R: Predictive model in prognosis scenarios (I)

pred_model_timeic-internal {sMSROC}

R Documentation

Predictive model in prognosis scenarios (I)

Estimation of the predictive model in prognosis scenarios under interval censorship.

pred_model_timeic(marker, left, right, outcome, time, meth)

`marker`	vector with the biomarker values.
`left`	vector containing the lower edges of the observed intervals. It is mandatory in prognosis scenarios and interval censorship and ignored in other situations.
`right`	vector with the upper edges of the observed intervals. It is mandatory as well in prognosis scenarios and interval censorship and ignored in other situations.
`outcome`	vector with the condition of the subjects as positive, negative or unknown at the considered time `time`.
`time`	point of time at which the sMS ROC curve estimator will be computed.
`meth`	method for approximating the predictive model `P(D\|X=x)`. The options are: “L”, for proportional hazards regression models taking into account the observation intervals (see Details). “S”, for proportional hazards regression models without taking into account the observation intervals (see Details).

If meth = “L”, the event times are assumed to come from a Cox proportional hazards regression model and the predictive model is estimated as indicated in doi:10.1080/00949655.2020.1736071.

P (T \leq t \;|\; X=x) = \frac{S(U|x) - S(t|x) }{S(U|x) - S(V|x)},

where U = \min{\{t, L\}} and V = \max {\{t, R\}}, being L and R the random variables that stand for the edges of the observable interval containing the event time.
If meth = “S”, the approximation is done by

P (T\leq t \;|\; X=x) = 1 - S(t|x),

being S(\cdot) the survival function at time t given the marker value, estimated through a proportional hazard model for interval censored data according to doi:10.2307/2530698.

The returned value is a list with three components:

`marker`	vector containing the ordered marker values.
`probs`	vector with the probabilities corresponding to each marker value estimated through the predictive model.
`outcome`	vector with the condition of the subjects as positive, negative or censored at the considered time `time`.