lincom implements linear combination methods for
biomarkers via empirical performance optimization with respect to two
performance metrics: (1) specificity at controlled sensitivity (or
sensitivity at controlled specificity) (Huang and Sanda, 2022), and (2)
weighted average of false positive rate and false negative rate. The
second method is a variant of the maximum score estimator (Manski, 1975,
1985). In both cases, the algorithm of Huang and Sanda (2022) is used to
provide a solution that balances between computational efficiency and
lincom is available on CRAN:
‘MOSEK’ solver is used and needs to be installed; an academic license for ‘MOSEK’ is free.
the case and control data, respectively.
The following code performs empirical maximization of specificity at 95% sensitivity.
n1 is the case size,
s0 is the
control level, and
grdpt specifies how initial value of the
optimization is obtained (logistic regression if
and coarse grid search with
grdpt grid points otherwise).
Additional arguments include
fixsens (fixing sensitivity if
TRUE and specificity otherwise), and
(larger biomarker values is more associated with cases if
TRUE and controls otherwise).
The outputs include the resulting combination coefficient
coef), maximum empirical value of the performance metric
hs), and the resulting threshold (
along with their initial value counterparts (from logistic regression or
coarse grid search).
The inputs and outputs are similar to those of
However, the initial value here is obtained through logistic regression
With cohort design, setting
r=n0/n1 leads to Manski’s
Huang, Y. and Sanda, M. G. (2022). Linear biomarker combination for constrained classification. The Annals of Statistics 50, 2793–2815.
Manski, C. F. (1975). Maximum score estimation of the stochastic utility model of choice. Journal of Econometrics 3, 205–228.
Manski, C. F. (1985). Semiparametric analysis of discrete response. Asymptotic properties of the maximum score estimator. Journal of Econometrics 27, 313–333.