Biostatistics & Clinical Trials
Pocock Win Ratio, Win Odds, and Net Treatment Benefit Formula
Analyze hierarchical composite clinical endpoints (death before hospitalization before biomarker) using Pocock’s Win Ratio, Dong’s tie-adjusted Win Odds, and Buyse’s Net Benefit.
Prioritize fatal events over non-fatal hospitalizations in composite endpoints
Conventional time-to-first-event Cox models treat a minor urgent clinic visit identically to cardiovascular death if the clinic visit happens first. Pocock et al. (2012) compare patient pairs hierarchically — checking Tier 1 (Survival) first, breaking Tier-1 ties on Tier 2 (Hospitalizations), and breaking remaining ties on Tier 3 (Quality-of-life score) — tallying total Treatment Wins N_W, Losses N_L, and Unresolved Ties N_T across N_pairs = N_W + N_L + N_T.
Check a 3-tier trial across N_pairs = 1,000 matched pairs: Tier 1 yields 90 Wins vs 60 Losses; Tier 2 yields 140 Wins vs 90 Losses; Tier 3 yields 130 Wins vs 90 Losses; leaving 400 ties (B2:C5). Total Wins N_W = 360 and Total Losses N_L = 240! Pocock’s Win Ratio is WR = 360 / 240 = 1.5000; Buyse’s (2010) Net Treatment Benefit is NTB = (360 - 240) / 1,000 = 0.1200 (+12.0% net excess wins); and Dong’s tie-adjusted Win Odds splits ties 50/50 as WO = (360 + 200) / (240 + 200) = 560 / 440 = 1.2727 (guaranteeing WO -> WR when ties = 0).
| Hierarchical Composite Metric | Pairwise Formula | Sample Output (1,000 Pairs) |
|---|---|---|
| Pocock Win Ratio (WR) | N_W / N_L (Ignores ties) | 1.5000 (360 / 240) |
| Matched-Pair 95% Lower WR Bound | EXP(LN(N_W / N_L) - 1.959964 * SQRT((N_W + N_L)/(N_W*N_L))) | 1.2740 (> 1.00 null!) |
| Dong Tie-Adjusted Win Odds (WO) | (N_W + 0.5 * N_T) / (N_L + 0.5 * N_T) | 1.2727 (Dampened by 40% ties) |
| Buyse Net Treatment Benefit (NTB) | (N_W - N_L) / (N_W + N_L + N_T) | +0.1200 (+12.0% net win edge) |
Pocock Hierarchical Win Ratio WR Formula
Sum treatment wins across all hierarchy tiers and divide by summed treatment losses, guarding zero losses explicitly.
=LET(n_win, SUM(B2:B4), n_los, SUM(C2:C4), IF(n_los <= 0, "Zero Treatment Losses", ROUND(n_win / n_los, 4)))Dong Tie-Adjusted Win Odds (WO) vs Win Ratio Convergence Check
Heavy tie rates make WR look dramatic on a tiny fraction of decisive pairs while WO reflects the full trial population! Verify by setting unresolved ties B5 = 0: Win Odds rises from 1.2727 to 1.5000, matching Win Ratio identically.
=LET(n_win, SUM(B2:B4), n_los, SUM(C2:C4), n_tie, B5, IF(OR(n_tie < 0, n_los + 0.5 * n_tie <= 0), "Invalid Pair Counts", ROUND((n_win + 0.5 * n_tie) / (n_los + 0.5 * n_tie), 4)))Try the example
Use the original values or change them to test your understanding.