Statistical analysis

All time-to-event outcomes were computed from the day of the salvage auto-HCT given after remobilization. OS was defined as the time from salvage auto-HCT to death from any cause and PFS was defined as the time from auto-HCT to relapse or progressive disease or death from any cause, whichever came first. Time to t-MDS/t-AML was defined as the time from salvage auto-HCT to therapy-related myelodysplastic syndrome or acute myeloid leukemia. Time to SPM was similarly defined, whilst time to any secondary malignancy was defined as the time to the first occurrence of either t-MDS/t-AML or SPM after salvage auto-HCT.

The Kaplan–Meier estimator and log-rank test were used for OS and PFS, and the crude cumulative incidence estimator and Gray’s test were used for competing events (progression/relapse and NRM; t-MDS/t-AML incidence and death without t-MDS/t-AML; SPM incidence and death without SPM; any secondary malignancy cumulative incidence, and death without any secondary malignancy). The median follow-up was calculated using the reverse Kaplan–Meier estimator [16].

The quality of data for calculating the cumulative incidence of t-MDS/t-AML and other SPM was checked for patients for whom additional data was obtained (n = 130). There was only one extra event discovered in those patients compared to the data already available in the EBMT database. Based on this information, the data quality was found reliable enough to extrapolate and report the results for the whole cohort of patients.

OS and PFS were also analyzed using a multivariable Cox model. Variables considered clinically meaningful and which were significant in univariable analyses were selected for inclusion in the multivariable models.

The unadjusted effect of time between penultimate auto-HCT and relapse on OS and PFS was modeled in two ways: using restricted cubic splines and using a linear effect.

The number of collected CD34 cells was log-transformed to comply with normality assumptions and compared between the first and salvage transplantation using a linear mixed effects (LME) model with a random effect for each patient. This allowed inclusion of patients contributing data to only one of the two transplantations. P-values were obtained using Satterthwaites degrees of freedom method.

Timing of recovery was compared between the first, second (if a tandem auto transplantation was performed), and salvage transplantation using Cox proportional hazard frailty models (including a gamma-distributed random effect for each patient) and using the exact method for tied observation times. We also compared timing of recovery after the salvage auto-HCT between patients who were infused with a mixture of old and new CD34 cells and those who were infused with only new CD34 cells using Kaplan–Meier plots and the log-rank test.

P-values < 0.05 were considered significant. All estimates are reported with accompanying 95% confidence intervals in brackets. All analyses were performed in R version 3.6.3 [17], using ‘survival’’, ‘cmprsk’’, ‘prodlim’’ and ‘lme4’’ packages.