Summary Measures for Clinical Trials with Survival Outcomes

Description

ClinicalTrialSummary provides estimates of several summary measures of the treatment effect for design and analysis of clinical trials with survival outcomes, introduced in Yang (2018). 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.

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 and the control group, respectively. The main function of the package, ypsummary, provides following five summary measures:

• the average hazard ratio (AHR): \int hr(x) dx

• the weighted average hazard ratio (WAHR): \int hr(x) dw(x) where dw(x) = dF_c(x)/F_c(\tau)

• the restricted superiority probability ratio (RSPR): \frac{\int S_c(x) dF_t(x)}{\int St(x) dF_c(x)}

• the restricted mean survival difference (RMSD): \int S_t(x) dx - \int S_c(x) dx

• the ratio of restricted mean times lost (RRMTL): \frac{\tau - \int S_t(x) dx}{\tau - \int S_c(x) dx}

Note that all integrals are taken over (0, \tau) for \tau less than or equal to the maximum follow-up duration of the trial. The asymptotic results for the average hazard ratio and the restricted mean survival difference were established in Yang and Prentice (2011) and Yang (2013), respectively. For other measures, the asymptotic results were established in Yang (2018).

The data used as an example in this package was from Gastrointestinal Tumor Study Group (1982) and the object returned by ypsummary can be formatted to a table using the function summary.

Details

Author(s)

Daewoo Pak and Song Yang

References

Yang, S. (2018). Improving testing and description of treatment effect in clinical trials with survival outcomes. Statistics in medicine.

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.

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

See Also

ypsummary

Examples

	library(ClinicalTrialSummary)
	data(ggas)
	result <- ypsummary(time=ggas$time, event=ggas$event, group=ggas$group, tau = 8.2)
	print(result)
	summary(result)

Internal Functions for Summary Measures for Clinical Trials with Survival Outcomes

Description

Internal functions for the ClinicalTrialSummary package.

Data from Gastrointestinal Tumor Study Group (1982)

Description

The Gastrointestinal Tumor Study Group (1982) compared chemotherapy with combined chemotherapy and radiation therapy, in the treatment of locally unresectable gastric cancer. Each treatment arm had 45 patients, with two observations of the chemotherapy group and six of the combination group censored. The plot of Kaplan-Meier survival curves show that the two curves cross at around 1000 days.

Usage

data(ggas)

Format

The data has the following information for the ninety subjects:

time

the vector for the pooled lifetimes of the two groups

event

the numeric vector of the right-censoring indicator (event = 1, censored = 0)

group

the numeric vector of the group indicator (treatment = 1, control = 0)

References

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

See Also

ypsummary

Examples

library(ClinicalTrialSummary)
data(ggas)

The main function of the package provides five summary measures of the treatment effect for clinical trials.

Description

ypsummary provides estimates of several summary measures of the treatment effect for design and analysis of clinical trials with survival outcomes, introduced in Yang (2018). The function utilizes the short-term and long-term hazard ratio model proposed in Yang and Prentice (2005), which can acccomodate various nonproportional hazard scenarios. The asymptotic properties of the summary measures are also discussed in Yang and Prentice (2011), Yang (2013), and Yang (2018).

Usage

## Default S3 method:
ypsummary(time, event, group, tau, alpha = 0.05, tie = TRUE, 
    bound = 50, repnum = 2000, ...)

Arguments

Details

The function ypsummary provides five summary measures of the treatment effect (see, Yang 2018), which can be utilized for various nonproportional haards scenarios:

• the average hazard ratio (AHR): \int hr(x) dx

• the weighted average hazard ratio (WAHR): \int hr(x) dw(x) where dw(x) = dF_c(x)/F_c(\tau)

• the restricted superiority probability ratio (RSPR): \frac{\int Sc(x) dF_t(x)}{\int S_t(x) dF_c(x)}

• the restricted mean survival difference (RMSD): \int S_t(x) dx - \int S_c(x) dx

• the ratio of restricted mean times lost (RRMTL): \frac{\tau - \int S_t(x) dx}{\tau - \int S_c(x) dx}

where hr(x) is the hazard ratio of the treatment group over the control group, F_t(x) and F_c(x) are the distribution functions for the treatment group and control group, respectively, and S_t(x) = 1 - F_t(x) and S_c(x) = 1 - F_c(x). Note that all integrals are taken from 0 to \tau.

Value

References

Yang, S. (2018). Improving testing and description of treatment effect in clinical trials with survival outcomes. Statistics in medicine.

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.

Examples

library(ClinicalTrialSummary)
data(ggas)
time <- ggas$time
event <- ggas$event
group <- ggas$group
result <- ypsummary(time, event, group, tau=8.2) # tau must be supplied.
result
summary(result)