Measurement error

library(tidyverse)
library(knitr)
library(kableExtra)

Background

On November 8 2026, the NEJM published “Left Bundle-Branch Pacing versus Right Ventricular Pacing for Atrioventricular Block”. This open-label, randomized, controlled trial assigned patients with atrioventricular block in a 1:1 ratio to receive left bundle-branch pacing or right ventricular pacing. The primary outcome was a composite of death from any cause, hospitalization for heart failure, or pacing-induced cardiomyopathy. At a median follow-up of 35.1 months (interquartile range, 23.6 to 40.7), the authors reported a primary-outcome event had occurred in 16 patients in the left bundle-branch pacing group and in 35 patients in the right ventricular pacing group (Kaplan–Meier 4-year cumulative incidence, 8.5% and 19.2%, respectively; hazard ratio, 0.41; 95% confidence interval, 0.23 to 0.75; P=0.003 by a stratified log-rank test). This lead the authors to conclude

Conclusion

“Among patients with atrioventricular block, left bundle-branch pacing was superior to right ventricular pacing in reducing the risk of a composite of death from any cause, hospitalization for heart failure, or pacing-induced cardiomyopathy.”

Nuances to the conclusion

The conclusion regarding the composite outcome certainly appears well supported by the reported data and statistical testing. However, the trial was unblinded and stopped early, features associated with exaggerated effect estimates. This matters because deaths (15 vs. 13) and heart-failure hospitalizations (2 vs. 7 as first events) were both rare and similar and the benefit thus rests on a substantial increase in unblinded, adjudicated echocardiographic cardiomyopathy (0 vs. 19). Inconsistent with this, atrial fibrillation, stroke, 6-minute walk distance, quality of life, and NYHA class did not differ between the groups. Moreover, zero cardiomyopathy events, as defined as a drop in ejection fraction of at least 10 points to below 50%, among 342 LBBP patients is surprising as temporal variability of 2D ejection fraction can exceed 10 points.

Simulating five protocol mandated follow-up echo-cardiograms per patient with a measurement SD of 4 points, measurement error alone would be expected to produce about five qualifying declines, even with no true change in ventricular function (Poisson probability of zero events ≈ 0.004).

## How surprising are 0 pacing-induced cardiomyopathy (PICM) events
## among 342 LBBP patients (OptimPacing, NEJM 2026)?
##
## Question: if every patient's TRUE ejection fraction were perfectly stable,
## how many would still meet the PICM echo definition through measurement
## variability alone?
## PICM definition: decrease >= 10 points from post-implant baseline,
## with resulting LVEF < 50%.
## Protocol (Table 1): pre-discharge baseline echo + 5 follow-up echoes
## (3, 6, 12, 24, 36 months).

set.seed(2026)
n      <- 342     # LBBP patients
n_fu   <- 5       # follow-up echoes per protocol
ef_mu  <- 63.2    # baseline mean LVEF, LBBP arm (Table 1)
ef_sd  <- 5.9     # observed baseline SD (includes measurement error)
nsim   <- 5000

sim_noise <- function(sd_meas) {
  sd_true <- sqrt(ef_sd^2 - sd_meas^2)   # true between-patient SD
  ev <- replicate(nsim, {
    ef_true <- rnorm(n, ef_mu, sd_true)                                 # true EF
    base    <- ef_true + rnorm(n, 0, sd_meas)                           # baseline = true + error
    fu      <- ef_true + matrix(rnorm(n * n_fu, 0, sd_meas), n, n_fu)   # 342 x 5 follow-up measurements
    sum(apply((base - fu >= 10) & (fu < 50), 1, any))
  })
  lambda <- mean(ev)                     # expected number of false events
  c(sd_meas         = sd_meas,
    p_per_patient   = lambda / n,
    expected_events = lambda,
    P0_simulated    = mean(ev == 0),
    P0_poisson      = exp(-lambda))      # Poisson P(0) = exp(-lambda)
}

res <- as.data.frame(t(sapply(c(3, 3.5, 4, 4.5, 5), sim_noise)))

kable(signif(res, 3),
      col.names = c("Measurement SD", "P(event) per patient", "Expected events",
                    "P(0 events), simulated", "P(0 events), Poisson")) |>
  kable_styling(full_width = FALSE)
## Preview image for the blog listing: must be a ggplot object, saved
## relative to this post's folder (Quarto renders from the post's directory)
p_prev <- ggplot(res, aes(sd_meas, expected_events)) +
  geom_line(linewidth = 1) +
  geom_point(size = 3) +
  geom_hline(yintercept = 0, linetype = "dashed", colour = "firebrick") +
  annotate("text", x = 3, y = 0.4, hjust = 0, colour = "firebrick",
           label = "Observed in LBBP arm: 0 events") +
  labs(x = "Echo measurement SD (LVEF points)",
       y = "Expected false PICM events (n = 342)",
       title = "Events expected from echo measurement error alone") +
  theme_minimal(base_size = 13)

ggsave("preview-image.png", p_prev, width = 8, height = 4.5, dpi = 150, bg = "white")

## Note: a 2D-echo temporal variability >10 points (Thavendiranathan et al.,
## JACC 2013) corresponds to a per-measurement SD of roughly 3.5-5 points.
## Any true intercurrent decline (ischemia, AF, valve disease) would only add
## events, so these probabilities of zero are upper bounds.

Table 1: Expected false-positive PICM events among 342 LBBP patients with perfectly stable true LVEF, by echo measurement SD (5000 simulations each)

Measurement SD	P(event) per patient	Expected events	P(0 events), simulated	P(0 events), Poisson
3.0	0.00376	1.29	0.2810	2.76e-01
3.5	0.00870	2.97	0.0552	5.11e-02
4.0	0.01590	5.42	0.0054	4.41e-03
4.5	0.02420	8.28	0.0002	2.54e-04
5.0	0.03300	11.30	0.0000	1.24e-05

p_prev

Expected number of false-positive PICM events from measurement error alone

Differential ascertainment or adjudication therefore seems a plausible explanation. A trial with blinded adjudication and clinical end points would seem needed.

Lessons

I wrote this up in a Letter to the NEJM, although their 175 word format means it is impossible to articulate the fill content of this blog and explains why I bothered with this post. Yet another reason is my NEJM letters’ acceptance rate is probably less than one in five.

1. Composite endpoints increase statistical power but with different health impacts the individual components should also be examined
2. Unblinded assessments of of judgmental (soft) outcomes may be subject to unintended ascertainment bias
3. Measurement error is a fact of clinical research and should not be overlooked. Here measurement error paradoxically provided additional support for the existence of ascertainment bias.