How to impute an ordinal variable with MICE but prevent it from taking one value?

Question

I have an ordinal variable, overall_tumor_grade, that can take on values of 1, 2, 3, or X if the measurement is indeterminable. There are some NAs that I want to impute using the mice package in R, but I know that the missing values cannot be "X" because their tumor sizes are greater than 0. I want to impute overall_tumor_grade but force mice to only choose from 1, 2, or 3.

Here is sample code for you to use:

df=data.frame(age=c(24,37,58,65,70,84),
    overall_tumor_grade=c(1,1,2,3,'X',NA),
    tumor_size=c(1.5,2.0,4.2,5.6,0,0.1))
imp=mice(df)
na_index=which(is.na(df$overall_tumor_grade))
    complete(imp)$overall_tumor_grade[na_index]  #This can never be 'X'

Thank you for your help and please let me know if you need more information.

---

New addition

@longrob suggested I temporarily remove the patients with 'X' observations, impute, then add them back in to the full dataset. Would the imputation lose power by removing all of those observations? Along longrob's suggestion, here is the work-around I have right now using a sample dataframe that is closer to what I'm really working with (several columns with missing values):

df=data.frame(age=rnorm(mean=45,sd=10,25),
overall_tumor_grade=factor(sample(c(1,2,3,'X'),25,replace=TRUE)),
tumor_size=runif(25)*10)
df[df$overall_tumor_grade=='X','tumor_size']=0 #Patients with Grade 'X' have tumorsz=0
    df[sample(1:25,3),'age']=NA   ##Setting some observations to NA
    df[sample(1:25,5),'overall_tumor_grade']=NA
    df[sample(1:25,1),'tumor_size']=NA
    ################ Imputation
    imp=mice(df,meth=c('pmm',"",'pmm'))  #Suppress imputation of overall_tumor_grade
    dfimp=complete(imp)
    dfimp2=dfimp[dfimp$overall_tumor_grade!='X',]  #I don't want to impute grade 'X' tumors
#so I am trying to remove those observations here and then use droplevels(), but for 
#a reason I can't figure out, that statement is setting all rows to NA where grade='X'

Any suggestions on how I accomplish what @longrob suggested?

Answer 1

Maybe there is a better way, but the only way I know is to remove the observations with tumor size X from the dataset, then remove the unused level X from the variable definitions (with droplevels() for example) and then run mice()

Update1: OK, there was a typo in my comment last night - I meant to change that line to dfimp2=dfimp[dfimp$overall_tumor_grade!='X' | is.na(dfimp$overall_tumor_grade),] Sorry about that. Anyway, here's my approach to this problem, based on your simulated dataset:

set.seed(100)
df=data.frame(age=rnorm(mean=45,sd=10,25), 
overall_tumor_grade=factor(sample(c(1,2,3,'X'),25,replace=TRUE)), 
tumor_size=runif(25)*10) 
df[df$overall_tumor_grade=='X','tumor_size']=0 #Patients with Grade 'X' have tumorsz=0 
df[sample(1:25,3),'age']=NA   ##Setting some observations to NA 
df[sample(1:25,5),'overall_tumor_grade']=NA 
df[sample(1:25,1),'tumor_size']=NA 

# output the data
df

        age overall_tumor_grade tumor_size
1        NA                   2         NA
2  46.31531                   1  8.5665304
3  44.21083                   1  7.7477889
4  53.86785                   2  8.3402710
5  46.16971                   3  0.9151028
6  48.18630                   2  4.5952549
7  39.18209                   1  5.9939816
8  52.14533                   1  9.1972191
9        NA                   3  9.8282408
10       NA                <NA>  0.3780258
11 45.89886                   2  5.7793740
12 45.96274                   3  7.3331417
13 42.98366                   X  0.0000000
14 52.39840                <NA>  3.0073652
15 46.23380                <NA>  7.3346670
16 44.70683                <NA>  9.0695438
17 41.11146                   2  2.0981677
18 50.10856                   2  3.5813799
19 35.86186                   1  4.4829914
20 68.10297                   3  9.0642643
21 40.61910                   2  3.8943930
22 52.64061                <NA>  5.1745975
23 47.61961                   3  1.2523909
24 52.73405                   X  0.0000000
25 36.85621                   3  7.7180549

# rows 13 and 24 have tumor grade X

# vector for which rows do not have tumor grade X
vx <- df$overall_tumor_grade!='X' | is.na(df$overall_tumor_grade) 
# remove those with tumor grade X
dfimp <- df[vx,]

# do the imputations
dfimp$overall_tumor_grade <- droplevels(dfimp$overall_tumor_grade)
imp=mice(dfimp, printFlag=F) 

# add back the rows we removed
(new_df1 <- rbind(complete(imp,1),df[!vx,]))

1  40.61910                   2  3.8943930
2  46.31531                   1  8.5665304
3  44.21083                   1  7.7477889
4  53.86785                   2  8.3402710
5  46.16971                   3  0.9151028
6  48.18630                   2  4.5952549
7  39.18209                   1  5.9939816
8  52.14533                   1  9.1972191
9  45.89886                   3  9.8282408
10 52.14533                   3  0.3780258
11 45.89886                   2  5.7793740
12 45.96274                   3  7.3331417
14 52.39840                   2  3.0073652
15 46.23380                   3  7.3346670
16 44.70683                   2  9.0695438
17 41.11146                   2  2.0981677
18 50.10856                   2  3.5813799
19 35.86186                   1  4.4829914
20 68.10297                   3  9.0642643
21 40.61910                   2  3.8943930
22 52.64061                   3  5.1745975
23 47.61961                   3  1.2523909
25 36.85621                   3  7.7180549
13 42.98366                   X  0.0000000
24 52.73405                   X  0.0000000

Answer 2

The following code defines and calls a dedicated imputation function that separates imputation of cases with tumor_size == 0 from tumor_size > 0.

## How to impute an ordinal variable with MICE but prevent it from taking one value?

df <- data.frame(age = c(24,37,58,65,70,84),
                 overall_tumor_grade = c(1,1,2,3,'X',NA),
                 tumor_size = c(1.5,2.0,4.2,5.6,0,0.1))

mice.impute.tumor <- function(y, ry, x, ...){
    ymis <- y[!ry]
    tmis <- x$tumor_size[!ry] > 0
        t  <- x$tumor_size > 0
    y[!ry] <- NA
    ymis[!tmis] <- "X"
    ymis[tmis] <- mice.impute.polyreg(y[t, drop = TRUE], ry[t], x[t,], ...)
    ymis
}

ini <- mice(df, maxit = 0)
meth <- ini$meth
meth["overall_tumor_grade"] <- "tumor"
imp <- mice(df, meth = meth, maxit = 1, m = 2)