---
title: "Cycle dependent"
author: "Sheeja Manchira Krishnan"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Cycle dependent}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

In this example we will model the cost effectiveness of lamivudine/zidovudine
combination therapy in HIV infection ([Chancellor, 1997] (https://pubmed.ncbi.nlm.nih.gov/10169387/))) and also described in Decision 
Modelling for Health Economic Evaluation, page 32 (Example 2.5). The solution 
can be downloaded from https://www.herc.ox.ac.uk/downloads/decision-modelling-for-health-economic-evaluation. We have implemented the scenario in which the effect of combination therapy of lamivudine/zidovudine (as the probability of moving to worse health states and 
having to accrue more cost) is only seen in first 2 years. This means that the transition probability and costs are dependent on first two cycles (As the 
cycle length is years).

This model aims to compare costs and utilities of two treatment
strategies, mono therapy and combined therapy.

Four states are described, from best to worst health-wise:

A: CD4 cells > 200 and < 500 cells/mm3;
B: CD4 < 200 cells/mm3, non-AIDS;
C: AIDS;
D: Death.
```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = ">",
 fig.width = 6, 
 fig.height = 4
)
```

```{r setup}
library(packDAMipd)
```

 Define health states for mono therapy - now the costs are just defined, but 
 not defined any value.

```{r}
A <- health_state("A", cost = "cost_health_A + cost_drug ",utility = 1)
B <- health_state("B", cost = "cost_health_B + cost_drug",utility = 1)
C <- health_state("C", cost = "cost_health_C + cost_drug",utility = 1)
D <- health_state("D", cost = 0, utility = 0)
```

 Define allowed transition probabilities and number them. The below matrix is 
 numbered so that the maximum entry in the matrix gives the total number of 
 allowed transitions. Column names and row names are just the names of the 
 health states.

```{r}
tmat <- rbind(c(1, 2,3,4), c(NA, 5,6,7),c(NA, NA, 8,9), c(NA,NA,NA,10))
colnames(tmat) <- rownames(tmat) <- c("A","B" ,"C","D")

```

 Define transition matrix now, but parameters are fine now
```{r}
tm <- populate_transition_matrix(4, tmat, c("tpAtoA", "tpAtoB", "tpAtoC",
                                            "tpAtoD",
                                   "tpBtoB", "tpBtoC", "tpBtoD",
                                   "tpCtoC","tpCtoD","tpDtoD" ))
```
 Combine the health states and define the strategy. The current strategy ie. 
 control or intervention - here it is mono therapy

```{r}
health_states <- combine_state(A,B,C,D)
mono_strategy <- strategy(tm, health_states, "mono")
```
Before we run the model, we need to give values to parameters, thus we define 
the parameter list. We need to make sure that the parameters with numerical 
values are given first and derived parameters later in the list. The parameters 
are assigned sequentially as given in the parameter list. So if there is any calculations needed (or using functions), they are defined earlier.

```{r}
mono_params = define_parameters(cost_zido = 2278,
cost_direct_med_A = 1701,
cost_comm_care_A = 1055,
cost_direct_med_B = 1774,
cost_comm_care_B = 1278,
cost_direct_med_C = 6948,
cost_comm_care_C = 2059,
tpAtoA = 1251/(1251 + 483),
tpAtoB = 350/(350 + 1384),
tpAtoC = 116/(116 + 1618),
tpAtoD = 17/(17 + 1717),
tpBtoB = 731/(731 + 527),
tpBtoC = 512/(512 + 746),
tpBtoD = 15/(15 + 1243),
tpCtoC = 1312/(1312 + 437),
tpCtoD = 437/(437 + 1312),
tpDtoD = 1,
cost_health_A = "cost_direct_med_A+ cost_comm_care_A",
cost_health_B = "cost_direct_med_B+ cost_comm_care_B",
cost_health_C = "cost_direct_med_C+ cost_comm_care_C",
cost_drug = "cost_zido")
```


