Survival analysis for droplet-freezing data: Kaplan–Meier confidence intervals and log-rank tests

Abstract. Droplet‑freezing assays underpin immersion‑mode ice‑nucleation research yet approaches to uncertainty quantification for fraction‑frozen curves and derived active‑site densities (n_s(T)) are inconsistent. Further, there is not currently a rigorous method for significance testing the difference between fraction frozen curves. To address these issues, we recast droplet‑freezing measurements as survival data and apply analysis techniques typically used in medical statistics. Using the Kaplan–Meier estimator, we derive nonparametric confidence intervals for droplet fraction frozen and n_s(T) without binning or model assumptions, matching Monte‑Carlo and studentized‑bootstrapped intervals on a literature volcanic ash ice nucleation dataset. Confidence intervals calculated for simulated datasets show precision improves with sample size and with steeper fraction frozen curves. Adapting the log-rank test, we introduce a method for comparing fraction frozen curves and demonstrate its application to literature and simulated droplet freezing datasets. We recommend reporting Kaplan–Meier confidence intervals on droplet freezing datasets and employing the log-rank test when comparing droplet fraction frozen curves.