For SAS users: reproducing PROC MIXED and PROC MI conventions

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The package was built by porting a SAS robustness package and validating every cell against it. The conventions below are what it took to agree with PROC MIXED and PROC MI to the sixth decimal.

SAS	ballast setting	Note
`REPEATED visit / SUBJECT=id TYPE=UN`	`covariance = "us"`	`ARH(1)` is `"ar1h"`, `AR(1)` `"ar1"`, `CS` `"cs"`, `CSH` `"csh"`, `TOEP` `"toep"`, `TOEPH` `"toeph"`
`DDFM=SATTERTHWAITE`	`method = "Satterthwaite", vcov = "Asymptotic"`
`DDFM=KR` (the default KR, not KR2)	`method = "Kenward-Roger", vcov = "Kenward-Roger-Linear"`	mmrm’s full Kenward-Roger vcov gives a smaller standard error than SAS
`EMPIRICAL` with any `DDFM`	`method = "Between-Within", vcov = "Empirical"`	SAS cannot combine the sandwich with Satterthwaite or KR and falls back to between-within degrees of freedom; with `sas_conventions = TRUE` the df is computed as observations minus subjects minus the rank of the within-subject design columns
`LSMEANS trt*visit / DIFF`	`weights = "equal"`	class covariates at equal weights over their levels, continuous covariates at their means
`LSMEANS ... OBSMARGINS`	`weights = "observed"`	the design averaged over the analysis rows
`LSMEANS ... AT x = value`	`stress_fit(spec, at = list(x = value))`
AICC in the fit statistics	the `aicc` column	the SAS REML definition: `-2 res. log lik + 2 d n* / (n* - d - 1)`, d covariance parameters, n* = N minus the rank of X
a `CLASS` variable with one level in a subset	dropped with a note	PROC MIXED zeroes the column; R refuses a one-level factor
`PROC MI ... FCS REG`	`stress_tipping()`	the regression method with a preliminary monotone fill and burn-in iterations
`MNAR ADJUST(... SHIFT=delta ADJUSTOBS=(trt='active'))` under FCS	`stress_tipping(deltas = ..., shift_every = TRUE)`	SAS adds the shift at every draw, so it propagates through later imputed visits; applying it only to the final draw gives a curve that declines markedly more slowly
`PROC MIANALYZE` without `EDF=`	Rubin’s rules in `mi_pool`	the pooled degrees of freedom can run into the hundreds of thousands when the between-imputation variance is tiny
`MODELOBS=` (copy reference as a monotone regression)	`stress_reference(methods = "CR")`	the package uses the multivariate-normal formulation of Carpenter, Roger and Kenward, validated against rbmi

REPEATED visit / SUBJECT=id TYPE=UN

covariance = "us"

ARH(1) is "ar1h", AR(1) "ar1", CS "cs", CSH "csh", TOEP "toep", TOEPH "toeph"

DDFM=SATTERTHWAITE

method = "Satterthwaite", vcov = "Asymptotic"

DDFM=KR (the default KR, not KR2)

method = "Kenward-Roger", vcov = "Kenward-Roger-Linear"

mmrm’s full Kenward-Roger vcov gives a smaller standard error than SAS

EMPIRICAL with any DDFM

method = "Between-Within", vcov = "Empirical"

SAS cannot combine the sandwich with Satterthwaite or KR and falls back to between-within degrees of freedom; with sas_conventions = TRUE the df is computed as observations minus subjects minus the rank of the within-subject design columns

LSMEANS trt*visit / DIFF

weights = "equal"

class covariates at equal weights over their levels, continuous covariates at their means

LSMEANS ... OBSMARGINS

weights = "observed"

the design averaged over the analysis rows

LSMEANS ... AT x = value

stress_fit(spec, at = list(x = value))

AICC in the fit statistics

the aicc column

the SAS REML definition: -2 res. log lik + 2 d n* / (n* - d - 1), d covariance parameters, n* = N minus the rank of X

a CLASS variable with one level in a subset

dropped with a note

PROC MIXED zeroes the column; R refuses a one-level factor

PROC MI ... FCS REG

stress_tipping()

the regression method with a preliminary monotone fill and burn-in iterations

MNAR ADJUST(... SHIFT=delta ADJUSTOBS=(trt='active')) under FCS

stress_tipping(deltas = ..., shift_every = TRUE)

SAS adds the shift at every draw, so it propagates through later imputed visits; applying it only to the final draw gives a curve that declines markedly more slowly

PROC MIANALYZE without EDF=

Rubin’s rules in mi_pool

the pooled degrees of freedom can run into the hundreds of thousands when the between-imputation variance is tiny

MODELOBS= (copy reference as a monotone regression)

stress_reference(methods = "CR")

the package uses the multivariate-normal formulation of Carpenter, Roger and Kenward, validated against rbmi

A spec in SAS terms

library(ballast)
# PROC MIXED; CLASS usubjid avisitn trtpn cohort site; MODEL pchg = base avisitn trtpn trtpn*avisitn cohort site / DDFM=SATTERTHWAITE;
# REPEATED avisitn / SUBJECT=usubjid TYPE=ARH(1); LSMEANS trtpn*avisitn / DIFF;
spec <- stress_spec(adeff, response = "pchg", subject = "usubjid", visit = "avisitn", treatment = "trtpn",
                    reference = "1", covariates = ~ base + cohort + site, contrast_visit = "7",
                    covariance = "ar1h", method = "Satterthwaite", vcov = "Asymptotic")

Visit as a factor must carry the visit order in its levels; stress_spec_adam() orders by AVISITN.

Things that do not reproduce exactly

Random-number-based methods (multiple imputation, re-randomisation tests, MM-type robust regression) agree with SAS within Monte Carlo error only; the package reports the Monte Carlo standard error in the row’s note. A spatial power covariance over days needs the time variable rescaled (days divided by 100, say) before mmrm converges; it is not among the structures the spec accepts.

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