Regression for Hierarchically Ordered Clinical Outcomes via Pairwise Comparisons (Bradley-Terry-Davidson Model)

Provides regression for hierarchically ordered clinical outcomes via pairwise comparisons, using a covariate-adjusted Davidson (Bradley-Terry with ties) model with U-statistic sandwich standard errors. A hierarchy of outcomes (binary, ordinal, continuous, and time-to-event, with eligibility guards and tie margins) is defined; all pairs of subjects are scored lexicographically; and the resulting win / loss / tie data are analysed. Unadjusted win statistics (net benefit, win ratio, win odds), diagnostics, and a worked example based on outcomes after allogeneic stem cell transplant are also provided. The computational engine is written in 'C++' using 'Rcpp' and 'RcppEigen'.

hpsreg

Regression analysis of hierarchically ordered clinical outcomes via pairwise comparisons (Bradley-Terry-Davidson Model).

1. Design a hierarchy of outcomes (hierarchy(), lvl_binary(), lvl_ordinal(), lvl_continuous(), lvl_tte(), lvl_custom(), lvl_group()), with tie margins and eligibility guards (when =).
2. Score all pairs of subjects (score_pairs()): the first level that separates a pair decides it. Compiled kernel with early exit; resolution() shows where pairs are decided.
3. Estimate: covariate-adjusted Davidson (Bradley-Terry with ties) model with U-statistic sandwich standard errors (btd()); unadjusted net benefit / win ratio / win odds (win_stats()); checks (btd_calibration()); predictions (predict(), btd_pair_probs()).

Quick start (from scratch)

Define the hierarchy from the columns of your data frame, score all pairs, and fit. Levels are listed from highest to lowest priority.

library(hpsreg)
dat <- simulate_hps(N = 613, seed = 1)          # stem cell transplant example data

h <- hierarchy(
  lvl_tte("death_day",   better = "later", name = "survival"),    # NA = no death by day 180
  lvl_tte("relapse_day", better = "later", name = "relapse"),
  lvl_group("GVHD",
    lvl_ordinal("gvhd_grade", better = "lower", name = "grade"),
    lvl_binary("gvhd_resolved", favorable = 1, when = "gvhd_grade > 0", name = "resolution"),
    lvl_continuous("gvhd_onset_day", better = "higher", when = "gvhd_grade > 0", name = "onset"))
)
pw  <- score_pairs(h, dat)                       # win / loss / tie for every pair
resolution(pw)                                   # where pairs are decided
fit <- btd(~ donor_type + age + dri, data = dat, pairs = pw)
summary(fit)

Two workflows

1. Pre-computed pairs. Score once, then reuse the pairs for diagnostics, win statistics and several covariate models. Best for exploration, because scoring is the only step that depends on the hierarchy.

pw   <- score_pairs(h, dat)
win_stats(pw, dat$year)         # unadjusted net benefit / win ratio / win odds
fit1 <- btd(~ donor_type + age, data = dat, pairs = pw)
fit2 <- btd(~ donor_type + age + dri, data = dat, pairs = pw)   # no rescoring

2. Inline scoring. Hand btd() the hierarchy and it scores the pairs itself. The pairs stay available as fit$pairs, so btd_calibration(fit) still works.

fit <- btd(~ donor_type + age + dri, data = dat, hierarchy = h)

In both workflows data must be the same data frame (same rows, same order) that is scored. Changing the hierarchy (reordering levels, adding a margin) means scoring again.

Worked examples (installed under system.file("examples", package = "hpsreg")): hps-example.Rmd (render with rmarkdown::render()) and hps_simulation_study.R.

Install

R CMD INSTALL hpsreg_0.1.0.tar.gz     # needs a C++ toolchain; Rcpp and RcppEigen

Large N: compact and streaming storage

All N(N-1)/2 pairs of N = 10,000 patients are 50 million pairs. btd() has four storage modes (storage = argument; "auto" picks one):

"auto" uses stored pairs up to about N = 2200, compact up to about N = 44,000 and streaming beyond that. Compact and streaming need a hierarchy of built-in levels (at most 84 comparisons for compact) and cannot take pre-computed pairs.

fit <- btd(~ donor_type + age, data = dat, hierarchy = h)                       # auto
fit <- btd(~ donor_type + age, data = dat, hierarchy = h, storage = "compact")  # explicit
resolution(h, data = dat)                     # counts per level, nothing stored
win_stats(h, dat$arm, data = dat)             # unadjusted win statistics, nothing stored
btd_calibration(fit)                          # works on compact and streamed fits

Optional multithreading (OpenMP; one thread by default, identical results for any thread count): btd(..., control = btd_control(threads = 4)) or options(hpsreg.threads = 4). openmp_threads() returns 0 if your build has no OpenMP (for example the default macOS toolchain); everything then runs single-threaded.

Scope and limitations

• Time-to-event levels: complete follow-up, or right censoring with the Gehan rule (uninformative pairs pass to the next level and are flagged). IPCW (Peron) scoring is not implemented; the rule is biased toward the null under heavy censoring.
• Pairs are all N(N-1)/2 pairs (or a supplied subset). Sandwich variances are exact in the U-statistic sense only for the complete set. Stored pairs cost about 20 bytes each (more at peak); max_pairs guards score_pairs(). Streaming (storage = "stream") avoids storing pairs.
• Compact and streaming modes need a hierarchy made of built-in levels (no lvl_custom()) and do not accept pre-computed or sampled pairs.
• Cross-arm-only pair sets with matching variance theory are not implemented.
• One tie parameter is shared by all levels; use btd_calibration() to check the single latent-scale assumption. Thresholds and censoring can make pairwise relations intransitive.
• The maintainer e-mail in DESCRIPTION is a placeholder.