Disease model
We begin by constructing the model for health state transitions, which is a function of input data (i.e., covariates) and a fitted multi-state model (or a parameter object). When separate multi-state models are fit by transition, the input data consists of one observation for each treatment strategy and patient combination (joint models consist of one observation for each treatment strategy, patient, and transition combination). It can be created easily by using the expand() function to expand the hesim_data() object created above.
transmod_data <- expand(hesim_dat,
by = c("strategies", "patients"))
head(transmod_data)
## strategy_id patient_id age female
## 1: 1 1 44.28040 1
## 2: 1 2 45.03292 0
## 3: 1 3 45.38090 1
## 4: 1 4 43.95674 1
## 5: 1 5 44.65803 0
## 6: 1 6 45.78530 1
“Clock reset” and “clock forward” transition models are created by combining the fitted models and input data with the transition matrix, desired number of PSA samples, the timescale of the model, and the starting age of each patient in the simulation (by default, patients are assumed to live no longer than age 100 in the individual-level simulation).
transmod_cr <- create_IndivCtstmTrans(wei_fits_cr, transmod_data,
trans_mat = tmat, n = n_samples,
clock = "reset",
start_age = patients$age)
transmod_cf <- create_IndivCtstmTrans(wei_fits_cf, transmod_data,
trans_mat = tmat, n = n_samples,
clock = "forward",
start_age = patients$age)
It is a good idea to evaluate the assumptions underlying multi-state models. hesim can help facilitate these analyses since hazards ($hazard()), cumulative hazards ($cumhazard()), and state probabilities ($stateprobs()) can be easily computed. As an illustration, we will predict hazards using the maximum likelihood estimates of the Weibull model for a single patient (patient_id = 1). To do so, we create new transition models based on a subset of the dataset transmod_data used above.
# Predict hazard
transmod_data_pat1 <- transmod_data[patient_id == 1]
predict_haz <- function(fits, clock){
transmod_cr_pat1 <- create_IndivCtstmTrans(fits, transmod_data_pat1,
trans_mat = tmat,
clock = clock,
point_estimate = TRUE)
haz <- transmod_cr_pat1$hazard(t = seq(0, 20, 1))
title_clock <- paste(toupper(substr(clock, 1, 1)),
substr(clock, 2, nchar(clock)), sep="")
haz[, clock := title_clock]
return(haz[, ])
}
We then plot the predicted hazard by treatment strategy and timescale.
# Plot hazards
library("ggplot2")
haz <- rbind(predict_haz(wei_fits_cr, "reset"),
predict_haz(wei_fits_cf, "forward"))
haz[, trans_name := factor(trans,
levels = 1:4,
labels = c("Healthy-> Sick",
"Healthy -> Dead",
"Sick -> Healthy",
"Sick -> Dead"))]
ggplot(haz[t > 0],
aes(x = t, y = hazard, col = clock, linetype = factor(strategy_id))) +
geom_line() +
facet_wrap(~trans_name) +
xlab("Years") + ylab("Hazard") +
scale_linetype_discrete(name = "Strategy") +
scale_color_discrete(name = "Clock") + theme_bw()
While the hazards from the healthy state are similar between the “clock forward” and “clock reset” approaches, they differ significantly in the sick state. Treatment effects (i.e., the hazard ratios between treatment strategies 1 and 2) are also largest in the sick state.
Additional analyses should be conducted as well. For instance, the hazards for treatment strategy 1 (the reference treatment strategy) could be assessed by comparing the Weibull model’s predictions with predictions from non-parametric (i.e., the Kaplan-Meier estimator) or semi-parametric (i.e., Cox) models. This can be performed using mstate, which can predict cumulative hazards and state probabilities in non-parametric and semi-parametric models. Furthermore, the Weibull model’s proportional hazards assumption should be tested using standard techniques such as plots of log time vs. the log cumulative hazard, inclusion of time-dependent covariates, and tests of the Schoenfeld residuals.
