Reproducing SAS PROC SEQDESIGN survival designs in gsDesign

In gsDesign: Group Sequential Design

knitr::opts_chunk$set(
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library(gsDesign)

Overview

This vignette emphasizes numerical reproduction of SAS PROC SEQDESIGN survival sample size outputs in gsDesign when design assumptions are matched. It is primarily about translating a SAS design specification to gsSurv(), not about post-design power sensitivity calculations. For an introductory survival sample size workflow that is not tied to SAS output, see vignette("gsSurvBasicExamples"). For the reverse question, where enrollment, dropout, analysis timing, and hazard ratio assumptions are fixed and the goal is to compute achieved power, see vignette("gsSurvPower").

We first reproduce the SAS fractional-time table to printed precision. We then show options that may lead to confusion when translating SAS PROC SEQDESIGN calls to gsDesign, including the event formula, alpha convention, and accrual and follow-up assumptions. The examples below touch three common survival design questions:

• Fix the enrollment pattern and duration, specify information fractions, and reproduce the sample size and event targets implied by the design.
• Fix enrollment rates over time and minimum follow-up, then solve the enrollment duration needed to power the trial.
• Fix enrollment rates and enrollment duration, then vary minimum follow-up to evaluate power. This is often a sensitivity question rather than a reliable sample size solver, since plausible follow-up durations may leave the trial consistently overpowered or underpowered.

Starting point: SAS PROC SEQDESIGN survival example

Consider the example described in the SAS Documentation: Computing Sample Size for Survival Data with Uniform Accrual. The first PROC SEQDESIGN call in that example does not specify ACCTIME; SAS therefore derives a range of possible accrual times. The comparison below uses the subsequent SAS call with ACCTIME=18, which fixes the maximum sample size at 15 * 18 = 270 subjects and asks SAS to solve the follow-up time needed for the target power. The SAS survival sample size model uses the Schoenfeld formula for the targeted event counts. The computed sample size and event counts at each analysis are continuous values, not rounded to integers.

proc seqdesign; /* Group sequential design procedure */
    ErrorSpend: design /* Label for this design block */
                nstages=4 /* Total analyses including final */
                method=errfuncobf /* Lan-DeMets O'Brien-Fleming spending */
                alt=twosided /* Two-sided alternative hypothesis */
                stop=reject /* Early stop only for efficacy */
                alpha=0.05 /* Total two-sided Type I error */
                beta=0.10 /* Type II error (90% power) */
                ;
    samplesize model= /* Survival model */
        twosamplesurvival( /* Two-sample survival endpoint */
        nullhazard = 0.03466 /* Control hazard under H0 */
        hazard     = 0.01733 /* Experimental hazard under H1 */
        accrual    = uniform /* Uniform enrollment */
        accrate    = 15 /* Subjects enrolled per time unit */
        acctime    = 18 /* Accrual duration in time units */
    );
run;

SAS assumptions summary:

• 4-stage group sequential design
• Lan-DeMets O'Brien-Fleming error spending function
• Two-sided symmetric test, total alpha = 0.05
• 90% power (beta = 0.10)
• Equally spaced information fractions: 0.25, 0.50, 0.75, 1.00
• Schoenfeld formula for required number of events
• Fixed accrual rate and duration, so the maximum sample size is $N = \text{ACCRATE} \times \text{ACCTIME} = 15 \times 18 = 270$
• Study duration $T$ solved to achieve the required events
• Hazard ratio $HR = 0.01733 / 0.03466 = 0.5$

SAS does produce a sample size in this example. In the "Sample Size Summary" table for the ACCTIME=18 case, it reports Max Sample Size = 270, Follow-up Time = 7.133226, and Total Time = 25.13323. The maximum sample size is not calculated from the event formula; it is implied directly by the fixed accrual rate and accrual duration: 15 subjects/time unit * 18 time units = 270 subjects.

The fractional-time design reports analyses at information fractions 0.25, 0.50, 0.75, and 1.00. We focus on that design, where the analysis times are not rounded.

sas_fractional <- data.frame(
  Analysis = 1:4,
  Events = c(22.26962, 44.53924, 66.80886, 89.07847),
  Calendar_time = c(11.2631, 16.2875, 20.4926, 25.13323),
  N = c(168.95, 244.31, 270.00, 270.00),
  Upper_Z = c(4.33263, 2.96333, 2.35902, 2.01409)
)

The rest of this vignette identifies the key assumptions in each system and explains why alternative parameter translations can produce different results. For additional background on the time-to-event methods in gsDesign, including the default Lachin-Foulkes calculations, see vignette("SurvivalOverview").

