# Date and Time Imputation

# Introduction

This vignette is broken into three major sections. The first section briefly explores the imputation rules used in `{admiral}`. The second section focuses on imputation functions that work on vectors with lots of small examples to explore the imputation rules. These vector-based functions form the backbone of `{admiral}`’s more powerful functions `derive_vars_dt()` and `derive_vars_dtm()` for building ADaM dataset. The final section moves into more detailed examples that a user might face while working on ADaMs in need of `*DT` and `*DTM` variables.

## Required Packages

The examples of this vignette require the following packages.

    library(admiral)
    library(lubridate)
    library(tibble)
    library(dplyr, warn.conflicts = FALSE)

# Imputation Rules

Date and time is collected in SDTM as character values using the extended ISO 8601 format. For example, `"2019-10-9T13:42:00"`. It allows that some parts of the date or time are missing, e.g., `"2019-10"` if the day and the time is unknown.

The ADaM timing variables like `ADTM` (Analysis Datetime) or `ADY` (Analysis Relative Day) are numeric variables. They can be derived only if the date or datetime is complete. Therefore `{admiral}` provides imputation functions which fill in missing date or time parts according to certain imputation rules.

In `{admiral}` users will primarily use two functions `derive_vars_dt()` and `derive_vars_dtm()` for date and datetime imputations respectively. In all other functions where dates can be passed as an argument, we expect full dates or datetimes (unless otherwise specified), so if any possibility of partials then these functions should be used as a first step to make the required imputation.

The functions that need to do date/time imputation follow a rule that we have called Highest Imputation, which has a corresponding argument in all our functions called `highest_imputation`. The rule is best explained by working through the examples below, but to put it briefly, this rule allows a user to control which components of the `--DTC` value are imputed if they are missing.

The default imputation for `_dtm()` functions, e.g. `impute_dtc_dtm()`, `derive_vars_dtm()`, is “h” (hours). A user can specify that that no imputation is to be done by setting `highest_imputation = n`. However, for for `_dt()` functions, e.g. `impute_dtc_dt()`, `derive_vars_dt()` the default imputation is already set as `highest_imputation = "n"`.

Care must be taken when deciding on level of imputation. If a component is at a higher level than the highest imputation level is missing, `NA_character_` is returned. For example, for `highest_imputation = "D"` `"2020"` results in `NA_character_` because the month is missing.

We encourage readers to explore in more detail the `highest_imputation` options in both the `_dtm()` and `_dt()` function documentations and in the examples below.

## Imputation on a Vector

In our first example, we will make use of `impute_dtc_dtm()` on `2019-10` setting `highest_imputation = "M"`. The argument `date_imputation` and `time_imputation` are given expressed inputs of the imputation we would like to see done.

    impute_dtc_dtm(
      "2019-10",
      highest_imputation = "M",
      date_imputation = "01-01",
      time_imputation = "00:00:00"
    )
    #> [1] "2019-10-01T00:00:00"

Next we impute using `2019-02`, which if done naively can result in invalid dates, e.g.,

    impute_dtc_dtm(
      "2019-02",
      highest_imputation = "M",
      date_imputation = "02-31",
      time_imputation = "00:00:00"
    )
    #> [1] "2019-02-31T00:00:00"

Therefore the keywords `"first"` or `"last"` can be specified in `date_imputation` to request that missing parts are replaced by the first or last possible value - giving us a valid date!

    impute_dtc_dtm(
      "2019-02",
      highest_imputation = "M",
      date_imputation = "last",
      time_imputation = "00:00:00"
    )
    #> [1] "2019-02-28T00:00:00"

For dates, there is the additional option to use keyword `"mid"` to impute missing day to `15` or missing day and month to `06-30`, but note the different behavior below depending on the `preserve` argument for the case when month only is missing:

    dates <- c(
      "2019-02",
      "2019",
      "2019---01"
    )
    impute_dtc_dtm(
      dates,
      highest_imputation = "M",
      date_imputation = "mid",
      time_imputation = "00:00:00",
      preserve = FALSE
    )
    #> [1] "2019-02-15T00:00:00" "2019-06-30T00:00:00" "2019-06-30T00:00:00"
    impute_dtc_dtm(
      dates,
      highest_imputation = "M",
      date_imputation = "mid",
      time_imputation = "00:00:00",
      preserve = TRUE
    )
    #> [1] "2019-02-15T00:00:00" "2019-06-30T00:00:00" "2019-06-01T00:00:00"

If you wanted to achieve a similar result by replacing any missing part of the date with a fixed value `06-15`, this is also possible, but note the difference in days for cases when month is missing:

    dates <- c(
      "2019-02",
      "2019",
      "2019---01"
    )
    impute_dtc_dtm(
      dates,
      highest_imputation = "M",
      date_imputation = "06-15",
      time_imputation = "00:00:00"
    )
    #> [1] "2019-02-15T00:00:00" "2019-06-15T00:00:00" "2019-06-15T00:00:00"

