In olssol/psrwe: PS-Integrated Methods for Incorporating RWE in Clinical Studies

suppressMessages(require(psrwe, quietly = TRUE))
options(digits = 3)
set.seed(1000)

Introduction

In the psrwe, PS-integrated survival analyses in randomized controlled trials (RCTs) with augmenting control arm (Chen, et al., to be submitted) are also implemented in three functions:

psrwe_survkm() for treatment effect test (Com-Nougue, et al., 1993).
psrwe_survlrk() for log-rank test (Klein and Moeschberger, 2003; Peto and Peto, 1972).
psrwe_survrmst() for restricted mean survival time (RMST) test (Royston and Parmar, 2013; Uno, et al., 2014).

These tests are non-parametric approaches for comparing two treatments with time-to-event endpoints. Therefore, these tests are only implemented for RCTs with augmenting control arm.

Similar with the approaches: PSPP (Wang, et al., 2019), PSCL (Wang, et al., 2020), and PSKM (Chen, et al., 2022), the PS-integrated study design functions, psrwe_est() and psrwe_borrow(), below estimate PS model, set borrowing parameters, and determine discounting parameters for borrowing information for a two-arm RCT with augmenting control arm from RWD.

data(ex_dta_rct)
dta_ps_rct <- psrwe_est(ex_dta_rct,
                        v_covs = paste("V", 1:7, sep = ""),
                        v_grp = "Group", cur_grp_level = "current",
                        v_arm = "Arm", ctl_arm_level = "control",
                        ps_method = "logistic", nstrata = 5,
                        stra_ctl_only = FALSE)
ps_bor_rct <- psrwe_borrow(dta_ps_rct, total_borrow = 30)

PS-integrated treatment effect test

Similar with the single arm study example (in psrwe/demo/sec_4_4_ex.r and demo("sec_4_5_ex", package = "psrwe")), the code below evaluates two-arm RCT. The results show the treatment effect which is the survival difference between two arms at one year or 365 days.

rst_km_rct <- psrwe_survkm(ps_bor_rct,
                           pred_tp = 365,
                           v_time = "Y_Surv",
                           v_event = "Status")
rst_km_rct

The estimated PSKM curves with confidence intervals can be visualized below.

plot(rst_km_rct, xlim = c(0, 730))

The inference is based on the treatment effect $S_{trt}(\tau) - S_{ctl}(\tau)$ at $\tau = 365$ days where $S_{trt}$ and $S_{ctl}$ are the survival probabilities of the treatment and control arms, respectively. i.e., the example tests $$ H_0: S_{trt}(\tau) - S_{ctl}(\tau) \leq 0 \quad \mbox{vs.} \quad H_a: S_{trt}(\tau) - S_{ctl}(\tau) > 0 . $$ The outcome analysis can be summarized below. Note that this is an one-sided test.

oa_km_rct <- psrwe_outana(rst_km_rct, alternative = "greater")
oa_km_rct

The details of estimates for each arm can be printed via the print() function with the option show_rct = TRUE.

print(oa_km_rct, show_rct = TRUE)

As the survival package, the results of other time points can be also predicted via the summary() with the option pred_tps.

summary(oa_km_rct, pred_tps = c(180, 365))

PS-integrated log-rank test

The log-rank test is another way to compare two treatments of time-to-event endpoint. Similar the PSKM for the two-arm test above, the function psrwe_survlrk() computes the statistic for each distinctive time point beased on the observed data then returns all necessary results for the down-streatm analyses such as tests and confidence intervals.

rst_lrk <- psrwe_survlrk(ps_bor_rct,
                         pred_tp = 365,
                         v_time = "Y_Surv",
                         v_event = "Status")
rst_lrk

The inference is based on the log-rank method to test whether two survival distributions are different from each other. The example tests $$ H_0: S_{trt}(t) = S_{ctl}(t) \quad \mbox{vs.} \quad H_a: S_{trt}(t) \neq S_{ctl}(t) 0 $$ for all $t \leq \tau$ where $\tau = 365$ days. The outcome analysis can be summarized below.

oa_lrk <- psrwe_outana(rst_lrk)
oa_lrk

The details of estimates for each arm can be printed via the print() function with the option show_rct = TRUE.

