0.2.0
An R package for Reference-based multiple imputation for sensitivity analysis of longitudinal trials with protocol deviation
We have ported the functionality of the Stata program mimix into the R package RefBasedMI, and added extra functionality including options for the Causal model and Delta adjustment.
The mimix program is described in the paper
Reference-based sensitivity analysis via multiple imputation for longitudinal trials with protocol deviation by Suzie Cro, Tim P. Morris, Michael G. Kenward, and James R. Carpenter https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5796638/
and can be accessed by typing (within Stata) "ssc install mimix" to install the code and "help mimix" to read help documentation.
The five reference-based imputation methods available in RefBasedMI are:
| Method | Abbreviation | Reference group required? |
|---|---|---|
| Randomized-arm | MAR | No |
| Jump to reference | J2R | Yes |
| Copy increments in reference | CIR | Yes |
| Copy reference | CR | Yes |
| Last mean carried forward | LMCF | No |
In the Causal model, the maintained treatment effect after treatment discontinuation is related to the final treatment effect: it is either a constant fraction (specified by K0), or decays exponentially by being multiplied by specifying a K1 value (0<=K1<=1) in every period. Values K0=1, K1=0 are equivalent to method J2R, whilst values K0=1, K1=1 are equivalent to method CIR.
Full details of the Causal model are in the paper by White, Royes and Best: https://www.tandfonline.com/doi/full/10.1080/10543406.2019.1684308.
In Delta adjustment, imputations differ sytematically from values imputed by the above methods to an extent specified by parameters delta and dlag.
These specify an increment which is added on to all values imputed after
treatment discontinuation, but not on to interim (intermediate) missing values.
Values of delta are cumulated after treatment discontinuation.
For example, for an individual who discontinued treatment at the 2nd time point, we take
the vector of delta's starting at the 3rd time point and add their cumulative sums to the imputed values.
Specifying dlag modifies this behaviour, so that the vector of delta's starting at the 3rd time point is
multipled elementwise by the vector dlag.
The formula for the increment at time k for an individual who discontinued after time p is
delta[p+1]*dlag[1] + delta[p+2]*dlag[2] + ... + delta[k]*dlag[k-p].
A common increment of 3 at all time points after treatment discontinuation is achieved
by setting delta=c(3,3,3,...) and dlag=c(1,0,0,...), both vectors having the length of the number of time points.
For further details of Delta adjustment,
see James Roger's SAS programs and user-guide under "Reference-based MI via Multivariate Normal RM (the "five macros" and MIWithD)" at
https://www.lshtm.ac.uk/research/centres-projects-groups/missing-data#dia-working-group.
Within the R environment type
if(!require(devtools)) install.packages('devtools')
library(devtools)
followed by
devtools::install_github("UCL/RefBasedMI")
RefBasedMI(data,covar,depvar,treatvar,idvar,timevar,..... options.....)
data dataset in wide (longitudinal data) format
covar baseline covariates and/or baseline depvar, must be complete (no missing vaules) and treated as numeric
depvar dependent variable
treatvar treatment group
idvar patient id
timevar time point for repeated measures
M number of imputations
reference reference group for J2R, CIR, CR and Causal methods
method imputation method
seed seed value to obtain same outputs
prior prior to use in mcmcNorm: jeffreys (default), uniform or ridge
burnin number of burnin iterations in MCMC
bbetween number of iterations between imputed data sets in MCMC
methodvar variable in data specifying the individual imputation method
referencevar variable in data specifying the individual reference group
delta vector of delta values to add onto imputed values (a values in Roger's paper) (non-mandatory)
dlag vector of dlag values (b values in Roger's paper)
K0 causal constant for use with Causal method
K1 exponential decaying causal constant for use with Causal method
asthmaJ2R <- RefBasedMI(data = asthma, covar = base, depvar = fev, treatvar = treat,
idvar = id, timevar = time, method = "J2R", reference = 2, M = 5, seed = 101,
prior = "ridge", burnin = 1000)`
Fit specified model to each imputed data set (assigned as mids class) and pool results together (Rubin's rules), functions from mice package:
library(mice)
fit<-with(as.mids(subset(asthmaJ2R,time==12)), lm(fev~treat+base))
summary(pool(fit))
impJ2Rridge <- RefBasedMI(data = asthma, covar = c(base), depvar = fev, treatvar = treat,
idvar = id, timevar = time, method = "J2R", reference = 2,
delta = c(-1, 0, 0, 0), M = 5, seed = 101, prior = "ridge")
fit<-with(as.mids(subset(impJ2Rridge,time==12)), lm(fev~treat+base))
summary(pool(fit))
methodcol and referencecol are variables in the data set
NOTE - either method or methodvar must specified but NOT both
antidepIndiv <- RefBasedMI(data = antidepressant, covar = c(basval, PATIENT.SEX),
depvar = HAMD17.TOTAL, treatvar = TREATMENT.NAME, idvar = PATIENT.NUMBER,
timevar = VISIT.NUMBER, methodvar = methodcol, referencevar = referencecol,
M = 5, seed = 54321)
antidepIndiv <- with(data = as.mids(subset(antidepIndiv, VISIT.NUMBER == 7)),
lm(HAMD17.TOTAL ~ TREATMENT.NAME + basval + PATIENT.SEX))
summary(pool(antidepIndiv))
We assume that the treatment effect halves every 1 time unit after treatment discontinuation, so K0 = 1 and K1 = 0.5. Note that K0=1, K1=0 would be equivalent to J2R, and K0=1, K1=1 would be equivalent to CIR.
acuCausal <- RefBasedMI(data = acupuncture, covar = c(head_base), depvar = head,
treatvar = treat, idvar = id, timevar = time, method = "Causal",
reference = 1, K0 = 1, K1 = 0.5, M = 5, seed = 54321)
acufit <- with(as.mids(subset(impCausalref, time == 12)), lm(head ~ treat + head_base))
summary(pool(acufit))