BACKGROUND: A large randomised treatment trial (SERVE-HF) showed that treatment of central sleep apnoea with adaptive servoventilation in patients with heart failure and reduced ejection fraction (HFREF) increased mortality, although the analysis of the composite primary endpoint (time to first event of death from any cause, life-saving cardiovascular intervention, or unplanned hospital admission for worsening heart failure) was neutral. This secondary multistate modelling analysis of SERVE-HF data investigated associations between adaptive servoventilation and individual components of the primary endpoint to try to better understand the mechanisms underlying the observed increased mortality. METHODS: In SERVE-HF, participants were randomly assigned to receive either optimum medical treatment for heart failure alone (control group), or in combination with adaptive servoventilation. We analysed individual components of the primary SERVE-HF endpoint separately in a multistate model, with and without three covariates suggested for effect modification (implantable cardioverter defibrillator at baseline, left ventricular ejection fraction [LVEF], and proportion of Cheyne-Stokes Respiration [CSR]). The SERVE-HF study is registered with ClinicalTrials.gov, number NCT00733343. FINDINGS: Univariate analysis showed an increased risk of both cardiovascular death without previous hospital admission (hazard ratio [HR] 2·59, 95% CI 1·54-4·37, p<0·001) and cardiovascular death after a life-saving event (1·57, 1·01-2·44, p=0·045) in the group receiving adaptive servoventilation versus the control group. Adjusted analysis showed that the increased risk attributed to adaptive servoventilation of cardiovascular death without previous hospital admission for worsening heart failure varied with LVEF and that the risk attributed to adaptive servoventilation of hospital admission for worsening heart failure varied with LVEF and CSR. In patients with LVEF less than or equal to 30%, use of adaptive servoventilation markedly increased the risk of cardiovascular death without previous hospital admission (HR 5·21, 95% CI 2·11-12·89, p=0·026). INTERPRETATION: Adaptive servoventilation is associated with an increased risk of cardiovascular death in patients with heart failure and reduced ejection fraction (LVEF ≤45%) treated for predominant central sleep apnoea. This multistate modelling analysis shows that this risk is increased for cardiovascular death in patients not previously admitted to hospital, presumably due to sudden death, and in patients with poor left ventricular function. FUNDING: ResMed.