print(oa_lrk, show_details = TRUE)

As the survival package, the results of other time points can be also predicted via the summary() with the option pred_tps.

summary(oa_lrk, pred_tps = c(180, 365))

PS-integrated restricted mean survival time (RMST) test

The restricted means survival time (RMST) between two treatments is to test whether areas under two survival distributions (AUC) are different from each other. Similar the log-rank test above, the function psrwe_survrmst() computes the statistic for each distinctive time point beased on the observed data then returns all necessary results for the down-streatm analyses such as tests and confidence intervals.

rst_rmst <- psrwe_survrmst(ps_bor_rct,
                           pred_tp = 365,
                           v_time = "Y_Surv",
                           v_event = "Status")
rst_rmst

The inference is based on the to compare whether AUCs are different from each other. The example tests $$ H_0: \int_0^{\tau} S_{trt}(t) dt = \int_0^{\tau} S_{ctl}(t) dt \quad \mbox{vs.} \quad H_a: \int_0^{\tau} S_{trt}(t) dt \neq \int_0^{\tau} S_{ctl}(t) dt $$ where $\tau = 365$ days. The outcome analysis can be summarized below. Note that this is a two-sided test.

oa_rmst <- psrwe_outana(rst_rmst)
oa_rmst

The details of estimates for each arm can be printed via the print() function with the option show_rct = TRUE.

print(oa_rmst, show_details = TRUE)

As the survival package, the results of other time points can be also predicted via the summary() with the option pred_tps.

summary(oa_rmst, pred_tps = c(180, 365))

Demo examples

The scripts in "psrwe/demo/sec_4_5_ex.r", "psrwe/demo/sec_4_6_ex.r", and "psrwe/demo/sec_4_7_ex.r" source files have the full examples for the PS-integrated survival analyses which can be run via the demo("sec_4_5_ex", package = "psrwe"), demo("sec_4_6_ex", package = "psrwe"), and demo("sec_4_7_ex", package = "psrwe"), respectively.

Two Jackknife standard errors are also demonstrated for each test method. Note that Jackknife standard errors may take a while to finish.

References

Chen, W.-C., Lu, N., Wang, C., Li, H., Song, C., Tiwari, R., Xu, Y., and Yue, L.Q. (to be submitted). Propensity Score-Integrated Statistical Tests for Survival Analysis: Leveraging External Evidence for Augmenting the Control Arm of a Randomized Controlled Trial.
Chen, W.-C., Lu, N., Wang, C., Li, H., Song, C., Tiwari, R., Xu, Y., and Yue, L.Q. (2022). Propensity Score-Integrated Approach to Survival Analysis: Leveraging External Evidence in Single-Arm Studies. Journal of Biopharmaceutical Statistics, 32(3), 400-413.
Com-Nougue, C., Rodary, C. and Patte, C. (1993). How to establish equivalence when data are censored: A randomized trial of treatments for B non-Hodgkin lymphoma. Statist. Med., Volume 12, pp. 1353-1364.
Klein, J. and Moeschberger, M. (2003). Survival Analysis: Techniques for Censored and Truncated Data. 2nd ed. New York: Springer.
Peto, R. and Peto, J. (1972). Asymptotically Efficient Rank Invariant Test Procedures. Journal of the Royal Statistical Society, Series A, 135(2), 185-207.
Royston, P. and Parmar, M. K. (2013). Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome. BMC Med Res Methodol, 13(152).
Uno, H., et al., (2014). Moving beyond the hazard ratio in quantifying the between-group difference in survival analysis. Journal of clinical oncology, Volume 32, 2380-2385.
Wang, C., Li, H., Chen, W. C., Lu, N., Tiwari, R., Xu, Y., and Yue, L.Q. (2019). Propensity score-integrated power prior approach for incorporating real-world evidence in single-arm clinical studies. Journal of Biopharmaceutical Statistics, 29(5), 731-748.
Wang, C., Lu, N., Chen, W. C., Li, H., Tiwari, R., Xu, Y., and Yue, L.Q. (2020). Propensity score-integrated composite likelihood approach for incorporating real-world evidence in single-arm clinical studies. Journal of Biopharmaceutical Statistics, 30(3), 495-507.