In this paper, we study the estimation and variable selection of the sufficient dimension reduction space for survival data via a new combination of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$L_1$$</EquationSource> </InlineEquation> penalty and the refined outer product of gradient method (rOPG; Xia et al. in J R Stat Soc Ser B 64:363–410, <CitationRef CitationID="CR28">2002</CitationRef>), called SH-OPG...</citationref></equationsource></inlineequation>