Description Usage Arguments Details Note References See Also Examples

Family object to fit a flexible additive joint model for longitudinal and survival data under a Bayesian approach as presented in Koehler et al. (2016). All parts of the joint model can be specified as structured additive predictors. See the details and examples.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | ```
## JM family object.
jm_bamlss(...)
## "bamlss.frame" transformer function
## to set up joint models.
jm.transform(x, y, data, terms, knots, formula,
family, subdivisions = 25,
timedependent = c("lambda", "mu", "alpha", "dalpha"),
timevar = NULL, idvar = NULL, alpha = .Machine$double.eps,
mu = NULL, sigma = NULL, sparse = TRUE, ...)
## Posterior mode optimizing engine.
jm.mode(x, y, start = NULL, weights = NULL,
offset = NULL, criterion = c("AICc", "BIC", "AIC"),
maxit = c(100, 1), nu = c("lambda" = 0.1, "gamma" = 0.1,
"mu" = 0.1, "sigma" = 0.1, "alpha" = 0.1, "dalpha" = 0.1),
update.nu = TRUE, eps = 0.0001, alpha.eps = 0.001,
ic.eps = 1e-08, nback = 40, verbose = TRUE,
digits = 4, ...)
## Sampler function.
jm.mcmc(x, y, family, start = NULL, weights = NULL,
offset = NULL, n.iter = 1200, burnin = 200, thin = 1,
verbose = TRUE, digits = 4, step = 20, ...)
## Predict function, set to default in jm_bamlss().
jm.predict(object, newdata,
type = c("link", "parameter", "probabilities", "cumhaz"),
dt, steps, id, FUN = function(x) { mean(x, na.rm = TRUE) },
subdivisions = 100, cores = NULL, chunks = 1,
verbose = FALSE, ...)
## Survival plot.
jm.survplot(object, id = 1, dt = NULL, steps = 10,
points = TRUE, rug = !points)
``` |

`x` |
The |

`y` |
The model response, as returned from function |

`data` |
A |

`terms` |
The corresponding |

`knots` |
An optional list containing user specified knots, see the documentation of
function |

`formula` |
The corresponding |

`family` |
The |

`subdivisions` |
How many time points should be created for each individual. |

`timedependent` |
A character vector specifying the names of parameters in |

`timevar` |
A character specifying the name of the survival time variable in the data set. |

`idvar` |
Depending on the type of data set, this is the name of the variable specifying identifier of individuals. |

`alpha` |
Numeric, a starting value for the intercept of the association parameter alpha. |

`mu` |
Numeric, a starting value for the intercept of the mu parameter. |

`sigma` |
Numeric, a starting value for the intercept of the sigma parameter. |

`sparse` |
Logical, should sparse matrix structures be used for updating and sampling of mu parameter model terms? |

`start` |
A named numeric vector containing possible starting values, the names are based on
function |

`weights` |
Currently not supported. |

`offset` |
Currently not supported. |

`criterion` |
Information criterion to be used, e.g., for smoothing
variance selection. Options are the corrected AIC |

`maxit` |
Vector containing the maximum number of iterations for the backfitting
algorithm with |

`nu` |
Vector of step lengths for parameter updates of one Newton-Raphson update for each predictor of the joint model. |

`update.nu` |
Should the updating step length be optimized in each iteration
of the backfitting algorithm? Uses |

`eps` |
The relative convergence tolerance of the backfitting algorithm. |

`alpha.eps` |
The relative convergence tolerance of the backfitting algorithm for predictor alpha. |

`ic.eps` |
The relative convergence tolerance of the information criterion used, e.g., for smoothing variance selection. |

`nback` |
For computing |

`verbose` |
Print information during runtime of the algorithm. |

`digits` |
Set the digits for printing when |

`n.iter` |
the number of MCMC iterations. |

`burnin` |
the burn-in phase of the sampler, i.e., the number of starting samples that should be removed. |

`thin` |
the thinning parameter for MCMC simulation. E.g., |

`step` |
How many times should algorithm runtime information be printed, divides |

`object` |
A |

`newdata` |
Dataset for which to create predictions. Not needed for conditional survival probabilities. |

`type` |
Character string indicating which type of predictions to compute. |

`id` |
Integer or character, that specifies the individual for which the plot should be created. |

`dt` |
The time window after the last observed measurement for which predictions should be computed.
The default is |

`steps` |
Integer, the number of steps for which to evaluate the conditional survival probability
up to |

`FUN` |
A function that should be applied on the samples of predictors or
parameters, depending on argument |

`cores` |
Specifies the number of cores that should be used for prediction. Note that
this functionality is based on the |

`chunks` |
Should computations be split into |

`points` |
Should longitudinal observations be added to the plot. |

`rug` |
Should longitudinal observed time points be added on the x-axis to the plot. |

`...` |
Currently not used. |

We refer to the paper of Koehler et al. (2016) for details on the flexible
additive joint model. In short, we model the hazard of subject *i* an event at time
*t* as

*h_{i}(t) = \exp [η_{λ i}(t) + η_{γ i}+η_{α i}(t) \cdot η_{μ i}(t)]*

with predictor *η_{λ}* for all survival covariates that are time-varying or have a
time-varying coefficient (including the log baseline hazard), predictor *η_{γ}* for
baseline survival covariates, predictor *η_{α}* representing the potentially
time-varying association between the longitudinal marker *η_{μ}* and the hazard. The
longitudinal response *y_{ij}* at time points *t_{ij}* is modeled as

*y_{ij}=η_{μ i}(t_{ij})+e_{ij}*

with independent normal errors *N(0, \exp[η_{σ i}(t_{ij})]^2)*.