## Imputation Level

The imputation level, i.e., which components are imputed if they are missing, is controlled by the `highest_imputation` argument. All components up to the specified level are imputed.

    dates <- c(
      "2019-02-03T12:30:15",
      "2019-02-03T12:30",
      "2019-02-03",
      "2019-02",
      "2019"
    )

    # Do not impute
    impute_dtc_dtm(
      dates,
      highest_imputation = "n"
    )
    #> [1] "2019-02-03T12:30:15" NA                    NA
    #> [4] NA                    NA

    # Impute seconds only
    impute_dtc_dtm(
      dates,
      highest_imputation = "s"
    )
    #> [1] "2019-02-03T12:30:15" "2019-02-03T12:30:00" NA
    #> [4] NA                    NA

    # Impute time (hours, minutes, seconds) only
    impute_dtc_dtm(
      dates,
      highest_imputation = "h"
    )
    #> [1] "2019-02-03T12:30:15" "2019-02-03T12:30:00" "2019-02-03T00:00:00"
    #> [4] NA                    NA

    # Impute days and time
    impute_dtc_dtm(
      dates,
      highest_imputation = "D"
    )
    #> [1] "2019-02-03T12:30:15" "2019-02-03T12:30:00" "2019-02-03T00:00:00"
    #> [4] "2019-02-01T00:00:00" NA

    # Impute date (months and days) and time
    impute_dtc_dtm(
      dates,
      highest_imputation = "M"
    )
    #> [1] "2019-02-03T12:30:15" "2019-02-03T12:30:00" "2019-02-03T00:00:00"
    #> [4] "2019-02-01T00:00:00" "2019-01-01T00:00:00"

For imputation of years (`highest_imputation = "Y"`) see next section.

## Minimum/Maximum Dates

In some scenarios the imputed date should not be before or after certain dates. For example an imputed date after data cut off date or death date is not desirable. The `{admiral}` imputation functions provide the `min_dates` and `max_dates` argument to specify those dates. For example:

    impute_dtc_dtm(
      "2019-02",
      highest_imputation = "M",
      date_imputation = "last",
      time_imputation = "last",
      max_dates = list(ymd("2019-01-14"), ymd("2019-02-25"))
    )
    #> [1] "2019-02-25T23:59:59"

It is ensured that the imputed date is not after any of the specified dates. Only dates which are in the range of possible dates of the `--DTC` value are considered. The possible dates are defined by the missing parts of the `--DTC` date, i.e., for “2019-02” the possible dates range from “2019-02-01” to “2019-02-28”. Thus “2019-01-14” is ignored. This ensures that the non-missing parts of the `--DTC` date are not changed.

If the `min_dates` or `max_dates` argument is specified, it is also possible to impute completely missing dates. For `date_imputation = "first"` the `min_dates` argument must be specified and for `date_imputation = "last"` the `max_dates` argument. For other imputation rules imputing the year is not possible.

    # Impute year to first
    impute_dtc_dtm(
      c("2019-02", NA),
      highest_imputation = "Y",
      min_dates = list(
        ymd("2019-01-14", NA),
        ymd("2019-02-25", "2020-01-01")
      )
    )
    #> [1] "2019-02-25T00:00:00" "2020-01-01T00:00:00"

    # Impute year to last
    impute_dtc_dtm(
      c("2019-02", NA),
      highest_imputation = "Y",
      date_imputation = "last",
      time_imputation = "last",
      max_dates = list(
        ymd("2019-01-14", NA),
        ymd("2019-02-25", "2020-01-01")
      )
    )
    #> [1] "2019-02-25T23:59:59" "2020-01-01T23:59:59"

# Imputation Flags

ADaM requires that date or datetime variables for which imputation was used are accompanied by date and/or time imputation flag variables (`*DTF` and `*TMF`, e.g., `ADTF` and `ATMF` for `ADTM`). These variables indicate the highest level that was imputed, e.g., if minutes and seconds were imputed, the imputation flag is set to `"M"`. The `{admiral}` functions which derive imputed variables are also adding the corresponding imputation flag variables.

Note: The `{admiral}` datetime imputation function provides the `ignore_seconds_flag` argument which can be set to `FALSE` in cases where seconds are expected. This is due to the following from ADaM IG: For a given SDTM `--DTC` variable, if only hours and minutes are ever collected, and seconds are imputed in `*DTM` as `00`, then it is not necessary to set `*TMF` to `"S"`.

