Imputing Partial Birth Dates Using Day of the Week

In de-identified data, exact birth dates are suppressed to maintain the confidentiality of research participants. When the partial birth date includes only the month and year, researchers who need exact dates must impute a day of the month. In some deidentified datasets, the day of the week is also provided, but this variable is uncommonly incorporated into the imputation of partial dates.

To examine the extent to which misclassification is reduced by incorporating the day of the week into partial birth date imputation.

We simulated a population of 594,677 people using the distribution of birthdays in England and Wales in 2024. We imputed birth dates using four methods: (1) the first day of the month, (2) the 15th of the month, (3) randomly selecting a day of the month and (4) randomly selecting a day of the month conditional on the day of the week. We quantified misclassification as the median number of days between the imputed and true birth date and as the cumulative percentage of the population whose imputed birth date fell within a given number of weeks of their true birth date.

Incorporating the day of the week reduced misclassification, with a median of 7 days between the imputed and exact birth dates compared to 8-15 for the other methods. For nearly a quarter of the population, their imputed birth date was their true birth date, compared to 3% in other methods. However, using the 15th day of the month was the best method to ensure that no misclassification was greater than 3 weeks.

Incorporating day of the week into random birth date selection reduced misclassification. This method is easily accomplished in standard statistical software.