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

Using the available longitudinal information up to a starting time point, this function computes an estimate of the prediction error of survival at a horizon time point based on joint models.

1 2 3 4 5 6 7 8 9 10 11 | ```
prederrJM(object, newdata, Tstart, Thoriz, ...)
## S3 method for class 'JMbayes'
prederrJM(object, newdata, Tstart, Thoriz,
lossFun = c("square", "absolute"), interval = FALSE, idVar = "id",
simulate = FALSE, M = 100, ...)
## S3 method for class 'mvJMbayes'
prederrJM(object, newdata, Tstart, Thoriz,
lossFun = c("square", "absolute"), interval = FALSE, idVar = "id",
M = 100, ...)
``` |

`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 |

`Tstart` |
numeric scalar denoting the time point up to which longitudinal information is to be used to derive predictions. |

`Thoriz` |
numeric scalar denoting the time point for which a prediction of the survival status is of interest; |

`lossFun` |
either the options |

`interval` |
logical; if |

`idVar` |
the name of the variable in |

`simulate` |
logical; if |

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

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

Based on a fitted joint model (represented by `object`

) and using the data supplied in argument `newdata`

, this function
computes the following estimate of the prediction:

*PE(u | t) = \{R(t)\}^{-1} ∑_{i: T_i ≥q s} I(T_i ≥q u)
L\{1 - Pr(T_i > u | T_i > t, \tilde{y}_i(t), x_i)\}*

*+ δ_i I(T_i < u) L\{0 - Pr(T_i > u | T_i > t, \tilde{y}_i(t), x_i)\}*

*+ (1 - δ_i) I(T_i < u) [S_i(u \mid T_i, \tilde{y}_i(t)) L\{1 - Pr(T_i > u | T_i > t, \tilde{y}_i(t), x_i)\}*

*+ \{1 - S_i(u \mid T_i, \tilde{y}_i(t))\} L\{0 - Pr(T_i > u | T_i > t, \tilde{y}_i(t), x_i)\}],*

where *R(t)* denotes the number of subjects at risk at time *t = * `Tstart`

, *\tilde{y}_i(t) = \{y_i(s), 0 ≤q s ≤q t\}* denotes the available
longitudinal measurements up to time *t*, *T_i* denotes the observed event time for subject *i*, *δ_i* is the event indicator,
*s* is the starting time point `Tstart`

up to which the longitudinal information is used, and *u > s* is the horizon time point `Thoriz`

.
Function *L(.)* is the loss function that can be the absolute value (i.e., *L(x) = |x|*), the squared value (i.e., *L(x) = x^2*),
or a user-specified function. The probabilities *Pr(T_i > u | T_i > t, \tilde{y}_i(t), x_i)* are calculated by `survfitJM`

.

When `interval`

is set to `TRUE`

, then function `prederrJM`

computes the integrated prediction error in the interval
*(u,t) =* `(Tstart, Thoriz)`

defined as

*IPE(u | t) = ∑_{i: t ≤q T_i ≤q u} w_i(T_i) PE(T_i | t),*

where

*w_i(T_i) = \frac{δ_i G(T_i) / G(t)}{∑_{i: t ≤q T_i ≤q u} δ_i G(T_i) / G(t)},*

with *G(.)* denoting
the Kaplan-Meier estimator of the censoring time distribution.

A list of class `prederrJM`

with components:

`prederr` |
a numeric scalar denoting the estimated prediction error. |

`nr` |
a numeric scalar denoting the number of subjects at risk at time |

`Tstart` |
a copy of the |

`Thoriz` |
a copy of the |

`interval` |
a copy of the |

`classObject` |
the class of |

`nameObject` |
the name of |

`lossFun` |
a copy of the |

Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl

Henderson, R., Diggle, P. and Dobson, A. (2002). Identification and efficacy of
longitudinal markers for survival. *Biostatistics* **3**, 33–50.

Rizopoulos, D. (2016). The R package JMbayes for fitting joint models for longitudinal and
time-to-event data using MCMC. *Journal of Statistical Software* **72(7)**, 1–45.
doi:10.18637/jss.v072.i07.

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.

`survfitJM`

, `aucJM`

, `dynCJM`

, `jointModelBayes`

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, 2), data = pbc2,
random = ~ ns(year, 2) | id)
survFit <- coxph(Surv(years, status2) ~ drug, data = pbc2.id, x = TRUE)
jointFit <- jointModelBayes(lmeFit, survFit, timeVar = "year")
# prediction error at year 10 using longitudinal data up to year 5
prederrJM(jointFit, pbc2, Tstart = 5, Thoriz = 10)
prederrJM(jointFit, pbc2, Tstart = 5, Thoriz = 6.5, interval = TRUE)
## End(Not run)
``` |

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