### Abstract

Background: Restricted mean survival time is a measure of average survival time up to a specified time point. There has been an increased interest in using restricted mean survival time to compare treatment arms in randomized clinical trials because such comparisons do not rely on proportional hazards or other assumptions about the nature of the relationship between survival curves. Methods: This article addresses the question of whether covariate adjustment in randomized clinical trials that compare restricted mean survival times improves precision of the estimated treatment effect (difference in restricted mean survival times between treatment arms). Although precision generally increases in linear models when prognostic covariates are added, this is not necessarily the case in non-linear models. For example, in logistic and Cox regression, the standard error of the estimated treatment effect does not decrease when prognostic covariates are added, although the situation is complicated in those settings because the estimand changes as well. Because estimation of restricted mean survival time in the manner described in this article is also based on a model that is non-linear in the covariates, we investigate whether the comparison of restricted mean survival times with adjustment for covariates leads to a reduction in the standard error of the estimated treatment effect relative to the unadjusted estimator or whether covariate adjustment provides no improvement in precision. Chen and Tsiatis suggest that precision will increase if covariates are chosen judiciously. We present results of simulation studies that compare unadjusted versus adjusted comparisons of restricted mean survival time between treatment arms in randomized clinical trials. Results: We find that for comparison of restricted means in a randomized clinical trial, adjusting for covariates that are associated with survival increases precision and therefore statistical power, relative to the unadjusted estimator. Omitting important covariates results in less precision but estimates remain unbiased. Conclusion: When comparing restricted means in a randomized clinical trial, adjusting for prognostic covariates can improve precision and increase power.

Original language | English (US) |
---|---|

Pages (from-to) | 178-188 |

Number of pages | 11 |

Journal | Clinical Trials |

Volume | 15 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2018 |

### Fingerprint

### Keywords

- Restricted mean
- covariate adjustment
- efficiency
- power

### ASJC Scopus subject areas

- Pharmacology

### Cite this

}

*Clinical Trials*, vol. 15, no. 2, pp. 178-188. https://doi.org/10.1177/1740774518759281

**Restricted mean survival time : Does covariate adjustment improve precision in randomized clinical trials?** / Karrison, Theodore; Kocherginsky, Masha.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Restricted mean survival time

T2 - Does covariate adjustment improve precision in randomized clinical trials?

AU - Karrison, Theodore

AU - Kocherginsky, Masha

PY - 2018/4/1

Y1 - 2018/4/1

N2 - Background: Restricted mean survival time is a measure of average survival time up to a specified time point. There has been an increased interest in using restricted mean survival time to compare treatment arms in randomized clinical trials because such comparisons do not rely on proportional hazards or other assumptions about the nature of the relationship between survival curves. Methods: This article addresses the question of whether covariate adjustment in randomized clinical trials that compare restricted mean survival times improves precision of the estimated treatment effect (difference in restricted mean survival times between treatment arms). Although precision generally increases in linear models when prognostic covariates are added, this is not necessarily the case in non-linear models. For example, in logistic and Cox regression, the standard error of the estimated treatment effect does not decrease when prognostic covariates are added, although the situation is complicated in those settings because the estimand changes as well. Because estimation of restricted mean survival time in the manner described in this article is also based on a model that is non-linear in the covariates, we investigate whether the comparison of restricted mean survival times with adjustment for covariates leads to a reduction in the standard error of the estimated treatment effect relative to the unadjusted estimator or whether covariate adjustment provides no improvement in precision. Chen and Tsiatis suggest that precision will increase if covariates are chosen judiciously. We present results of simulation studies that compare unadjusted versus adjusted comparisons of restricted mean survival time between treatment arms in randomized clinical trials. Results: We find that for comparison of restricted means in a randomized clinical trial, adjusting for covariates that are associated with survival increases precision and therefore statistical power, relative to the unadjusted estimator. Omitting important covariates results in less precision but estimates remain unbiased. Conclusion: When comparing restricted means in a randomized clinical trial, adjusting for prognostic covariates can improve precision and increase power.

AB - Background: Restricted mean survival time is a measure of average survival time up to a specified time point. There has been an increased interest in using restricted mean survival time to compare treatment arms in randomized clinical trials because such comparisons do not rely on proportional hazards or other assumptions about the nature of the relationship between survival curves. Methods: This article addresses the question of whether covariate adjustment in randomized clinical trials that compare restricted mean survival times improves precision of the estimated treatment effect (difference in restricted mean survival times between treatment arms). Although precision generally increases in linear models when prognostic covariates are added, this is not necessarily the case in non-linear models. For example, in logistic and Cox regression, the standard error of the estimated treatment effect does not decrease when prognostic covariates are added, although the situation is complicated in those settings because the estimand changes as well. Because estimation of restricted mean survival time in the manner described in this article is also based on a model that is non-linear in the covariates, we investigate whether the comparison of restricted mean survival times with adjustment for covariates leads to a reduction in the standard error of the estimated treatment effect relative to the unadjusted estimator or whether covariate adjustment provides no improvement in precision. Chen and Tsiatis suggest that precision will increase if covariates are chosen judiciously. We present results of simulation studies that compare unadjusted versus adjusted comparisons of restricted mean survival time between treatment arms in randomized clinical trials. Results: We find that for comparison of restricted means in a randomized clinical trial, adjusting for covariates that are associated with survival increases precision and therefore statistical power, relative to the unadjusted estimator. Omitting important covariates results in less precision but estimates remain unbiased. Conclusion: When comparing restricted means in a randomized clinical trial, adjusting for prognostic covariates can improve precision and increase power.

KW - Restricted mean

KW - covariate adjustment

KW - efficiency

KW - power

UR - http://www.scopus.com/inward/record.url?scp=85045333014&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85045333014&partnerID=8YFLogxK

U2 - 10.1177/1740774518759281

DO - 10.1177/1740774518759281

M3 - Article

VL - 15

SP - 178

EP - 188

JO - Clinical Trials

JF - Clinical Trials

SN - 1740-7745

IS - 2

ER -