constRecal {ClinicalUtilityRecal}

Constrained Logistic Recalibration

Description

When recalibrating a risk model, where the intended purpose of the risk model is to prescribe an intervention to those deemed at high risk, it is desirable to have good calibration at the clinically relevant threshold used to define high risk (i.e. threshold used to identify who recieves treatment). This can be achieved by maximizing the clinical utilty of a risk model, which should in turn produce good calibration near the clinical relevant risk threshold. This function realibrates risk scores (predicting binary outcome) by estimating the recalibration intercept and slope by maximizing the logistic likelihood over a restricted parameter space (Mishra et al. [2020]).

The restricted space only includes recalibration parameters alpha_0 and alpha_1 that produce a recalibrated risk model with high sNB. The restricted parameter space is defined all alpha parameters that result in a recalibrated risk score within one-standard-error of the maximum possible sNB. See Mishra et al (2020), for full details

Usage

constRecal(y,p,r,int=NULL,alphaLB=c(-10,0),
            alphaUB=c(10,10),ftol=1e-8,xtol=1e-4,maxeval=1e6)

Arguments

y

Vector of binary outcomes, with 1 indicating event (case) and 0 indicating no event (controls)

p

Vector of risk score values

r

Clinically relevant risk threshold

int

Two-dimensional vector of initial recalibration parameter (alpha) values. If not specified the recalibration parameters estimated under standard logistic recalibration will be used

alphaLB

Lower bound of box-contrained search space

alphaUB

Upper bound of box-contrained search space

ftol

Controls tolerance of optimization procedure with respect to changes in sNB

xtol

Controls tolerance of optimization procedure with respect to changes in alpha

maxeval

Maximum number of interations performed during optimization procedure

Details

To solve this optimization problem the DIRECT optimization method is implemented via the NLOPTR package. See Jones et al (1993) and Ypma et al (2014) for full description of optimization method and implementation details. Note this is not a convex optimization problem, so a global optimizer is used.

Value

alpha

Recalibration parameters obtained from Constrained Logistic Recalibration

y

Vector of binary outcomes, with 1 indicating event (case) and 0 indicating no event (controls)

p.const

Vector of constrained logistic reclaibrated risk scores

snbLB

Lower bound used to define constraint region. The solution is constrained to the region where recalibration parameters result in risk model with sNB greater or equal to this bound. This is one-standard error lower than the maximum sNB

optimRes

Full output from the NLOPTR optimization routine

Author(s)

Anu Mishra

References

Mishra, A. (2019). Methods for Risk Markers that Incorporate Clinical Utility (Doctoral dissertation). (Available Upon Request)

Ypma, J., Borchers, H. W., Eddelbuettel, D., & Ypma, M. J. (2020). Package ‘nloptr’.

Ypma, J. (2014). Introduction to nloptr: an R interface to NLopt. Tech. rep.

D. R. Jones, C. D. Perttunen, and B. E. Stuckmann, "Lipschitzian optimization without the lipschitz constant," J. Optimization Theory and Applications, vol. 79, p. 157 (1993).

Examples

## Not run: 
### Load data ##
data(fakeData)

## Implementing standard logistic recalibration
stdRecal.res <- stdRecal(y = fakeData$y,p = fakeData$p)
stdRecal.res$alpha #standard recalibration parameters
p.std <- stdRecal.res$p.std

## Look at potential sNB under recalibration plot
snbRecalPlot(p = fakeData$p,p.std = p.std,y = fakeData$y,r = 0.3)

## Implementing constrained logistic recalibration
constRecal.res <- constRecal(y = fakeData$y,p = fakeData$p,r = 0.3)
constRecal.res$alpha #constrained logistic recalibration parameters
p.recal <- constRecal.res$p.const

## comparing standardized net benefit of the two
nb(y = fakeData$y,p = fakeData$p,r = 0.3)$snb #original
nb(y = stdRecal.res$y,p = stdRecal.res$p.std,r = 0.3)$snb #std recal
nb(y = constRecal.res$y,p = constRecal.res$p.const,r = 0.3)$snb #weighted

## Generate calibration plots

### Calibration curve of only original, standard and weighted recalibrated risk score
calCurvPlot(y=fakeData$y,p=fakeData$p,p.std=p.std,p.recal=p.recal,
            stdPlot=TRUE, recalPlot=TRUE,
            xlim=c(0,1),ylim=c(0,1),
            label="Original Risk Score",
            label2 = "Standard Recalibrated Risk Score",
            label3 = "Weighted/Constrained Recalibrated Risk Score",
            legendLab = c("Orig.", "Std.", "Wt."),
            mainTitle="Calibration of Risk Score",
            hist=TRUE,ylimHist = c(0,0.5),
            r=0.3,rl = -Inf, ru = Inf)


## End(Not run)