Community Mental Health Services Outpatient Appointment Interval Length and Crisis Relapse Detection in Rwandan Health Centres: A Regression Discontinuity in Scheduling Thresholds

Scheduling thresholds in community mental health services create natural discontinuities in the intensity of outpatient contact, yet the consequences of these discontinuities for crisis relapse detection remain poorly specified. The framework treats the threshold as a locally randomised assignment mechanism and specifies the conditions under which a discontinuity in detection rates can be attributed to interval length rather than to patient composition. Using published DHS Program data on family planning messages at community meetings across fifteen African countries (2021-2025), the analysis establishes the distributional context for community-level health messaging against which mental health scheduling operates: the mean indicator value was 29.733 (SD = 17.495, N = 15), ranging from 6.60 in Mali to 73.40 in Malawi. These values characterise the community health information environment within which appointment intervals are embedded, not the scheduling effect itself. It argues that the regression discontinuity design is appropriate for scheduling thresholds precisely because it exploits the administrative rule rather than requiring experimental manipulation, and it identifies the conditions under which the design fails.