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.