Introduction to remiod • remiod

Data from an antidepressant clinical trial

The example data can be found in DIA Missing Data webpage. Original data was from an antidepressant clinical trial with four treatments; two doses of an experimental medication, a positive control, and placebo. Hamilton 17-item rating scale for depression (HAMD17) was observed at baseline and its change scores at weeks 1, 2, 4, 6, and 8 ( Goldstein et al. 2004). To mask the real data Week-8 observations were removed. The example data is a sub-sample of the original data: two arms were created; the original placebo arm and a “drug arm” created by randomly selecting patients from the three non-placebo arms.

data(antidep)
head(antidep) %>% kbl(align = "c") %>% 
  kable_classic(full_width = F, html_font = "Cambria") %>%
  column_spec(1:2, width = "2cm") %>%
  add_header_above(c(" " = 1, " "=1, "Responses at the baseline, week 1, 2, 4, and 6" = 5))

		Responses at the baseline, week 1, 2, 4, and 6
PID	tx	y0	y1	y2	y4	y6
1503	1	32	-11	-12	-13	-15
1507	0	14	-3	0	-5	-9
1509	1	21	-1	-3	-5	-8
1511	0	21	-5	-3	-3	-9
1513	1	19	5	NA	NA	NA
1514	0	21	2	NA	NA	NA

Missing pattern is displayed in the following plot:

Missing pattern of antidepressant data

The planned statistical method to analyze this endpoint was mixed-effects model with last-observation-carry-forward (LOCF) as the imputation method. In this example, missing values are imputed with GLM models. This is implemented through family argument, say, family = gaussian() (its default link is identity). The same imputation setting is applied for imputing y2 and y4, i.e. argument models is set to be glm_gaussian_identity. We run the GLM imputation model with an adaptation of 10000 and 2000 iterations for 4 chains. Chains run in parallel, which is set through doFuture package:

registerDoFuture()
plan(multisession(workers = 4))

an.test = remiod(formula=y6 ~ tx + y0 + y1 + y2 + y4, data=antidep, family = gaussian(),
                 models = c(y2="glm_gaussian_identity",y4="glm_gaussian_identity"),
                 n.iter = 100000,  n.chains = 4, n.adapt = 10000, thin=100,
                 algorithm = "jags", trtvar = 'tx', method="MAR", mess=TRUE, warn=FALSE)

plan(sequential)

The following plots show trace plots and the estimated intervals as shaded areas under the posterior density curves for the parameters of treatment variable tx in imputation models:

beta[2] is the coefficient of tx in imputation model y6 ~ tx + y0 + y1 + y2 + y4;
alpha[2] is the coefficient of tx in imputation model y4 ~ tx + y0 + y1 + y2;
alpha[7] is the coefficient of tx in imputation model y2 ~ tx + y0 + y1;

The specified set of parameters can be submitted through argument subset with keyword selected_vars (alternatively, keyword selected_parms can be used):

mcsub = get_subset(object = an.test$mc.mar, subset=c(selected_vars = list("tx")))

color_scheme_set("purple")
mcmc_trace(mcsub, facet_args = list(ncol = 1, strip.position = "left"))

Traceplot for coefficients of tx in imputation models

mcmc_areas(
  mcsub, 
  prob = 0.95, # 95% intervals
  prob_outer = 0.99, 
  point_est = "mean"
)

Intervals under the estimated posterior density curves for coefficients of tx in imputation models

To obtain jump-to-reference analysis, we extract MI data with method="J2R", and pool analysis results with miAnalyze:

j2r = extract_MIdata(object=an.test, method="J2R", M=1000, minspace=4)
res.j2r = miAnalyze(formula = y6 ~ y0 + tx, data = j2r, family = gaussian())

data.frame(res.j2r$Est.pool) %>% select(-6) %>%
  mutate_if(is.numeric, format, digits=4,nsmall = 0) %>%
  kbl(align = "c") %>% 
  kable_classic(full_width = F, html_font = "Cambria")

	Estimate	SE	CI.low	CI.up	t
(Intercept)	1.0433	1.82704	-2.5376	4.6243	0.5711
y0	-0.3292	0.09697	-0.5192	-0.1391	-3.3945
tx	-2.3558	1.04973	-4.4133	-0.2984	-2.2442

Reference

Wang, T. and Liu, Y. 2022. “Remiod: Reference-Based Controlled Multiple Imputation of Longitudinal Binary and Ordinal Outcomes with Non-Ignorable Missingness.” arxiv 2203.02771.

Goldstein, David J. MD, PhD; Lu, Yili; Detke, Michael J.; Wiltse, Curtis; Mallinckrodt, Craig; Demitrack, Mark A. Duloxetine in the Treatment of Depression Journal of Clinical Psychopharmacology: 2004, 24(4) p 389-399 doi: 10.1097/01.jcp.0000132448.65972.d9

Example: Continuous data imputation through GLM

Data from an antidepressant clinical trial

Reference