# ddhazard

0th

Percentile

##### Fitting Dynamic Hazard Models

Function to fit dynamic hazard models using state space models.

##### Usage
ddhazard(formula, data, model = "logit", by, max_T, id, a_0, Q_0,
Q = Q_0, order = 1, weights, control = ddhazard_control(),
verbose = F)
##### Arguments
formula

coxph like formula with Surv(tstart, tstop, event) on the left hand site of ~.

data

data.frame or environment containing the outcome and covariates.

model

"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.

by

interval length of the bins in which parameters are fixed.

max_T

end of the last interval interval.

id

vector of ids for each row of the in the design matrix.

a_0

vector $$a_0$$ for the initial coefficient vector for the first iteration (optional). Default is estimates from static model (see static_glm).

Q_0

covariance matrix for the prior distribution.

Q

initial covariance matrix for the state equation.

order

order of the random walk.

weights

weights to use if e.g. a skewed sample is used.

control

list of control variables from ddhazard_control.

verbose

TRUE if you want status messages during execution.

##### Details

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().

##### Value

A list with class ddhazard. The list contains

formula

the passed formula.

call

the matched call.

state_vecs

2D matrix with the estimated state vectors (regression parameters) in each bin.

state_vars

3D array with smoothed variance estimates for each state vector.

lag_one_cov

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.

n_risk

the number of observations in each interval.

times

the interval borders.

risk_set

the object from get_risk_obj if saved.

data

the data argument if saved.

weights

weights used in estimation if saved.

id

ids used to match rows in data to individuals.

order

order of the random walk.

F_

matrix which map from one state vector to the next.

method

method used in the E-step.

est_Q_0

TRUE if Q_0 was estimated in the EM-algorithm.

family

Rcpp Module with C++ functions used for estimation given the model argument.

discrete_hazard_func

the hazard function corresponding to the model argument.

terms

the terms object used.

has_fixed_intercept

TRUE if the model has a time-invariant intercept.

xlev

a record of the levels of the factors used in fitting.

##### References

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.

plot, residuals, predict, static_glm, ddhazard_app, ddhazard_boot

• ddhazard
##### Examples
# NOT RUN {
# 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)

# }

Documentation reproduced from package dynamichazard, version 0.6.5, License: GPL-2

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