Multistate Survival Models as Transient Electrical Network

Ron Butler

October 2, 2009 3:00 pm

In multistate survival analysis, the sojourn of a patient through the various clinical states is shown to correspond to the diffusion of 1 coulomb of electrical charge though an electrical network. The essential comparison has differentials of probability for the patient correspond to differentials of charge and equates clinical states to electrical nodes. Indeed, if the death state of the patient corresponds to the sink node of the circuit, then the transient current that would be seen on an oscilloscope as the sink output is equivalent to the probability density for the survival time of the patient.

 

This electrical circuit analogy is further explored by considering the simplest possible survival model with two clinical states - alive and dead. The corresponding states of a circuit are its source and sink nodes. For the survival model, if the patient's lifetime is subject to independent right censoring and left truncation, then Kaplan-Meier is the appropriate estimate for survival time free from censoring risk and truncation. When appropriate analogs to censoring and truncation are incorporated into an electrical circuit, then the sink output that would be seen on an oscilloscope is also the Kaplan-Meier mass function.

 

A competing risks setting has multiple death states and corresponds to a circuit with multiple sinks. Again, after adjusting for censoring and truncation, Kaplan-Meier mass functions are the outputs at the sink nodes for the corresponding circuits.

 

If covariates are present, then the electrical analogy provides for an intuitive understanding of partial likelihood and the various baseline hazard estimates that are often used with the proportional hazards model.