Key differences: SAS SEQDESIGN vs. R gsDesign

There are three practical translation points that affect the output from the example above.

1. Event formula

• SAS: @Schoenfeld1981. Uses only the null-hypothesis variance.
• gsDesign: @LachinFoulkes by default. Use method = "Schoenfeld" to match the SAS event formula. The default Lachin-Foulkes method is slightly more conservative for this example, so matching the event formula matters for numerical reproduction.

2. Alpha handling in gsDesign() and gsSurv()

gsDesign() stores and spends the one-sided Type I error. Thus, for a symmetric two-sided design (test.type = 2), alpha = 0.025 means 0.025 in each tail, or 0.05 total two-sided Type I error.

gsSurv() follows the same convention internally. If a user prefers to enter the total two-sided alpha, alpha = 0.05, sided = 2 is equivalent to alpha = 0.025, sided = 1 for this example because gsSurv() passes alpha / sided to gsDesign().

Here we use test.type = 2 and alpha = 0.025 to make the symmetric two-sided gsDesign() object match the SAS two-sided total alpha of 0.05.

3. Accrual duration and follow-up time

With ACCTIME=18, SAS fixes the accrual duration and total maximum sample size and solves for the additional follow-up time. To match this in gsSurv(), set both T = NULL and minfup = NULL. This tells gsSurv() to keep the input accrual rate and accrual duration fixed, then solve the follow-up duration needed for the final group sequential event requirement.

This is a common source of apparent disagreement. For a fixed-duration survival design, T is the total study duration and minfup is the minimum follow-up after enrollment closes. Specifying both can therefore change which quantity gsSurv() solves for. The SAS comparison fixes accrual at 18 time units and lets the total time be derived.

The translation used below is summarized as follows:

knitr::kable(
  data.frame(
    Quantity = c(
      "Two-sided Type I error",
      "Symmetric two-sided design",
      "Analysis timing input",
      "Event formula",
      "Accrual duration",
      "Total study duration",
      "Follow-up after accrual"
    ),
    SAS = c(
      "alpha = 0.05 total",
      "Early stop to reject either side",
      "Information fractions 0.25, 0.50, 0.75, 1.00",
      "Schoenfeld log-rank information",
      "ACCTIME = 18",
      "Total Time = 25.13323",
      "Derived as 7.133226"
    ),
    gsDesign = c(
      "alpha = 0.025 per tail",
      "test.type = 2",
      "gsSurv(timing = c(.25, .50, .75, 1))",
      "method = \"Schoenfeld\"",
      "R = 18",
      "T = NULL",
      "minfup = NULL"
    ),
    Reason = c(
      "gsDesign stores and spends one-sided alpha",
      "Mirrors the upper and lower efficacy boundaries",
      "Uses the SAS fractional information schedule",
      "Avoids Lachin-Foulkes default event calculation",
      "Keeps the same fixed accrual duration",
      "Lets gsSurv() solve total time from fixed accrual",
      "Lets gsSurv() solve the follow-up duration"
    ),
    check.names = FALSE
  ),
  caption = "Translation from the SAS PROC SEQDESIGN example to gsDesign inputs."
)

Reproducing the fractional-time design with gsSurv()

gsSurv() with aligned parameters

Let's start our work with gsDesign by defining parameters to match the SAS fractional-time design:

k <- 4
alpha_sas <- 0.05 # Two-sided total alpha (SAS convention)
alpha_gsdesign <- alpha_sas / 2 # gsDesign uses one-sided alpha
beta <- 0.10 # 1 - power = 0.10 -> 90% power
lambdaC <- 0.03466 # Control hazard rate
lambdaE <- 0.01733 # Experimental hazard rate
HR <- lambdaE / lambdaC # = 0.5
timing <- c(0.25, 0.50, 0.75, 1.00) # Equally spaced information fractions
accrate <- 15 # Uniform accrual rate (subjects per time unit)
accrual_duration <- 18 # Accrual duration (time units)
sas_total_time <- 25.13323
sas_followup_time <- sas_total_time - accrual_duration
N <- accrate * accrual_duration

Instead of starting with a call to gsDesign::gsDesign(), we begin with gsDesign::gsSurv(). The gsSurv() function combines nSurv() with gsDesign() (group sequential boundaries) in one call. It is the standard gsDesign function for designing time-to-event trials.

