Prism 8 and 9

The relationships between groups were compared using a t-test or the nonparametric Mann–Whitney U test. For multiple group comparisons, the Dunnett test was employed. PFS and OS were defined as the time from the initial mogamulizumab administration until the first observation of disease progression and death from any cause, respectively. PFS and OS were investigated with the Kaplan–Meier method and were compared among the groups using the log-rank test or Cox regression proportional hazards analysis. Statistical analysis was performed with GraphPad Prism8 and 9 (GraphPad Software, San Diego, CA) or R version 3.1.1 (R Foundation for Statistical Computing, Vienna, Austria). P values less than 0.05 were considered significant.

Statistical analysis was performed using GraphPad Prism 8 and 9 (GraphPad Software, Inc., La Jolla, CA) or R (R 4.0.3 GUI 1.73; R Studio, Version 1.3.1093, lme4, ggplot2, FactoMineR and factoextra packages). Principal component analysis was generated with R using the mRNA expression of 52 genes of 440 single CD56^bright ihNK cells or pbNK cells. Wilcoxon matched-pairs signed rank test was used to determine differences between paired samples with assumed non-normal distribution. To assess normal distribution within small sample sizes, the Shapiro-Wilk test was applied and subsequently, the paired t test was used. A mixed-effects model with random intercept, considering intra-sample correlations, was used to compare the single-cell mRNA expression data from different donors (or groups). To limit the detection of false positives, the p-values were adjusted by the Benjamini and Hochberg False Discovery Rate (FDR) method between each comparison groups (cutoff of 0.05). P values <0.05 were considered statistically significant. Statistical analysis for additional data presented in the figures are provided in the respective figure legends.

Graphs and statistical analysis were performed using Microsoft Excel and GraphPad Prism 8 and 9 software. Data groups were compared via a one-way ANOVA. Tukey’s and Dunnet’s test were used for the statistical hypothesis testing, and the family-wise alpha threshold and confidence level was set at 0.05 (95% confidence level). The P values of the data sets are provided in the Source data.

All statistical tests were performed using Prism 8 and 9 (GraphPad, Boston, USA). For non‐parametric unpaired or paired datasets, the Mann–Whitney U‐test or the Wilcoxon test were used for comparisons respectively. Spearman's rank‐order correlation was used to analyse the correlation for non‐parametric data. Correlation matrixes were generated in R using the Hmisc and corrplot packages. Non‐numerical data were grouped and analysed using Fisher's exact test. The significance levels were defined as *P < 0.05, **P < 0.01, ***P < 0.001 and ****P < 0.0001.