Handling coarsened age information in the analysis of emergency department presentations

Administrative databases offer vast amounts of data that provide opportunities for cost-effective insights. They simultaneously pose significant challenges to statistical analysis such as the redaction of data because of privacy policies and the provision of data that may not be at the level of detail required. For example, ages in years rather than birthdates available at event dates can pose challenges to the analysis of recurrent event data.

Hu and Rosychuk provided a strategy for estimating age-varying effects in a marginal regression analysis of recurrent event times when birthdates are all missing. They analyzed emergency department (ED) visits made by children and youth and privacy rules prevented all birthdates to be released, and justified their approach via a simulation and asymptotic study. With recent changes in data access rules, we requested a new extract of data for April 2010 to March 2017 that includes patient birthdates. This allows us to compare the estimates using the Hu and Rosychuk (HR) approach for coarsened ages with estimates under the true, known ages to further examine their approach numerically. The performance of the HR approach under five scenarios is considered: uniform distribution for missing birthdates, uniform distribution for missing birthdates with supplementary data on age, empirical distribution for missing birthdates, smaller sample size, and an additional year of data.

Data from 33,299 subjects provided 58,166 ED visits. About 67% of subjects had one ED visit and less than 9% of subjects made over three visits during the study period. Most visits (84.0%) were made by teenagers between 13 and 17 years old. The uniform distribution and the HR modeling approach capture the main trends over age of the estimates when compared to the known birthdates. Boys had higher ED visit frequencies than girls in the younger ages whereas girls had higher ED visit frequencies than boys for the older ages. Including additional age data based on age at end of fiscal year did not sufficiently narrow the widths of potential birthdate intervals to influence estimates. The empirical distribution of the known birthdates was close to a uniform distribution and therefore, use of the empirical distribution did not change the estimates provided by assuming a uniform distribution for the missing birthdates. The HR approach performed well for a smaller sample size, although estimates were less smooth when there were very few ED visits at some younger ages. When an additional year of data is added, the estimates become better at these younger ages.

Overall the Hu and Rosychuk approach for coarsened ages performed well and captured the key features of the relationships between ED visit frequency and covariates.