R vs SAS - Restricted Mean Survival Time (RMST)

Comparison of R vs SAS

The following table lists the methods for RMST analysis in R and SAS.

Method	Supported in R	Supported in SAS	Results Match	Notes
1. Inverse probability censoring weighting (IPCW)	Yes - `survRM2`	Yes - PROC RMSTREG	Yes	`survRM2` allows only 2 strata
2. Pseudo-value estimation	Yes - `survival` + `geepack`	Yes - PROC RMSTREG	Yes
3. Area under the curve	Yes - `survRM2`	Yes - PROC LIFETEST	Yes

Results from the examples shown for R here and SAS here were compared below.

Method 1: Inverse probability censoring weighting (IPCW)

Comparing the identity-link results side-by-side, the RMST estimates, standard errors (SEs), confidence intervals (CIs) and p-values match exactly across R and SAS.

	R – {survRM2}					SAS – PROC RMSTREG
	Estimate	SE	95% CI	z	p	Estimate	SE	95% CI	Chi-Square	p
Intercept	380.8065	48.9428	284.8804, 476.7327	7.7806	0.0000	308.8065	48.9428	284.8804, 476.7327	60.54	< 0.0001
trt01p-2	−9.8835	14.8654	-39.0192, 19.2521	−0.6649	0.5061	−9.8835	14.8654	-39.0192, 19.2521	0.44	0.5061
sex-M	−54.2552	15.5813	-84.7940, -23.7163	−3.4821	0.0005	−54.2552	15.5813	-84.7940, -23.7163	12.12	0.0005
age	−1.3874	0.7904	-2.9366, 0.1618	−1.7553	0.0792	−1.3874	0.7904	-2.9366, 0.1618	3.08	0.0792

The same is true of the RMST ratios (computed with the log-link function). Note that survRM2 provides exponentiated versions of the CI values, whereas SAS provides them on the log scale.

	R – {survRM2}					SAS – PROC RMSTREG
	Estimate	SE	95% CI^a	z	p	Estimate	SE	95% CI	Chi-Square	p
Intercept	6.0191	0.1888	5.6491, 6.3892	31.8783	0.0000	6.0191	0.1888	5.6491, 6.3692	1,016.23	< 0.0001
trt01p-2	−0.0367	0.0575	-0.1493, 0.0760	−0.6381	0.5234	−0.0367	0.0575	-0.1493, 0.0760	0.41	0.5234
sex-M	−0.2085	0.0605	-0.3271, -0.0899	−3.4463	0.0006	−0.2085	0.0605	-0.3271, -0.0899	11.88	0.0006
age	−0.0054	0.0031	-0.0115, 0.0007	−1.7348	0.0828	−0.0054	0.0031	-0.0155, 0.0007	3.01	0.0828
^a Default exponentiated CI values have been log-transformed.

If needed, the exponentiated CI values returned by survRM2 can simply be log-transformed:

# Get log CIs from survRM2 object `RMST.comp1`
logCIs <- log(RMST.comp1$RMST.ratio.adjusted[, 6:7])
round(logCIs, digits = 4) # Display rounded to 4 decimal places

          lower .95 upper .95
intercept    5.6491    6.3892
arm         -0.1493    0.0760
sexM        -0.3271   -0.0899
age         -0.0115    0.0007

Method 2: Pseudo-value estimation

The R vs SAS comparison of this method is yet to be completed.

Method 3: Area under the curve

For the RMST of individual strata, both R and SAS return RMST estimates with SEs, and survRM2 additionally provides confidence intervals. Both R and SAS return the RMST difference between the two strata. For the variance of the difference, SAS provides the SE, whereas survRM2 provides CI values.

	R – {survRM2}					SAS – PROC RMSTREG
	Estimate	SE	95% CI	z	p	Estimate	SE	95% CI	Chi-Square	p
Stratum 1	248.2156	9.2343	230.1166, 266.3146	–	–	248.2156	9.2343	–	–	–
Stratum 2	272.9520	11.9889	249.4542, 296.4499	–	–	272.9520	11.9889	–	–	–
Difference	−24.7364	15.1330^a	-54.3965, 4.9237	–	0.1021	−24.7364	15.1330	–	2.6719	0.1021
^a Derived from the estimate and lower CI.

If needed, the SE of the RMST difference for the survRM2 output can be easily inferred from the (Wald) CI by subtracting the lower CI from the mean and dividing the result by a percentile of a standard normal distribution, e.g., the 97.5th percentile for the default 95% confidence level:

# Get SE of RMST difference from survRM2 object `RMST.comp4`
RMSTdiffSE <- (RMST.comp4$unadjusted.result[1,1] - RMST.comp4$unadjusted.result[1,2])/
             qnorm(p = 0.975, mean = 0, sd = 1)
round(RMSTdiffSE, digits = 4)  # Display rounded to 4 decimal places

[1] 15.133