# Imputation Functions

`{admiral}` provides the following functions for imputation:

- `derive_vars_dt()`: Adds a date variable and a date imputation flag variable (optional) based on a –DTC variable and imputation rules.
- `derive_vars_dtm()`: Adds a datetime variable, a date imputation flag variable, and a time imputation flag variable (both optional) based on a –DTC variable and imputation rules.
- `impute_dtc_dtm()`: Returns a complete ISO 8601 datetime or `NA` based on a partial ISO 8601 datetime and imputation rules.
- `impute_dtc_dt()`: Returns a complete ISO 8601 date (without time) or `NA` based on a partial ISO 8601 date(time) and imputation rules.
- `convert_dtc_to_dt()`: Returns a date if the input ISO 8601 date is complete. Otherwise, `NA` is returned.
- `convert_dtc_to_dtm()`: Returns a datetime if the input ISO 8601 date is complete (with missing time replaced by `"00:00:00"` as default). Otherwise, NA is returned.
- `compute_dtf()`: Returns the date imputation flag.
- `compute_tmf()`: Returns the time imputation flag.

# Examples

## Create an Imputed Datetime and Date Variable and Imputation Flag Variables

The `derive_vars_dtm()` function derives an imputed datetime variable and the corresponding date and time imputation flags. The imputed date variable can be derived by using the `derive_vars_dtm_to_dt()` function. It is not necessary and advisable to perform the imputation for the date variable if it was already done for the datetime variable. CDISC considers the datetime and the date variable as two representations of the same date. Thus the imputation must be the same and the imputation flags are valid for both the datetime and the date variable.

    ae <- tribble(
      ~AESTDTC,
      "2019-08-09T12:34",
      "2019-04-12",
      "2010-09",
      NA_character_
    ) %>%
      derive_vars_dtm(
        dtc = AESTDTC,
        new_vars_prefix = "AST",
        highest_imputation = "M",
        date_imputation = "first",
        time_imputation = "first"
      ) %>%
      derive_vars_dtm_to_dt(exprs(ASTDTM))

AESTDTC | ASTDTM | ASTDTF | ASTTMF | ASTDT
--- | --- | --- | --- | ---
2019-08-09T12:34 | 2019-08-09 12:34:00 | NA | NA | 2019-08-09
2019-04-12 | 2019-04-12 00:00:00 | NA | H | 2019-04-12
2010-09 | 2010-09-01 00:00:00 | D | H | 2010-09-01
NA | NA | NA | NA | NA

## Create an Imputed Date Variable and Imputation Flag Variable

If an imputed date variable without a corresponding datetime variable is required, it can be derived by the `derive_vars_dt()` function.

    ae <- tribble(
      ~AESTDTC,
      "2019-08-09T12:34:00",
      "2019-04-12",
      "2010-09",
      NA_character_
    ) %>%
      derive_vars_dt(
        dtc = AESTDTC,
        new_vars_prefix = "AST",
        highest_imputation = "M",
        date_imputation = "first"
      )

AESTDTC | ASTDT | ASTDTF
--- | --- | ---
2019-08-09T12:34:00 | 2019-08-09 | NA
2019-04-12 | 2019-04-12 | NA
2010-09 | 2010-09-01 | D
NA | NA | NA

## Impute Time without Imputing Date

If the time should be imputed but not the date, the `highest_imputation` argument should be set to `"h"`. This results in `NA` if the date is partial. As no date is imputed the date imputation flag is not created.

    ae <- tribble(
      ~AESTDTC,
      "2019-08-09T12:34",
      "2019-04-12",
      "2010-09",
      NA_character_
    ) %>%
      derive_vars_dtm(
        dtc = AESTDTC,
        new_vars_prefix = "AST",
        highest_imputation = "h",
        time_imputation = "first"
      )

AESTDTC | ASTDTM | ASTTMF
--- | --- | ---
2019-08-09T12:34 | 2019-08-09 12:34:00 | NA
2019-04-12 | 2019-04-12 00:00:00 | H
2010-09 | NA | NA
NA | NA | NA

## Avoid Imputed Dates Before a Particular Date

Usually the adverse event start date is imputed as the earliest date of all possible dates when filling the missing parts. The result may be a date before treatment start date. This is not desirable because the adverse event would not be considered as treatment emergent and excluded from the adverse event summaries. This can be avoided by specifying the treatment start date variable (`TRTSDTM`) for the `min_dates` argument.

