Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The study will conduct enrollment over a period of two years, with the option to extend to a third year if feasible. During this period, we will track interim outcomes while continuing to enroll participants. The primary comparison will be between individuals who receive the full suite of Shelter Diversion Program services, including rental assistance and case management, and those who do not receive these services.
For two years of enrollment, we anticipate enrolling approximately 1,760 individuals, with ~213 individuals in the treatment group and ~1,547 in the control group. According to STEH data, 14.9% of callers who are eligible for Shelter Diversion but do not receive those services entered shelter within 12 months. With an expected take-up rate of 75-90% in the treatment group, we are powered to detect an 8.3-9.2 percentage point decrease in the likelihood of emergency shelter use from this baseline, which corresponds to a 55.6-61.6% decline.
Additionally, we will measure additional calls to the CAP Helpline. According to STEH data, about 54.7 percent of callers eligible for Shelter Diversion but who do not receive services call back the CAP Helpline within 12 months. . With the anticipated sample size and take-up rate, we will be able to detect an 11.6-12.9 percentage point decrease in the likelihood of repeated CAP Helpline calls from this baseline, representing a 21.2-23.6% decline.
If enrollment is extended to three years, increasing the sample size to approximately 2,640 individuals, the minimum detectable effect sizes will be smaller. For emergency shelter use, the detectable effect size will decrease to 6.8-7.5 percentage points, representing a 45.5-50.2% decline. For repeated CAP Helpline calls, the detectable effect size will decrease to 9.5-10.5 percentage points, representing a 16.4-19.2% decline.
Combining two to three years of enrollment, and depending on program take-up and study duration, we are powered to detect a 45-62% decline in shelter use and a 16-24% decline in calling CAP again within the 12 months after randomization.