Time to Take a Chance: The Promise of Royston-Parmar Proportional Hazard Models for Understanding Caseload Transitions

In this letter to the editor, we compare six different event history models to estimate which eligible families participated in a subsidized rental housing program and when. Answering these questions can inform efforts to improve program marketing and outreach, staffing and budgeting, triage, bias identification, as well as benchmarking and evaluation. One of six specifications clearly outperforms the others and understanding how will inform similar research pursuits. Although decision-relevant participation patterns are available in state administrative records, deciphering them is difficult for several well-known reasons. Participants enter and exit the eligible risk pool at different times, for different reasons, and at different rates. To answer our questions of when and whom, we restructure the data from calendar to relative months and then employ event history models designed to accurately estimate a complete hypothetical risk trajectory from observed spells of varying lengths, many of which ended before families took up the rental subsidy, (i.e., censored observation spells). We find that eligible parents most likely to take up the subsidy live in high-rent counties, have relatively strong recent work history, short prior adult lifetime TANF receipt, and medium-size families. Program take-up fell substantially during the COVID-19 pandemic. Contrasting the application of six parallel specifications, we find that a Royston-Parmar proportional hazard model achieves an exceptional balance between the descriptive accuracy of discrete time approaches and the elegance of Cox regression.