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Table 1 Overview of symbols

From: Accurate training of the Cox proportional hazards model on vertically-partitioned data while preserving privacy

Symbol

Definition

m

Number of parties involved in the MPC protocol

N

Secret-sharing modulus

n

Number of subjects

\({\mathcal {I}}\)

Set of all subjects

J

Number of distinct event times

\({\mathcal {D}}_j\)

Set of subjects that experience an event at time \(t_j\)

\(d_j\)

Number of subjects that experience an event at time \(t_j\); \(|{\mathcal {D}}_j|\)

\({\mathcal {R}}_j\)

Set of subjects at risk (alive and uncensored) at time \(t_j\)

\(L(\cdot )\)

Log-likelihood function for CPH model

p

Number of covariates

\(\varvec{Z}\)

p-Dimensional vector of explanatory covariates

\(\varvec{\beta }\)

p-Dimensional vector of model parameters

\(\varvec{Z}^I\)

Realisation of the p-dimensional covariate vector \(\varvec{Z}\) for subject I