Surrogacy of progression free survival for overall survival in   metastatic breast cancer studies: meta-analyses of published studies
  Purpose: PFS is often used as a surrogate endpoint for OS in metastatic breast cancer studies. We have evaluated the association of treatment effect on PFS with significant HR$_{OS}$ (and how this association is affected by other factors) in published prospective metastatic breast cancer studies.   Methods: A systematic literature search in PubMed identified prospective metastatic breast cancer studies. Treatments effects on PFS were determined using hazard ratio (HR$_{PFS}$), increase in median PFS ($\Delta$MED$_{PFS}$) and % increase in median PFS (%$\Delta$MED$_{PFS}$). Diagnostic accuracy of PFS measures (HR$_{PFS}$, $\Delta$MED$_{PFS}$ and %$\Delta$MED$_{PFS}$) in predicting significant HR$_{OS}$ was assessed using receiver operating characteristics (ROC) curves and classification trees approach.   Results: Seventy-three cases (i.e., treatment to control comparisons) from 64 individual publications were identified for the analyses. Of these, 16 cases reported significant treatment effect on HR$_{OS}$ at 5% level of significance. Median number of deaths reported in these cases were 156. Area under the ROC curve (AUC) for diagnostic measures as HR$_{PFS}$, $\Delta$MED$_{PFS}$ and %$\Delta$MED$_{PFS}$ were 0.69, 0.70 and 0.75, respectively. Classification tree results identified %$\Delta$MED$_{PFS}$ and number of deaths as diagnostic measure for significant HR$_{OS}$. Only 7.9\% (3/39) cases with $\Delta$MED$_{PFS}$ shorter than 48.27\% reported significant HR$_{OS}$. There were 7 cases with $\Delta$MED$_{PFS}$ of 48.27\% or more and number of deaths reported as 227 or more -- of these 5 cases reported significant HR$_{OS}$.   Conclusion: %$\Delta$MED$_{PFS}$ was found as better diagnostic measure for significant HR$_{OS}$. Our analysis results also suggest that consideration of total number of deaths may further improve its diagnostic performance. 
Madan G. Kundu and Suddhasatta Acharyya
stat.AP q-bio.QM