Function to fit dynamic hazard models using state space models.
ddhazard(
formula,
data,
model = "logit",
by,
max_T,
id,
a_0,
Q_0,
Q = Q_0,
order = 1,
weights,
control = ddhazard_control(),
verbose = FALSE
)A list with class ddhazard. The list contains
the passed formula.
the matched call.
2D matrix with the estimated state vectors (regression parameters) in each bin.
3D array with smoothed variance estimates for each state vector.
3D array with lagged correlation matrix for each for each change in the state vector. Only present when the model is logit and the method is EKF.
the number of observations in each interval.
the interval borders.
the object from get_risk_obj if saved.
the data argument if saved.
weights used in estimation if saved.
ids used to match rows in data to individuals.
order of the random walk.
matrix which map from one state vector to the next.
method used in the E-step.
TRUE if Q_0 was estimated in the EM-algorithm.
Rcpp Module with C++ functions used for estimation given the model argument.
the hazard function corresponding to the model argument.
the terms object used.
TRUE if the model has a time-invariant intercept.
a record of the levels of the factors used in fitting.
coxph like formula with Surv(tstart, tstop, event) on the left hand site of ~.
data.frame or environment containing the outcome and covariates.
"logit", "cloglog", or "exponential" for
respectively the logistic link function with discrete outcomes,
the inverse cloglog link function with discrete outcomes,
or for the continuous time model with piecewise constant exponentially
distributed arrival times.
interval length of the bins in which parameters are fixed.
end of the last interval interval.
vector of ids for each row of the in the design matrix.
vector \(a_0\) for the initial coefficient vector for the first iteration (optional). Default is estimates from static model (see static_glm).
covariance matrix for the prior distribution.
initial covariance matrix for the state equation.
order of the random walk.
weights to use if e.g. a skewed sample is used.
list of control variables from
ddhazard_control.
TRUE if you want status messages during execution.
This function can be used to estimate survival models where the regression parameters follows a given order random walk. The order is specified by the order argument. 1. and 2. order random walks is implemented. The regression parameters are updated at time by, 2by, ..., max_T. See the vignette("ddhazard", "dynamichazard") for details.
All filter methods needs a state covariance matrix Q_0 and state vector a_0. An estimate from a time-invariant model is used for a_0 if it is not supplied (the same model you would get from static_glm). A diagonal matrix with large entries is recommended for Q_0. What is large dependents on the data set and model. Further, a covariance matrix for the first iteration Q is needed. The Q and a_0 are estimated with an EM-algorithm.
The model is specified through the model argument. The discrete
outcome models are where outcomes are binned into the intervals.
Be aware that there can be "loss" of information due to binning if outcomes
are not discrete to start with. It is key for these models that the
id argument is provided if individuals in the data set have
time-varying covariates. The the exponential model use a piecewise constant
exponential distribution
for the arrival times where there is no "loss" information due to binning.
Though, one of the assumptions of the model is not satisfied if outcomes
are only observed in discrete time intervals.
It is recommended to see the Shiny app demo for this function by calling ddhazard_app().
Fahrmeir, Ludwig. Dynamic modelling and penalized likelihood estimation for discrete time survival data. Biometrika 81.2 (1994): 317-330.
Durbin, James, and Siem Jan Koopman. Time series analysis by state space methods. No. 38. Oxford University Press, 2012.
Christoffersen, Benjamin. dynamichazard: Dynamic Hazard Models Using State Space Models. Journal of Statistical Software 99.7 (2021): 1-38.
plot, residuals, predict, static_glm, ddhazard_app, ddhazard_boot
# example with first order model
library(dynamichazard)
fit <- ddhazard(
Surv(time, status == 2) ~ log(bili), pbc, id = pbc$id, max_T = 3600,
Q_0 = diag(1, 2), Q = diag(1e-4, 2), by = 50,
control = ddhazard_control(method = "GMA"))
plot(fit)
# example with second order model
fit <- ddhazard(
Surv(time, status == 2) ~ log(bili), pbc, id = pbc$id, max_T = 3600,
Q_0 = diag(1, 4), Q = diag(1e-4, 2), by = 50,
control = ddhazard_control(method = "GMA"),
order = 2)
plot(fit)
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