r – How to copy a value from one column to a new column if column A > column B?

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I am looking to create a new column called true_water_on in the dataframe trial_A.

  study_ID       randomisation            water_on           water_off
1        5 2021-01-01 11:00:00 2021-01-01 13:00:00 2021-01-01 18:00:00
2        6 2021-01-02 10:00:00 2021-01-02 09:00:00 2021-01-02 18:00:00
3        7 2021-01-03 10:00:00                <NA>                <NA>
4        8 2021-01-04 10:00:00 2021-01-04 09:45:00 2021-01-04 11:00:00

The conditions to populate it are as follows

  1. If “water_on” date and time precedes the time and date in “randomisation” then the randomisation data and time for that row is copied across into “true_water_on”. This occurs for study_ID 6 and 8; as demonstrated by
trial_A %>% mutate(TD_ran_waterstart = water_on - randomisation, units="mins")

  1. If “water_on” date and time occurs after the time and date in
    “randomisation” then the water_on data for that row is copied across
    into “water_drug_on”

  2. If there is no data and time recorded in “water_on” then NA is
    marked in “true_water_on”

Data

trial_A <- 
  data.frame(study_ID=c(5, 6, 7, 8), 
             randomisation=as.POSIXlt(c("2021-01-01 11:00", "2021-01-02 10:00", 
                                        "2021-01-03 10:00", "2021-01-04 10:00")), 
             water_on=as.POSIXlt(c("2021-01-01 13:00", "2021-01-02 09:00", NA, 
                                   "2021-01-04 09:45")), 
             water_off=as.POSIXlt(c("2021-01-01 18:00", "2021-01-02 18:00", NA, 
                                    "2021-01-04 11:00")))

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