Prognosis of cancer survivors: estimation based on differential equations

Pål C Ryalen; Bjørn Møller; Christoffer H Laache; Mats J Stensrud; Kjetil Røysland

doi:10.1093/biostatistics/kxab009

Prognosis of cancer survivors: estimation based on differential equations

Biostatistics. 2023 Apr 14;24(2):345-357. doi: 10.1093/biostatistics/kxab009.

Authors

Pål C Ryalen¹, Bjørn Møller², Christoffer H Laache³, Mats J Stensrud¹, Kjetil Røysland⁴

Affiliations

¹ Department of Mathematics, EPFL, Station 8, CH-1015 Lausanne, Switzerland.
² Department of Registration, Cancer Registry of Norway, Ullernchausseen 64, 0379 Oslo, Norway.
³ Department of Registration, Cancer Registry of Norway, Ullernchausseen 64, 0379 Oslo, Norway, and Department of Biostatistics, University of Oslo, 1122 Blindern, 0317 Oslo, Norway.
⁴ Department of Biostatistics, University of Oslo, 1122 Blindern, 0317 Oslo, Norway.

Abstract

We present a method for estimating several prognosis parameters for cancer survivors. The method utilizes the fact that these parameters solve differential equations driven by cumulative hazards. By expressing the parameters as solutions to differential equations, we develop generic estimators that are easy to implement with standard statistical software. We explicitly describe the estimators for prognosis parameters that are often employed in practice, but also for parameters that, to our knowledge, have not been used to evaluate prognosis. We then apply these parameters to assess the prognosis of five common cancers in Norway.

Keywords: Cancer; Cancer survivors; Conditional survival; Prognosis; Survival analysis.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Cancer Survivors*
Humans
Models, Statistical
Neoplasms* / diagnosis
Norway
Prognosis
Software