R project

In this study, the software and online tools used included MATLAB (R2021b and R2022a, MathWorks Inc., Natick, MA), R-project (version 4.0.4, R-project.org">www.R-project.org), MeV (version 4.9.0, MEV, LLC., Walnut Creek, CA, http://www.tm4.org/mev.html), the Venny diagram^{21 (link)}, Gene Ontology (http://geneontology.org/), g:Profier (ELIXIR, Tartu, Estonia, https://biit.cs.ut.ee/gprofiler/gost), and SigmaPlot 14 (Systat Software, San Jose, CA).
In this study, the statistical methods included Student’s t-test, the standard Bonferroni adjusted t-test, and the Wilcoxon-Mann–Whitney test if the data distribution was not the standard distribution.

Data are presented as mean and standard deviation (SD) on median and interquartile range (IQR). Categorical variables were reported as the percentage. Intergroup comparisons were performed with the χ² test (categorical variables). All analyses and data modelling were performed using R-project (R Core Team 2013, Vienna, Austria; R-project.org">http://www.R-project.org).

Statistical analysis was performed via SPSS version 24.0 software (IBM Corp). Propensity score matching (PSM) (1:1) was performed to ensure well-balanced characteristics between the CHT/TRT and CHT-alone groups. The propensity score was calculated by a multivariable logistic regression model, with TRT as the dependent variable and age, sex, ECOG PS score, smoking index, metastatic organs, number of metastases, brain metastasis, liver metastasis, bone metastasis, weight loss, and PCI as the covariates. Chi-square and Fisher’s exact tests were employed to compare baseline characteristics between groups. Survival information, including OS, progression-free survival (PFS) and local recurrence-free survival (LRFS), was collected until October 31, 2019. OS was calculated from the date of diagnosis to death or the period up to the observation point. PFS was defined as the time of diagnosis until disease progression or death. LRFS was defined as the date of diagnosis until the time of local recurrence or death. Kaplan–Meier curves including the numbers at risk were plotted using R-project (version 4.0.3, http://www.Rproject.org). Univariable and multivariate Cox regression analyses were performed to identify the potential predictors of ES-SCLC patients. All statistical analyses were two-sided, and a P value < 0.05 was considered statistically significant.

Error calculations were performed in R-Project (R-Project.org" xmlns:xlink="http://www.w3.org/1999/xlink">http://www.R-Project.org).
S.d. for a single variable were computed via equation 1.

S.e.m. of the mean were calculated with equation 2.

To calculate errors for diverse factors, for example, independent variables, the simplified version of the Gaussian error formula (the variance formula), as shown in equation 3, was used. Those errors were marked as ‘MSE'.

Exploratory data analysis, visualization, and statistical testing were performed with R‐project (http://www.R-project.org) or perl scripts using unpaired two‐sample unequal variances t‐test (Welsh's t‐test), Mann–Whitney test, Kolmogorov–Smirnov test, linear regression model, Pearson's correlation test as indicated in figure legends. Venn diagrams were produced using Venn Diagram Plotter (Pan‐Omics Research). RNA‐Seq read coverage was calculated with coverageBed from BEDTools suite (Quinlan & Hall, 2010).

The area under the receiver-operator-curve (ROC curve) was calculated based on the overall ability of the given attributes to discriminate between patients that either responded or progressed under immune-checkpoint inhibition therapy. To visualize the effects of the attributes on the class probabilities (response/progress under therapy), we generated a nomogram using a Naïve-Bayes classifier that was trained on the attributes of treatment results as described previously²⁴ . Statistical analysis was performed with Python (version 3.7, https://www.python.org/), R, the R Project (version 4.0.3, https://www.r-project.org/) and the statistical software package IBM SPSS (version 25.0). Statistical testing was carried out by using X² test, Fisher’s test or Student's t-test. Survival rates were calculated by the Kaplan–Meier method and compared using log-rank. p < 0.05 was considered to be significant.