Statistical Analysis
Continuous variables were expressed as mean +/- standard deviation; categorical variables as absolute and percentage values.  OS was defined as the time span from first administration of 223Ra until death from any cause or censoring at last follow‐up time. The Kaplan‐Meier estimator was used to estimate survival curves. Univariate analysis using a Cox regression model were used to assess potential prognostic factors. A multivariable Cox regression model was then estimated where the final set of predictors was selected based on minimization of the Akaike Information Criterion in stepwise selection stages. The stepwise selection criterion protects from collinearity issues, which were also checked for the final selected model using Variance Inflaction Factors. No issues with collinearity were present in the models reported. We performed a principal component analysis (PCA) on the questionnaires’ results compiled at baseline to reduce the data to a one-dimensional score. Data reduction was done considering the correlation matrix of the whole questionnaire with nineteen items (15 for the EORTC QLQ‐C30 and 4 for the EORTC QLQ‐BM22). PCA optimally assigns weights to each item, with each principal component (PC) resulting as a weighted linear combination of the original variables. The first PC has the largest possible variance and can be used as a univariate score summarizing the whole questionnaire. Data reduction was satisfactory as about 90% of total variance was captured by the first PC. Univariate and multivariate analyses using Cox models were then repeated to evaluate the role of the first principal component as a potential prognostic factor. Only baseline measurements were used for performing PCA in order to avoid attrition bias in estimating weights. Weights for the first PC were then used to build scores also at different follow-up times. In order to evaluate the relationship between the resulting time-dependent QoL scores and OS (and the relationship between trends and OS) we used Joint Models for survival and longitudinal data, where a single shared parameter captured the association of interest. Joint models allow to assess relationships with longitudinal markers and survival in an unbiased manner. The prognostic significance of the new scores was evaluated via time-dependent receiver operating characteristic (ROC) curves. The final cut-off was selected by maximizing the sum of sensitivity and specificity. A p  < 0.05 was considered as statistically significant and all tests were two-sided. All statistical analyses were performed with the software R version 3.5.1.