---
title: "markovMSM: An R package for checking the Markov condition in multi-state survival data"
author: "Gustavo Soutinho and Luis Meira-Machado"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{markovMSM: An R package for checking the Markov condition in multi-state survival data}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

The purpose of the present vignette is to demonstrate the capacities of the R package *markovMSM*, as a tool to check the Markov condition. To this end, in the folowing example, we use data from a study with liver
cirrhosis patients subjected to prednisone treatment (Andersen et al., 1993).

## Application of the markovMSM for testing Markov assumption for more complex multi-state models

The proposed methods can also be used in reversible multi-state models such as those applied
to the data set of liver cirrhosis patients who were included in a randomized clinical trial at several
hospitals in Copenhagen between 1962 and 1974. The study aimed to evaluate whether a treatment
based on prednisone prolongs survival for patients with cirrhosis Andersen et al. (1993). State 1
corresponds to ‘normal prothrombin level’, State 2 to ‘low (or abnormal) prothrombin level’, and
State 3 to ‘dead’. The movement of the patients among these three states can be modeled using the
reversible illness-death model shown in the next figure.


Note that the original data set prothr is already in the long format. Thus to obtain the probability 
values for transitions from State 2, the input command is the following:


```{r include=TRUE}
library(markovMSM)

data("prothr")

set.seed(1234)

res8 <- AUC.test(data = prothr, from=2, to=3, type='global', replicas=2, 
                 limit=0.90, quantiles=c(.05, .10, .20, .30, 0.40))

round(res8$globalTest,5)

round(res8$localTests,4)


```
Below we report, for the same data set prothr, the results for global and local tests proposed by
Titman and Putter (2020), which are based on log-rank statistics, for transition 4 (between the states 2
and 3) and transition 3, (between the states 2 and 1), with times corresponding to the percentiles 5,
10, 20, 30, and 40 (the default percentile values also used by the AUC global test). The corresponding
input commands are the following:


```{r include=TRUE}
set.seed(1234)

times <- c(73.5, 117, 223, 392, 681)

res9 <- LR.test(data=prothr, times=times, from = 2, to = 3, replicas = 10)

res9$localTestLR

res9$globalTestLR

set.seed(1234)

res10 <- LR.test(data=prothr, times=times, from = 2, to = 1, replicas = 10)

res10$localTestLR

res10$globalTestLR


```

## References


* Soutinho G., Meira-Machado L. *Methods for checking the  Markov condition in multi-state survival data*, Computational Statistics, 2021. 

* de Una-alvarez J., Meira-Machado L. *Nonparametric estimation of transition probabilities in the non-Markov illness-death model: A comparative study*, Biometrics, 71(2), 364-375, 2015. 

* Putter H., Spitoni C. *Non-parametric estimation of transition probabilities in non-Markov multi-state models: The landmark Aalen-Johansen estimator*, Statistical Methods in Medical Research, 27, 2081-2092, 2018. 

* Meira-Machado L., Sestelo M. *Estimation in the progressive illness-death model: A nonexhaustive review*, Biometrical Journal, 61(2), 245-263, 2019

* Titman A.C., Putter H. *General tests of the Markov property in multi-state models*, Biostatistics, 2020