The call below uses the same two-sided symmetric structure as SAS:

• test.type = 2 for symmetric two-sided boundaries;
• alpha = 0.025, the one-sided alpha corresponding to SAS's total two-sided alpha of 0.05;
• method = "Schoenfeld" for the SAS event formula;
• T = NULL and minfup = NULL so the accrual rate and accrual duration remain fixed while gsSurv() solves the follow-up duration.

des_2 <- gsSurv(
  k = 4,
  test.type = 2, # Symmetric two-sided design
  alpha = alpha_gsdesign, # One-sided alpha; SAS total alpha is 2 * this
  beta = 0.10,
  sfu = sfLDOF,
  timing = c(.25, .50, .75, 1),
  lambdaC = 0.03466,
  hr = 0.5,
  eta = 0, # Assume no dropout
  gamma = accrate,
  R = accrual_duration,
  T = NULL,
  minfup = NULL,
  ratio = 1,
  method = "Schoenfeld"
)
des_2

Observations:

Using gsSurv() with parameters that align with SAS settings, the event counts, sample size, and analysis times reproduce the SAS fractional-time output to the printed precision available. The final follow-up duration is r round(des_2$minfup, 5), giving total study duration r round(des_2$T[des_2$k], 5). Small fifth-decimal differences in Z-boundary comparisons may reflect limited SAS printed precision unless the SAS output is rerun with more digits.

gs_fractional <- data.frame(
  Analysis = 1:k,
  Events_SAS = sas_fractional$Events,
  Events_gsDesign = des_2$n.I,
  Time_SAS = sas_fractional$Calendar_time,
  Time_gsDesign = des_2$T,
  N_SAS = sas_fractional$N,
  N_gsDesign = rowSums(des_2$eNC) + rowSums(des_2$eNE),
  Z_SAS = sas_fractional$Upper_Z,
  Z_gsDesign = des_2$upper$bound
)

knitr::kable(
  round(gs_fractional, 5),
  caption = "Fractional-time SAS output compared with gsSurv()."
)

The final event count is 89.07847 in both systems. The print() and gsBoundSummary() methods display rounded integer sample sizes and events, but the object retains the fractional values shown above.

If the follow-up time is fixed instead, gsSurv() can answer a different sample size question: keeping enrollment rates and minimum follow-up fixed, how long must enrollment continue to power the trial? The translation is T = NULL with minfup set to the fixed follow-up time. In this SAS example, the solution returns the same accrual duration because the fixed follow-up time is the one SAS solved from the fixed-accrual design:

des_fixed_followup <- gsSurv(
  k = 4,
  test.type = 2,
  alpha = alpha_gsdesign,
  beta = 0.10,
  sfu = sfLDOF,
  timing = c(.25, .50, .75, 1),
  lambdaC = 0.03466,
  hr = 0.5,
  eta = 0,
  gamma = accrate,
  R = accrual_duration,
  T = NULL,
  minfup = sas_followup_time,
  ratio = 1,
  method = "Schoenfeld"
)

fixed_followup_check <- data.frame(
  Quantity = c(
    "Final study duration",
    "Accrual duration",
    "Final events",
    "Final N"
  ),
  Solved_followup = c(
    des_2$T[k],
    sum(des_2$R),
    des_2$n.I[k],
    sum(des_2$eNC[k, ] + des_2$eNE[k, ])
  ),
  Specified_followup = c(
    des_fixed_followup$T[k],
    sum(des_fixed_followup$R),
    des_fixed_followup$n.I[k],
    sum(des_fixed_followup$eNC[k, ] + des_fixed_followup$eNE[k, ])
  )
)
fixed_followup_check[-1] <- lapply(fixed_followup_check[-1], round, digits = 5)

knitr::kable(
  fixed_followup_check,
  caption = "Both fixed-accrual translations produce the same final design."
)

A third use case is to keep both the enrollment rates and enrollment duration fixed, then vary minimum follow-up and evaluate power. That is useful for sensitivity analysis, but it is not always a stable sample size workflow: for some assumptions the trial remains overpowered or underpowered for all plausible follow-up durations. Use gsSurvPower() when the design quantities are fixed and the question is achieved power.

References

gsDesign documentation built on July 20, 2026, 9:06 a.m.