Tecnical question: How observed parameters are calculated with imputations

[Gero1999]

Hello everyone!

I remember that @billdenney mentioned me in a past issue in aNCA that observed variables such as cmax, tmax do not consider the imputations done when performing pk.nca, and that if they do so, that would be a bug. I am not sure if I am missing something here, but when I try to run the same dataset with/without imputations, then tmax, cmax values change:

# Dataset examples
d_conc <- data.frame(Subject = 1, 
                     Dose = 1,
                     conc = 6:1,
                     Time = c(-1, 1:5),
                     volume = NA,
                     duration = 0)

## Generate the dosing data
d_dose <- data.frame(Subject = 1,
                     Dose = 1, 
                     Time = 0,
                     volume = NA,
                     duration = 0)

## Create a PKNCA concentration object
conc_obj <-
  PKNCAconc(
    d_conc %>%
      filter(Subject == 1, Time!=0),
    conc~Time|Subject
  )
## Create a PKNCA dosing object
dose_obj <-
  PKNCAdose(
    d_dose,
    Dose~Time|Subject
  )

# Create two identical PKNCAdata objects
data_obj <- PKNCAdata(conc_obj, dose_obj)
data_obj_with_predose = data_obj

# Add a impute rule to one PKNCAdata
data_obj_with_predose$intervals$impute = c("start_logslope", "start_logslope")
data_obj_with_predose$impute = "impute"

## Calculate the NCA parameters for each PKNCAdata
results_obj <- pk.nca(data_obj)
results_obj_with_predose <- pk.nca(data_obj_with_predose)

# Check the results for each PKNCAdata
results_obj$result %>% filter(PPTESTCD == "tmax")
results_obj_with_predose$result %>% filter(PPTESTCD == "tmax")

The output then differs for each on PKNCA_0.11.0.9000 as you can see in this console print:

> results_obj$result %>% filter(PPTESTCD == "tmax")
# A tibble: 1 × 6
  Subject start   end PPTESTCD PPORRES exclude
    <dbl> <dbl> <dbl> <chr>      <dbl> <chr>  
1       1     0   Inf tmax           1 NA     
> results_obj_with_predose$result %>% filter(PPTESTCD == "tmax")
# A tibble: 1 × 6
  Subject start   end PPTESTCD PPORRES exclude
    <dbl> <dbl> <dbl> <chr>      <dbl> <chr>  
1       1     0   Inf tmax           0 NA     

If this is a bug, I guess it would be interesting to open a new issue, fix it and perhaps also add tests to these functions as in #361
Otherwise, if it is indeed because I am missing something in the code then please do not hesitate to let me know!

[Gero1999]

If this is indeed an issue I would naively propose a solution in pk.nca.interval() of this kind:

Delete these two lines (367, 368):

    conc <- impute_data$conc
    time <- impute_data$time

And add the impute_data conditionally in the args_call assignation later:

  # Do the calculations
  for (n in names(all_intervals)) {
  
  # Rest of the code...  
        observed_params <- c("cmax", "tmax")
        
        if (arg_mapped == "conc") {
          if (n %in% observed_params) {
                call_args[[arg_formal]] <- conc
          }  else {
                call_args[[arg_formal]] <- impute_data$conc
            }
        } else if (arg_mapped == "time") {
          # Realign the time to be relative to the start of the
          # interval
          if (n %in% observed_params) {
            call_args[[arg_formal]] <- time - interval$start[1]
          } else {
            call_args[[arg_formal]] <- impute_data$time - interval$start[1]
          }
  
  # Rest of the code...  

[billdenney]

Hmm. This is a complicated one to me. Doing the imputation of trough concentrations before calculation could affect cmin and ctrough. Imputation of C0 should happen by using the AUCiv parameters instead because, otherwise, the percent back extrapolation calculation will be inaccurate as 0. (I am okay with the inclusion of the imputation suggested in #361 because it enables plotting more easily. I also strongly believe that software should enable users to do what they want and need rather than forcing them to use it just one way.)

That said, I agree that parameters that are observed should not be affected by imputation.

I would propose that a preferred solution would be to add an argument to add.interval.col() called use_impited_conc = TRUE and for parameters that don't use the imputed concentrations it is set to false. That would then be detected similarly to what you proposed but not hard-coded for Cmax and Tmax, rather using the new flag ``use_impited_concfromget.ingerval.cols()`.

Does that make sense?

Also, that new column should have an indicator added to the parameters description table in the intervals vignette.

[Gero1999]

After reading your response I actually agree, we should elude hard-coding implementations and keep the package flexible. I like your solution. I will just propose two alternatives that I feel can also make sense:

1. Make a function that only and simply modifies the PKNCAdata$intervals, i.e, remove_impute_for_params(PKNCAdata, params). The function identifies rows/intervals where param = TRUE & !is.na(impute), set in those param = FALSE and create duplicates where param = TRUE, impute = NA

2. Make it part of PKNCAdata in a similar way (or fused with) units. Then in that PKNCAdata$param_settings table we can include the flag use_imputed_conc or any other future column that we may think of.

You have a better perspective of the overall, so let me know which of the three strategies you think is the best or if we still should think about it, but I believe it can be something useful to implement!

[billdenney]

I've been thinking about this for a couple of days, and I don't yet have what feels like a complete answer in my mind.

I lean somewhat toward either your first suggestion or my suggestion in that it moves most of the work of thinking about imputation subtleties outside of the main calculation engine. I want the result to also match what people will expect (while they have the ability to change it).

In short, I'm still thinking...

[Gero1999]

Completely understandable! I agree with you, it is better to think this thoughtfully. Probably in the meantime I will end up coding in aNCA a temporary solution, very likely something similar to 1. Perhaps if we end up going that way in PKNCA we could also recycle it

[billdenney]

I've come to a conclusion that you're right that we need a set of interval-support functions. I'm trying to think of all of the general ideas that we could use to create and modify intervals. For the question in this discussion about concentration-imputation, I like the idea that you proposed as 1 above. I'm going to make this into an issue for discussion of the specific interface.

[billdenney]

The issue is in #379