The Guyot algorithm (2012), explained

Updated 2026-09-25 · TrialCurve methods team

Inputs

• Digitised step points (t_k, S_k) along the curve, starting at (0, 1).
• Times t_i of the numbers-at-risk table and the counts n_i.
• Optionally, the total number of events, which fixes the final interval.

The algorithm, step by step

1. Split the curve into intervals at the at-risk table times. Each interval i runs from t_i to t_i+1 and contains the digitised points in between.
2. First guess of censorings: nc_i = round(n_i × S(t_i+1)/S(t_i) − n_i+1).
3. Distribute censorings evenly across the interval (the key assumption), giving the censorings between consecutive digitised points.
4. Derive events at each point so that the KM estimate reproduces the digitised drop: d_k = round(n̂_k × (1 − S_k/Ŝ_last)), then update the number at risk n̂_k+1 = n̂_k − d_k − c_k.
5. Adjust and repeat: if the implied n̂ at t_i+1 differs from the published n_i+1, shift the censoring count by the difference and recompute until they agree.
6. Final interval: use the average censoring rate from earlier intervals, or adjust censoring so the total events match the reported count.
7. Write out IPD: events at the digitised step times, censorings at the midpoints between points, and anyone still at risk censored at the last time.

Code

In R, the IPDfromKM package (Liu et al. 2021) and reconstructKM implement the algorithm on coordinates you have already digitised. Once you have IPD, the analysis is standard:

library(survival)
ipd <- read.csv("reconstructed_ipd.csv")          # arm, time, event
fit <- coxph(Surv(time, event) ~ arm, data = ipd)
summary(fit)                                        # HR, 95% CI
survfit(Surv(time, event) ~ arm, data = ipd)        # medians

In Python, lifelines gives the same (CoxPHFitter, KaplanMeierFitter). TrialCurve runs a faithful port of the original algorithm server-side, with guards for degenerate input, and returns the IPD directly from an image.

Assumptions and limitations

• Censoring is uniform within each at-risk interval. This is fine when table times are close together and weaker when they are years apart.
• Events happen exactly at digitised step times, so digitisation precision limits event-time precision.
• With no at-risk table, only the initial N constrains the result and the tail becomes uncertain.
• Validation studies report good agreement with published HRs when the table is available (Saluja et al. 2019: mean HR error 0.0094).

Newer methods

Recent work automates the digitisation step. SurvdigitizeR (2024) traces curves automatically. KM-GPT (2025) and KMGen (2026) combine language models with computer vision. RESOLVE-IPD (2025) extracts from vector PDFs and models censor marks. They all feed a Guyot-style reconstruction; the tool comparison summarises how they differ.

FAQ