Mapping Treatment Effects Across Routes From Vascular Events to Death

Why event sequences matter

A patient in a diabetes trial may experience a cardiovascular event, a microvascular complication, both in either order, or death without either preceding event. Comparing survival alone does not separate these routes. An earlier complication also changes which patients remain at risk of later events.

In their preprint, Yuhao Deng, Haoyu Wei, Donglin Zeng, Rui Song and Xiao-Hua Zhou develop a statistical framework for studying these interconnected histories. Their application uses the LEADER trial, which randomized 9,340 people with type 2 diabetes at high cardiovascular risk to liraglutide or placebo.

Combining transition risks, not biological mechanisms

The method represents clinical histories as movements between states. Each possible movement has a hazard: its instantaneous event rate among patients currently at risk, given their baseline characteristics and event history.

The researchers construct hypothetical processes that borrow selected transition hazards from the liraglutide arm and the remaining hazards from placebo. For example, they can switch the hazard of a first cardiovascular event while leaving subsequent death hazards at placebo levels. They then calculate the probability of reaching an outcome by a specified time.

Switching one transition defines a transition-targeted effect. Switching all transitions into an event defines an event-targeted effect; switching transitions along a route defines a path-targeted effect. These contrasts describe hypothetical combinations of observed-history risks, not independently controllable components of a drug or established biological pathways.

Estimation with conditional safeguards

The authors derive a one-step estimator that adds a bias-correction term to initial model-based estimates. Its multiple-robustness property means that some models can be wrong without invalidating the estimate, provided specified combinations of the other models are correct. It is not protection against arbitrary modeling errors.

In simulations, the corrected estimator showed little bias under the particular misspecifications examined, whereas the uncorrected estimator became biased for an intermediate outcome. However, confidence-interval coverage deteriorated late in follow-up, especially for death, when censoring weights became large and variable. The simulations therefore support specific robustness claims rather than universal reliability.

What the LEADER analysis found

The analysis used a 54-month horizon. Cardiovascular outcomes were grouped as expanded major adverse cardiovascular events, or EMACE, including heart attack, stroke, unstable angina, heart failure, coronary revascularization and cardiovascular death. Microvascular events comprised nephropathy and retinopathy.

Comparing all-liraglutide with all-placebo hazards, the estimated average survival gain within 54 months was 0.36 months, with a standard error of 0.18 months and P = 0.043. This restricted-mean measure summarizes survival over the observation window; it is not an estimate of lifetime extension for each patient. Simultaneous confidence bands for the mortality difference did not exclude zero over follow-up, an important distinction from the restricted-mean test.

Starting from all-placebo hazards, switching transitions into first EMACE produced an estimated 0.90 months of additional EMACE-free time, with P = 0.003. Switching transitions into microvascular events produced 0.53 months of additional microvascular-event-free time, with P = 0.004.

For survival, the strongest transition-targeted result concerned first EMACE from the initial event-free state. An order-averaged allocation attributed 0.35 months of survival gain to that transition, with a standard error of 0.12 months. Ordinary targeted effects need not sum to the total; the authors use Shapley averaging across switching orders to obtain an additive allocation.

Why fatal-event classification matters

The main analysis classified fatal first cardiovascular events as first EMACE. Its separate death-targeted intervention therefore excluded those fatalities. Switching the remaining death hazards produced no detectable survival change, not evidence that every death-related transition was unaffected.

A secondary analysis regrouped fatal first EMACE with cardiovascular deaths. Under that definition, switching cardiovascular-death hazards yielded an estimated 0.33 months of survival gain, mostly associated with fatal first EMACE. The results point toward first cardiovascular-event hazards, including fatal events, rather than clearly demonstrating improved survival after a nonfatal event.

Boundaries of the interpretation

Identification still requires assumptions about treatment assignment, censoring, consistency and overlap between event histories in the two arms. Randomization supports the treatment-assignment assumption, but does not automatically establish the others. The implementation also relies on fitted hazard models.

A sensitivity analysis varying shared latent patient heterogeneity changed selected targeted estimates by at most 0.03 months across the examined range. That exercise changes what the hypothetical intervention holds fixed; it does not establish an absence of unmeasured confounding.

The authors also caution that a null targeted effect need not mean no biological effect: changes in the mix of patients still at risk can offset one. Interpreting hazard combinations as actual treatment-switching strategies requires additional, unverified assumptions. The preprint offers a framework for examining event histories, not a clinical recommendation or proof of how liraglutide works.