Please note that `TRTSDTM` is used as imputed date only if the non missing date and time parts of `AESTDTC` coincide with those of `TRTSDTM`. Therefore `2019-10` is not imputed as `2019-11-11 12:34`. This ensures that collected information is not changed by the imputation.

    ae <- tribble(
      ~AESTDTC, ~TRTSDTM,
      "2019-08-09T12:34", ymd_hm("2019-11-11T12:34"),
      "2019-10", ymd_hm("2019-11-11T12:34"),
      "2019-11", ymd_hm("2019-11-11T12:34"),
      "2019-12-04", ymd_hm("2019-11-11T12:34")
    ) %>%
      derive_vars_dtm(
        dtc = AESTDTC,
        new_vars_prefix = "AST",
        highest_imputation = "M",
        date_imputation = "first",
        time_imputation = "first",
        min_dates = exprs(TRTSDTM)
      )

AESTDTC | TRTSDTM | ASTDTM | ASTDTF | ASTTMF
--- | --- | --- | --- | ---
2019-08-09T12:34 | 2019-11-11 12:34:00 | 2019-08-09 12:34:00 | NA | NA
2019-10 | 2019-11-11 12:34:00 | 2019-10-01 00:00:00 | D | H
2019-11 | 2019-11-11 12:34:00 | 2019-11-11 12:34:00 | D | H
2019-12-04 | 2019-11-11 12:34:00 | 2019-12-04 00:00:00 | NA | H

## Avoid Imputed Dates After a Particular Date

If a date is imputed as the latest date of all possible dates when filling the missing parts, it should not result in dates after data cut off or death. This can be achieved by specifying the dates for the `max_dates` argument.

Please note that non missing date parts are not changed. Thus `2019-12-04` is imputed as `2019-12-04 23:59:59` although it is after the data cut off date. It may make sense to replace it by the data cut off date but this is not part of the imputation. It should be done in a separate data cleaning or data cut off step.

    ae <- tribble(
      ~AEENDTC, ~DTHDT, ~DCUTDT,
      "2019-08-09T12:34", ymd("2019-11-11"), ymd("2019-12-02"),
      "2019-11", ymd("2019-11-11"), ymd("2019-12-02"),
      "2019-12", NA, ymd("2019-12-02"),
      "2019-12-04", NA, ymd("2019-12-02")
    ) %>%
      derive_vars_dtm(
        dtc = AEENDTC,
        new_vars_prefix = "AEN",
        highest_imputation = "M",
        date_imputation = "last",
        time_imputation = "last",
        max_dates = exprs(DTHDT, DCUTDT)
      )

AEENDTC | DTHDT | DCUTDT | AENDTM | AENDTF | AENTMF
--- | --- | --- | --- | --- | ---
2019-08-09T12:34 | 2019-11-11 | 2019-12-02 | 2019-08-09 12:34:59 | NA | NA
2019-11 | 2019-11-11 | 2019-12-02 | 2019-11-11 23:59:59 | D | H
2019-12 | NA | 2019-12-02 | 2019-12-02 23:59:59 | D | H
2019-12-04 | NA | 2019-12-02 | 2019-12-04 23:59:59 | NA | H

## Imputation Without Creating a New Variable

If imputation is required without creating a new variable the `convert_dtc_to_dt()` function can be called to obtain a vector of imputed dates. It can be used for example in conditions:

    mh <- tribble(
      ~MHSTDTC,     ~TRTSDT,
      "2019-04",    ymd("2019-04-15"),
      "2019-04-01", ymd("2019-04-15"),
      "2019-05",    ymd("2019-04-15"),
      "2019-06-21", ymd("2019-04-15")
    ) %>%
      filter(
        convert_dtc_to_dt(
          MHSTDTC,
          highest_imputation = "M",
          date_imputation = "first"
        ) < TRTSDT
      )

MHSTDTC | TRTSDT
--- | ---
2019-04 | 2019-04-15
2019-04-01 | 2019-04-15

## Using More Than One Imputation Rule for a Variable

Using different imputation rules depending on the observation can be done by using `slice_derivation()`.

    vs <- tribble(
      ~VSDTC, ~VSTPT,
      "2019-08-09T12:34", NA,
      "2019-10-12", "PRE-DOSE",
      "2019-11-10", NA,
      "2019-12-04", NA
    ) %>%
      slice_derivation(
        derivation = derive_vars_dtm,
        args = params(
          dtc = VSDTC,
          new_vars_prefix = "A"
        ),
        derivation_slice(
          filter = VSTPT == "PRE-DOSE",
          args = params(time_imputation = "first")
        ),
        derivation_slice(
          filter = TRUE,
          args = params(time_imputation = "last")
        )
      )

VSDTC | VSTPT | ADTM | ATMF
--- | --- | --- | ---
2019-10-12 | PRE-DOSE | 2019-10-12 00:00:00 | H
2019-08-09T12:34 | NA | 2019-08-09 12:34:59 | NA
2019-11-10 | NA | 2019-11-10 23:59:59 | H
2019-12-04 | NA | 2019-12-04 23:59:59 | H