Description Usage Arguments Details Value Author(s) References See Also Examples

This function computes a dynamic discrimination index for joint models based on a weighted average of time-dependent AUCs.

1 2 3 4 5 |

`object` |
an object inheriting from class |

`newdata` |
a data frame that contains the longitudinal and covariate information for the subjects for which prediction
of survival probabilities is required. The names of the variables in this data frame must be the same as in the data frames that
were used to fit the linear mixed effects model (using |

`Dt` |
a numeric scalar denoting the time frame within which the occurrence of events is of interest. |

`idVar` |
the name of the variable in |

`t.max` |
a numeric scalar denoting the time maximum follow-up time up to which the dynamic discrimination index is to be calculated.
If |

`simulate` |
logical; if |

`M` |
a numeric scalar denoting the number of Monte Carlo samples; see |

`weightFun` |
a function of two arguments the first denoting time and the second the length of the time frame of interest, i.e., |

`...` |
additional arguments; currently none is used. |

(**Note:** The following contain some math formulas, which are better viewed in the pdf version
of the manual accessible at https://cran.r-project.org/package=JM.)

Function `dynC`

computes the following discrimination index

*\mbox{C}_{dyn}^{Δ t} = \int_0^{t_{max}} \mbox{AUC}(t, Δ t) \,
\mbox{Pr} \{ {\cal E}(t, Δ t) \} \; dt \Big / \int_0^{t_{max}} \mbox{Pr} \{ {\cal E}(t, Δ t) \} \; dt,*

where

*\mbox{AUC}(t, Δ t) = \mbox{Pr} \bigl [ π_i(t + Δ t \mid t) <
π_j(t + Δ t \mid t) \mid \{ T_i^* \in (t, t + Δ t] \} \cap \{ T_j^* > t + Δ t \} \bigr ],*

and

*{\cal E}(t, Δ t) = \bigl [ \{ T_i^* \in (t, t + Δ t] \} \cap \{ T_j^* > t +
Δ t \} \bigr ],*

with *i* and *j* denote a randomly selected pair subjects, and
*π_i(t + Δ t \mid t)* and *π_j(t + Δ t \mid t)* denote the conditional survival probabilities calculated by
`survfitJM`

for these two subjects, for different time windows *Δ t* specified by argument `Dt`

.
The upper limit of integral in specified by argument `t.max`

. The integrals in the numerator and denominator
are approximated using a 15-point Gauss-Kronrod quadrature rule.

Index *\mbox{C}_{dyn}^{Δ t}* is in the spirit of Harrell's *c*-index, that is for the comparable
subjects (i.e., the ones whose observed event times can be ordered), we compare their dynamic survival
probabilities calculated by `survfitJM`

. As with Harrell's *c*-index,
*\mbox{C}_{dyn}^{Δ t}* does not take into account censoring, and therefore is expected to mask the
true discriminative capability of the joint model under heavy censoring.

A list of class `dynCJM`

with components:

`dynC` |
a numeric scalar denoting the dynamic discrimination index. |

`times` |
a numeric vector of time points at which the AUC was calculated. |

`AUCs` |
a numeric vector of the estimated AUCs at the aforementioned time points. |

`weights` |
a numeric vector of the estimated weights at the aforementioned time points. |

`t.max` |
a copy of the |

`Dt` |
a copy of the |

`classObject` |
the class of |

`nameObject` |
the name of |

Dimitris Rizopoulos [email protected]

Antolini, L., Boracchi, P., and Biganzoli, E. (2005). A time-dependent discrimination index
for survival data. *Statistics in Medicine* **24**, 3927–3944.

Harrell, F., Kerry, L. and Mark, D. (1996). Multivariable prognostic models: issues in
developing models, evaluating assumptions and adequacy, and measuring and reducing errors.
*Statistics in Medicine* **15**, 361–387.

Heagerty, P. and Zheng, Y. (2005). Survival model predictive accuracy and ROC curves.
*Biometrics* **61**, 92–105.

Rizopoulos, D. (2012) *Joint Models for Longitudinal and Time-to-Event Data: with
Applications in R*. Boca Raton: Chapman and Hall/CRC.

Rizopoulos, D. (2011). Dynamic predictions and prospective accuracy in joint models for
longitudinal and time-to-event data. *Biometrics* **67**, 819–829.

Rizopoulos, D., Murawska, M., Andrinopoulou, E.-R., Lesaffre, E. and Takkenberg, J. (2013).
Dynamic predictions with time-dependent covariates in survival analysis: A comparison between
joint modeling and landmarking. *under preparation*.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
## Not run:
# we construct the composite event indicator (transplantation or death)
pbc2$status2 <- as.numeric(pbc2$status != "alive")
pbc2.id$status2 <- as.numeric(pbc2.id$status != "alive")
# we fit the joint model using splines for the subject-specific
# longitudinal trajectories and a spline-approximated baseline
# risk function
lmeFit <- lme(log(serBilir) ~ ns(year, 3),
random = list(id = pdDiag(form = ~ ns(year, 3))), data = pbc2)
survFit <- coxph(Surv(years, status2) ~ drug, data = pbc2.id, x = TRUE)
jointFit <- jointModel(lmeFit, survFit, timeVar = "year",
method = "piecewise-PH-aGH")
# dynamic discrimination index up to year 10 using a two-year interval
dynCJM(jointFit, pbc2, Dt = 2, t.max = 10)
## End(Not run)
``` |

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