Each predictor *η_{ki}* is a structured additive predictor, i.e. a sum of functions of
covariates *η_{ki} = ∑_{m=1}^{M_k} f_{km}(\bm{x}_{ki})*. Each of these functions can be
modeled parametrically or using basis function evaluations from the smooth constructors in
mgcv such as `s`

, `te`

and `ti`

and can
include smooth time-varying, random or spatial effects. For the Bayesian estimation of these effects
we specify corresponding priors: For linear or parametric terms we use vague normal priors, smooth
and random effect terms are regularized by placing generic multivariate normal priors on the
coefficients and for anisotropic smooths, when multiple smoothing variance parameters are involved,
more complex prior are in place (cf. Koehler et al., 2016). We use inverse Gamma
hyper-priors, i.e. IG(0.001, 0.001) to obtain an inverse Gamma full conditional for the variance
parameters. We estimate the posterior mode by maximizing the log-posterior of the model using a
Newton-Raphson procedure, the posterior mean is obtained via derivative-based Metropolis-Hastings
sampling. We recommend to use posterior mode estimates for a quick model assessment. In order to
draw correct inferences from the model, posterior mean estimates should be computed.
We approximate integration in the survival part of the likelihood using trapezoidal rule. For
posterior mode estimation.

Please note that in order to make use of the sparse setup in fitting random slopes (cf. first example), no observation time should be exactly 0.

Koehler M, Umlauf N, Beyerlein, A., Winkler, C. Ziegler, A.-G., Greven S (2016). Flexible Bayesian Additive Joint Models with an Application to Type 1 Diabetes Research. arXiv:1611.01485 [stat], http://arxiv.org/abs/1611.01485.

Umlauf N, Klein N, Zeileis A (2016). Bayesian Additive Models for Location
Scale and Shape (and Beyond). *(to appear)*

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 | ```
## Not run: set.seed(123)
## Simulate survival data
## with random intercepts/slopes and a linear effect of time,
## constant association alpha and no effect of the derivative
d <- simJM(nsub = 200, long_setting = "linear",
alpha_setting = "constant",
dalpha_setting = "zero", full = FALSE)
# remove 0s from the longitudinal time variable to allow sparse calculations
d$obstime <- d$obstime - sqrt(.Machine$double.eps)
## Formula of the according joint model
f <- list(
Surv2(survtime, event, obs = y) ~ s(survtime, bs = "ps"),
gamma ~ s(x1, bs = "ps"),
mu ~ obstime + s(id, bs = "re") +
s(id, obstime, bs = "re"),
sigma ~ 1,
alpha ~ 1,
dalpha ~ -1
)
## Joint model estimation
## jm_bamlss() sets the default optimizer and sampler function.
## First, posterior mode estimates are computed using function
## jm.mode(), afterwards the sampler jm.mcmc() is started.
b <- bamlss(f, data = d, family = "jm",
timevar = "obstime", idvar = "id")
## Plot estimated effects.
plot(b)
## Predict event probabilities for two individuals
## at 12 time units after their last longitudinal measurement.
## The event probability is conditional on their survival
## up to their last observed measurement.
nd <- subset(d, id %in% c(192, 127))
p <- predict(b, type = "probabilities", dt = 12, FUN = c95)
print(p)
## Plot of survival probabilities and
## corresponding longitudinal effects
## for individual id.
jm.survplot(b, id = 3)
jm.survplot(b, id = 30)
## Simulate survival data
## with functional random intercepts and a nonlinear effect
## of time, time-varying association alpha and no effect
## of the derivative.
## Note: This specification is the simJM default.
d <- simJM(nsub = 200, full = FALSE)
## Formula of the according joint model
## number of knots for the smooth nonlinear effect of time
klong <- 8
f <- list(
Surv2(survtime, event, obs = y) ~ s(survtime, bs = "ps"),
gamma ~ s(x1, bs = "ps"),
mu ~ ti(id, bs = "re") +
ti(obstime, bs = "ps", k = klong) +
ti(id, obstime, bs = c("re", "ps"),
k = c(nlevels(d$id), klong)) +
s(x2, bs = "ps"),
sigma ~ 1,
alpha ~ s(survtime, bs = "ps"),
dalpha ~ -1
)
## Estimating posterior mode only using jm.mode()
b_mode <- bamlss(f, data = d, family = "jm",
timevar = "obstime", idvar = "id", sampler = FALSE)
## Estimating posterior means using jm.mcmc()
## with starting values generated from posterior mode
b_mean <- bamlss(f, data = d, family = "jm",
timevar = "obstime", idvar = "id", optimizer = FALSE,
start = parameters(b_mode), results = FALSE)
## Plot effects.
plot(b_mean, model = "alpha")
## End(Not run)
``` |

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