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Table 1 Summary of current methods for each definition

From: Time-dependent ROC curve analysis in medical research: current methods and applications

Definition and marker time Sensitivity and specificity Estimation method and R software (when available) Pros/Cons
C/D
t = 0
\( \begin{array}{l} S{e}^C\left( c, t\right)= P\left({X}_i> c\Big|{T}_i\le t\right)\\ {} S{p}^D\left( c, t\right)= P\left({X}_i\le c\Big|{T}_i> t\right)\end{array} \) CD1
survivalROC
Pro: Easy Cons:
a) Produce non-monotone sensitivity and specificity
b) Not robust to marker-dependent censoring
Pro: Clinically relevant since many clinical experiments aim to discriminate individuals with disease prior to specific time and healthy individual beyond that time
Con: Use redundant information in separating cases and controls
CD2
survivalROC
Pros:
a) Produce monotone sensitivity and specificity
b) Allow censoring to depend on marker
Con: Does involve smoothing parameter
CD3
Programme code
Pro: Does not involve any smoothing parameter
Cons:
a) Does involve recursive computation
b) Produce non-monotone specificity
CD4
survAUC
Pros:
a) Produce monotone sensitivity and specificity if the score is produced from a survival model
b) Allow censoring to depend on marker
Con: Not invariant to an increasing transformation of the marker
CD5
timeROC
Pros:
a) Produce monotone sensitivity and specificity
b) More robust than CD1 and CD3
Con: Does not robust to marker dependent censoring
CD6
timeROC
Pros:
a) Produce monotone sensitivity and specificity
b) Robust to marker-dependent censoring
c) More less biased than CD2 when censoring strongly depends on marker
CD8, VL Cox
survival
Pro: Straightforward to implement
VL Aalen
timereg
VL KM
prodlim
C/D
A longitudinal time point
\( \begin{array}{l} S{e}^C\left( c, t\right)= P\left({Y}_{i k}> c\Big|{T}_i-{s}_{i k}\le t\right)\\ {} S{p}^D\left( c,{t}^{*}\right)= P\left({Y}_{i k}\le c\Big|{T}_i-{s}_{i k}> t\right)\end{array} \) AD4 (ECD2) Pros:
a) Produce monotone sensitivity and specificity
b) Allow censoring to depend on marker
Con: Does involve smoothing parameter
Pro: Use the most recent marker value prior to prediction time
Con: Just use a marker value at a particular time instead of using all serial of marker value
I/D
t = 0
\( \begin{array}{l} S{e}^I\left( c, t\right)= P\left({X}_i> c\Big|{T}_i= t\right)\\ {} S{p}^D\left( c, t\right)= P\left({X}_i\le c\Big|{T}_i> t\right)\end{array} \) ID1
risksetROC
Pros: Produce consistent sensitivity and specificity if the control set is unbiased Pro: Allow time-averaged summaries that directly relate to a familiar concordance measures such as Kendall’s tau or c-index
Con: Require an exact time of interest which often just a few individual has an event at a particular point
ID2 Pro: Potentially more robust than ID1
Con: Computationally intensive
ID3
Programme code
Pros:
a) Easier especially when involve a large number of marker
b) Understandable since it is a “regression-type” model
I/S
t = 0
\( \begin{array}{l} S{e}^I\left( c, t\right)= P\left({Y}_i> c\Big|{T}_i= t\right)\\ {} S{p}^S\left( c,{t}^{*}\right)= P\left({Y}_i\le c\Big|{T}_i>{t}^{*}\right)\end{array} \) None Pro: Allow separation of long-term survivors from healthy individual within a fixed follow-up
Con: Require an exact time of interest which often just a few individual has an event at a particular point
I/S
A longitudinal time point
\( \begin{array}{l} S{e}^I\left( c, t\right)= P\left({Y}_{i k}> c\Big|{T}_i-{s}_{i k}= t\right)\\ {} S{p}^S\left( c,{t}^{*}\right)= P\left({Y}_{i k}\le c\Big|{T}_i-{s}_{i k}>{t}^{*}\right)\end{array} \) IS1 Pro: Provides unbiased estimates of model parameters of sensitivity and specificity
Con: Computationally intensive since involve spline functions
Pro: Use the most recent marker value prior to prediction time
Con: Just use a most recent of marker value instead of all marker values
IS2 Pro: Use the most recent marker value prior to prediction time
Con: not a natural companion to hazard models
Other
All longitudinal time points
ROC(t, p) = S[a 0(T ik ) + a 1(T ik )S − 1(p)] AD1
Programme code
Pro: Use all marker value along visit times in the estimation of ROC curve
Con: Do not incorporate censored outcomes