Data model and censoring

  • Each case contributes to time-to-event analysis with:
    • event=1: approved (closed)
    • event=0: pending (right-censored at analysis date)
  • Two endpoints are modeled:
    • total time: receipt -> I-485 approval
    • interview lag: interview -> I-485 approval
  • Primary model fits use all office-filtered rows with valid timing information; they are not restricted to a fixed receipt-year cohort.
  • When the site shows temporal comparisons for receipt -> interview, it stratifies by interview timing so early-2026 office activity is visible even when those cases have 2025 receipt dates.

Non-parametric baseline

  • Kaplan-Meier estimator is computed over unique event/censor times.
  • Published curves include event and censor rug markers.

Parametric baseline

  • Total-time distribution is fit with censored lognormal MLE:
    • likelihood uses log-PDF for events and log-survival for right-censored rows.
    • optimization uses Nelder-Mead on (mu, log_sigma).
  • Interview->approval uses shifted lognormal (t + 0.5) to handle zero-day approvals.

USCIS-tail mixture (optional)

  • Fast regime: censored-lognormal baseline.
  • Slow regime: delayed exponential tail beginning at day 300.
  • Calibration anchors:
    • F(300)=0.80
    • F(629)=0.93
  • If the fitted baseline is already slower than the day-300 anchor, the calibration falls back to p_slow = 0 rather than forcing an infeasible negative slow mass.
  • Conditional pending-case probabilities are computed under both baseline and updated mixture model for all pending office-filtered cases with a known receipt date.