optim.fit: Fit multi-state model for optimization

In OptimalTiming: Optimal Timing Identification

Description

This function produces transition probabilities for given covariates values in multi-state models.

Usage

optim.fit(data, transM, nstate, state_label, event_label, treatment = NULL,
  absorb, cov, cov_value)

Arguments

data	Data frame in wide format where each row in the data corresponds to a single subject. Time to a state and the occurrence of the state come in pairs. If a state is not occur, use the time to an absorbing state or censoring time instead. Covariates are added at the end of each row.
transM	A nstate \times nstate matrix used to indicate the transitions in multi-state model. If a transition exists between two states, set 1 in a corresponding location, otherwise set 0.
nstate	Number of states incorporated in the multi-state model.
state_label	A character vector of length nstate containing the names of states. The elements in state_label are extracted from the column names of data, except for the first one, which is a potential state at the initiation of a study for each subject. Assume all subjects have the same initial state.
event_label	A character vector of length nstate-1, indicating the occurrence of each state. The first state in state_label do not need an indiator, as it always exists.
treatment	A character vector of length 2, indicating whether there is a treatment variable available. If true, the name and indicator of this treatment extracted from state_label and event_label consist of treatment. If not, treatment=NULL. See details. The default value is NULL.
absorb	A character vector of length 2, indicating the name and indicator of the absorb state.
cov	A character vector containing the names of covariates that have some effect to transition probabilities.
cov_value	A numeric vector containing the values of covariates corresponding to cov. cov_value are used to calculated subject specified transition probabilities.

Details

For optim.fit, transition probabilities are estimated under Markov assumption, which implies that the probability of transition to a future state depends only on the present state, not on the history. Taking covariates at baseline into consideration, transition probabilities can be subject-specific. Cox proportional hazards model is used to fit transition hazards among multiple states by assuming each transition has its own baseline hazard, and covariates have different effects on different transitions.

Let \mathbf{S}={1,2,\cdots,S} denote the states in the multi-state model and X(t) be a random process taking values from \mathbf{S}. Denote α_{gh}(t) as hazard ratio or transition intensity and Z as baseline covariates. The instantaneous risk of a transition from state g into state h at time t can be fitted by semi-parametric Cox model:

α_{gh}(t|Z)=α_{gh,0}exp(β^{T}Z_{gh}).

The cumulative hazard ratio is defined as A_{gh}(t)=\int_0^t α_{gh}(u)du. Primary interest in this function is to estimate transition probability P_{gh}(s,t)=P(X(t)=h|X(s)=g), indicating the chance of transition from state g at time s to state h at time t. Written in matrix form, transition probability matrix \mathbf{P}(t) can be calculated by means of a product integral: \mathbf{P}(s,t)=∏_{(s,t]}(\mathbf{I}+d\mathbf{A}(u)), where \mathbf{A}(t) is a transition intensity matrix. Both \mathbf{P} and \mathbf{A} are S \times S matrix.

The data format required by this function is wide format, which can be regarded as the augmented data used in single event survival analysis. For example, if there is a "recurrence" state in a multi-state model, two variable are needed to describe this event, namely, "rec" and "rec.s". The former is a time variable, indicating the time from initiation of the study to the occurrence of this state, while the latter is an indicator variable with 1 for occurrence and 0 for censoring. If the event is censored for some patients, use the maximum follow-up instead of the event time. Other states are prepared in the same way. Thus, each row in the augmented data summarize all possible events for a single subject. For covariates, they are located at the end of each row.

If the time of new treatment initiation is provided in data, the argument treatment should be assigned as, eg.treatment=c("sct","sct.s"). Additionally, the argument state_lable and event_label shoud be arranged in such order: pre-treatment state, treatment state, post-treatment states and absorbing state. Assume treatment may take place at any pre-treatment states. In this case, optim.fit function automatically fit two multistate models, one for post-treatment states if a new treatment is carried out , and the other for pre-treatment states if a new treatment is not carried out. Thus, comparison among strategies of whether and when to initiate new treatment can be performed in sim.MTL function. If treatment=NULL, a single multistate model will be fitted.

Value

If treatment is NULL, a list object called "overall" is output with elements:

transMat	A transition matrix describing the states and transitions in multi-state model.
tranProb	A list of size nstate recording the transition probabilities form each state to another along with standard errors. Element [[s]] is a data frame containing transition probabilities from state s to state 1,2,...,nstate.These transition probabilities are time-varying over distinct transition time points.
coxobj	An object returned by coxph() function in survival package.
ntrans	The number of available transitions among multiple states.
...	Other variables that extracted from the original input.

If treatment is not NULL, three list objects called "overall", "treat","no_treat" are output. A list "overall" contains elements:

transMat	A transition matrix describing the states and transitions in multi-state model.
ntrans	The number of available transitions among multiple states.
...	Other variables that extracted from the original input.

A list "no_treat" contains elements by fitting a model for pre-treatment states:

transMat	A transition matrix describing the states and transitions if the new treatment is not carried out.
tranProb	A list recording the transition probabilities among pre-treatment states.
coxobj	An object returned by coxph() function in survival package.
ntrans	The number of available transitions among pre-treatment states.
data	A data set contaning states if the new treatment is not carried out.
nstate	The number of pre-treatment states.
...	Other variables that extracted from the original input.

A list "treat" contains elements by fitting a model if a new treatment is carried out:

transMat	A transition matrix describing the states and transitions if the new treatment is carried out.
tranProb	A list recording the transition probabilities among post-treatment states.
coxobj	An object returned by coxph() function in survival package.
ntrans	The number of available transitions among post-treatment states.
data	A data set contaning states if the new treatment is carried out.
nstate	The number of post-treatment states.
...	Other variables that extracted from the original input.

References

de Wreede LC, Fiocco M, and Putter H (2010). The mstate package for estimation and prediction in non- and semi-parametric multi-state and competing risks models. Computer Methods and Programs in Biomedicine 99, 261–274.

Examples

## Not run: 
library(OptimalTiming)
## read data
data(SimCml)

## fit multistate model if the time to new treatment initiation is available in SimCml
fit=optim.fit(data=SimCml,
         transM=matrix(c(0,1,0,0,0,1,0,0,0,1,0,1,1,1,0,0,0,1,1,1,1,
         0,0,0,0,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0),7,byrow=TRUE),
         nstate=7,state_label=c("diagnose","cp1","ap","cp2","bc","sct","death"),
         event_label=c("cp1.s","ap.s","cp2.s","bc.s","sct.s","death.s"),
         treatment=c("sct","sct.s"),absorb=c("death","death.s"),
         cov=c("age"),cov_value=c(0))

## view the content of this object
objects(fit)

## output transition probabilities
fit$treat$tranProb
fit$no_treat$tranProb
## End(Not run)

OptimalTiming documentation built on May 2, 2019, 1:45 p.m.