SN - 0003-1305

IS - 3

ER -