Summary Measures for Clinical Trials with Survival Outcomes

Provides estimates of several summary measures for clinical trials including the average hazard ratio, the weighted average hazard ratio, the restricted superiority probability ratio, the restricted mean survival difference and the ratio of restricted mean times lost, based on the short-term and long-term hazard ratio model (Yang, 2005 ) which accommodates various non-proportional hazards scenarios. The inference procedures and the asymptotic results for the summary measures are discussed in Yang (2018, ).

ClinicalTrialSummary provides estimates of several summary measures for assessing the treatment effect in comparison of two groups. These estimates are obtained under the short-term and long-term hazard ratio model (Yang and Prentice, 2005) which allows a range of time-varying hazard ratio shapes including crossing hazards situations.

Summary Measures

Let $hr(x) = \lambda_{t}(x)/\lambda_{c}(x)$ be the hazard ratio function, where $\lambda_t(x)$ and $\lambda_c(x)$ are the hazard functions for the treatment group ($t$) and the control group ($c$), respectively.

  • The average hazard ratio (AHR): $\int _{0}^{\tau} hr(x) dx$

  • The weighted average hazard ratio (WAHR): $\int_{0}^{\tau} hr(x) dw(x)$ where $dw(x) = dF_c(x)/F_c(\tau)$

  • The restricted superiority probability ratio (RSPR): $\frac{\int_{0}^{\tau} S_c(x) dF_t(x)}{\int_{0}^{\tau} S_t(x) dF_c(x)}$

  • The restricted mean survival difference (RMSD): $\int_{0}^{\tau} S_t(x) dx - \int_{0}^{\tau} S_c(x) dx$

  • The ratio of restricted mean times lost (RMSR): $\frac{\tau - \int_{0}^{\tau} S_t(x) dx}{\tau - \int_{0}^{\tau} S_c(x) dx}$

Here, $\tau$ is the value less than or equal to the maximum follow-up duration of the trial. The asymtoptic results for the average hazard ratio and the restricted mean survival were established in Yang and Prentice (2011) and Yang (2013), respectively. The asymtoptic results for other measures were established in Yang (2017).




result <- ypsummary(time=ggas$time, event=ggas$event, group=ggas$group, tau=8.2)

The data "ggas" is from Gastrointestinal Tumor Study Group (1982) and the value for tau must be user-specified. The object result can be formatted to a table using the function summary.



Yang S, and Ross L. Prentice (2005). Semiparametric analysis of short-term and long-term hazard ratios with two-sample survival data. Biometrika, 92.1:1-17.

Yang S, and Ross L. Prentice (2011). Estimation of the 2-sample hazard ratio function using a semiparametric model. Biostatistics, 12.2:354-368.

Yang S. (2013). Semiparametric inference on the absolute risk reduction and the restricted mean survival difference in clinical trials. Special issue on risk assessment. Lifetime Data analysis, 19:219-241.

Yang, S (2017). Improving testing and description of treatment effect in clinical trials with survival outcomes. Pre-print.

Gastrointestinal Tumor Study Group (1982). A comparison of combination chemotherapy and combined modality therapy for locally advanced gastric carcinoma. Cancer.


ClinicalTrialSummary 0.1.0

  • The initial version.

Reference manual

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1.1.1 by Daewoo Pak, a month ago

Browse source code at

Authors: Daewoo Pak and Song Yang

Documentation:   PDF Manual  

GPL (>= 3) license

Imports Rcpp

Linking to Rcpp

See at CRAN