# AUC bug with interval

**URL:** <https://discourse.pumas.ai/t/auc-bug-with-interval/990>\
**Category:** Pumas issues\
**Created:** [March 10, 2024, 3:26am UTC](https://discourse.pumas.ai/t/auc-bug-with-interval/990 "2024-03-10T03:26:06Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![donaldlee3](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/donaldlee3/32/165_2.png) [@donaldlee3](https://discourse.pumas.ai/u/donaldlee3)\
**Post date:** [March 10, 2024, 3:26am UTC](https://discourse.pumas.ai/t/auc-bug-with-interval/990/1 "2024-03-10T03:26:06Z")

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Hello,

It appears that auc calculations, when an interval is specified, will do the lamdaz calculation, even when it shouldn’t. This results in missing auc, when the lamdaz calculation fails, even though the data is present to calculate the auc on the specified interval.

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**Author:** ![vijay](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/vijay/32/96_2.png) [@vijay](https://discourse.pumas.ai/u/vijay)\
**Post date:** [March 10, 2024, 4:51am UTC](https://discourse.pumas.ai/t/auc-bug-with-interval/990/2 "2024-03-10T04:51:23Z")

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Hi @donaldlee3, a reproducer would be helpful. I’ve made certain assumptions and tried to reproduce what you are asking for, and here is what I see. Please note the following points:

1. default `NCA.auc` computes `0-inf`.
2. when you specify an interval calculation using the `kwarg` `interval = (tstart, tstop)`, if you are `tstop` is `missing` concentration, than the interval calculation will be missing as expected as there is no way of learning what that data point is without having a `lambdaz` to begin with.

Here is reproducer you can go through and let us know if you still think this is an issue.

```julia
julia> using NCA

julia> using PharmaDatasets

julia> df1 = DataFrame(;
                  id = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2],
                  time = [0, 1, 2, 3, 4, 0, 1, 2, 3, 4],
                  amt = [10, 0, 0, 0, 0, 10, 0, 0, 0, 0],
                  conc = [missing, 8, 6, 4, 2, missing, 8, 6, missing, missing],
                  route = ["iv", "iv", "iv", "iv", "iv", "iv", "iv", "iv", "iv", "iv"],
              )
10×5 DataFrame
 Row │ id time amt conc route
     │ Int64 Int64 Int64 Int64? String
─────┼──────────────────────────────────────
   1 │ 1 0 10 missing iv
   2 │ 1 1 0 8 iv
   3 │ 1 2 0 6 iv
   4 │ 1 3 0 4 iv
   5 │ 1 4 0 2 iv
   6 │ 2 0 10 missing iv
   7 │ 2 1 0 8 iv
   8 │ 2 2 0 6 iv
   9 │ 2 3 0 missing iv
  10 │ 2 4 0 missing iv

julia> ncapop = read_nca(df1)
NCAPopulation (2 subjects):
  Number of missing observations: 4
  Number of blq observations: 0

julia> NCA.lambdaz(ncapop)
[ Info: ID 2 errored: lambdaz calculation needs at least three data points between Cmax and the last positive concentration
2×2 DataFrame
 Row │ id lambdaz
     │ String Float64?
─────┼────────────────────────
   1 │ 1 0.549306
   2 │ 2 missing

julia> NCA.auc(ncapop)
[ Info: ID 2 errored: lambdaz calculation needs at least three data points between Cmax and the last positive concentration
2×2 DataFrame
 Row │ id auc
     │ String Float64?
─────┼──────────────────────
   1 │ 1 27.9743
   2 │ 2 missing

julia> NCA.auc(ncapop, interval = (0, 2))
2×2 DataFrame
 Row │ id auc0_2
     │ String Float64
─────┼─────────────────
   1 │ 1 16.3333
   2 │ 2 16.3333

julia> NCA.auc(ncapop, interval = (0, 3))
[ Info: ID 2 errored: lambdaz calculation needs at least three data points between Cmax and the last positive concentration
2×2 DataFrame
 Row │ id auc0_3
     │ String Float64?
─────┼──────────────────────
   1 │ 1 21.3333
   2 │ 2 missing

```

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<div class="post-metadata">

**Author:** ![donaldlee3](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.pumas.ai/donaldlee3/32/165_2.png) [@donaldlee3](https://discourse.pumas.ai/u/donaldlee3)\
**Post date:** [March 10, 2024, 8:50pm UTC](https://discourse.pumas.ai/t/auc-bug-with-interval/990/3 "2024-03-10T20:50:13Z")

</div>

Hi @vijay,

I’ve identified the source of the problem. I have multiple dose data and group by occasion, as opposed to using `ii`. I still give the `read_NCA` `time = :time` as opposed to `time = :tad`. It appears that the auc function with a time interval is calculating `tad` itself for all the occasions, which is resulting in numerical/decimal issues. For example, my last `tad` should be 27.9999, but if I manually create my own `tad` column, and give `time = :tad` to `read_NCA`, I will get `missing` from the auc calculation on a time interval, due to the last time being 27.999899999999997.

I have fixed this issue by correcting the numerical issues:  
`df.tad .= ifelse.(df.tad .> 27, 27.9999, df1.tad)`

It would be great if there were a way for the user to not have to deal with these numerical issues.