We run the model with strategy mono_strategy for 20 cycles with initial state
values 1,0,0,0 corresponding to A,B, C and D. Costs and qualys are discounted following the values given in discount. Parameter values will have any parameter defined as health state values or transition probabilities, but not their
values were assigned
```{r}
mono_markov <- markov_model(mono_strategy, 20, initial_state = c(1,0,0,0), 
                            discount = c(0.06,0), mono_params, FALSE, FALSE, 
                            method = "half cycle correction")
```
Now for combination therapy, the transition probabilities and cost are 
dependent on the years or the cycle number. Thus we need to define functions 
that given the correct output to calculate the probabilities and costs as a 
function of cycle
```{r}
 #Define function to set the cost to be differnt for first two cycles
define_comb_cost = function(cycle,cost_lami) {
  if (cycle == 0  || cycle == 1 || cycle == 2)
    return(cost_lami)
  else
    return(0)
}
 #Define function to set the risk ratio to be different for first two cycles

define_rr = function(cycle,rr) {
  if (cycle == 1 || cycle == 2)
    return(rr)
  else
    return(1)
}

```

 Define health states - now the costs are just defined, but not defined any value.
```{r}
A <-  health_state("A", cost = "cost_health_A + cost_drug",utility = 1)
B <- health_state("B", cost = "cost_health_B + cost_drug",utility = 1)
C <- health_state("C", cost = "cost_health_C + cost_drug",utility = 1)
D <- health_state("D", cost = 0, utility = 0)

```

Define allowed transition probabilities and number them. The below matrix is 
numbered so that the maximum entry in the matrix gives the total number of
allowed transitions. Column names and row names are just the names of the 
health states.


```{r}
tmat <- rbind(c(1, 2,3,4), c(NA, 5,6,7),c(NA, NA, 8,9), c(NA,NA,NA,10))
colnames(tmat) <- rownames(tmat) <- c("A","B" ,"C","D")

```
Define transition matrix now, but parameters are changed to indicate that 
they are dependent on value of "rr"
```{r}
tm <- populate_transition_matrix(4, tmat, c("tpAtoA_rr","tpAtoB_rr","tpAtoC_rr","tpAtoD_rr",
                                   "tpBtoB_rr", "tpBtoC_rr", "tpBtoD_rr",
                                   "tpCtoC_rr","tpCtoD_rr","tpDtoD_rr" ), colnames(tmat) )

```
Before we run the model, we need to give values to parameters, thus we define 
the parameter list.
```{r}
comb_params <- define_parameters(cost_zido = 2278,
                     cost_direct_med_A = 1701,
                     cost_comm_care_A = 1055,
                     cost_direct_med_B = 1774,
                     cost_comm_care_B = 1278,
                     cost_direct_med_C = 6948,
                     cost_comm_care_C = 2059,
                     tpAtoA = 1251/(1251 + 483),
                     tpAtoB = 350/(350 + 1384),
                     tpAtoC = 116/(116 + 1618),
                     tpAtoD = 17/(17 + 1717),
                     tpBtoB = 731/(731 + 527),
                     tpBtoC = 512/(512 + 746),
                     tpBtoD = 15/(15 + 1243),
                     tpCtoC = 1312/(1312 + 437),
                     tpCtoD = 437/(437 + 1312),
                     tpDtoD = 1,
                     rr = 0.509,
                     cost_lami = 2086.50,
                     rr_cycle = "define_rr(markov_cycle,rr)",
                     tpAtoA_rr = "1-tpAtoB*rr_cycle-tpAtoC*rr_cycle-tpAtoD*rr_cycle",
                     tpAtoB_rr = "tpAtoB*rr_cycle",
                     tpAtoC_rr = "tpAtoC*rr_cycle",
                     tpAtoD_rr = "tpAtoD*rr_cycle",
                     tpBtoB_rr = "1-tpBtoC*rr_cycle-tpBtoD*rr_cycle",
                     tpBtoC_rr = "tpBtoC*rr_cycle",
                     tpBtoD_rr = "tpBtoD*rr_cycle",
                     tpCtoC_rr = "1-tpCtoD*rr_cycle",
                     tpCtoD_rr = "tpCtoD*rr_cycle",
                     tpDtoD_rr = 1,
                     cost_health_A = "cost_direct_med_A + cost_comm_care_A",
                     cost_health_B = "cost_direct_med_B + cost_comm_care_B",
                     cost_health_C = "cost_direct_med_C + cost_comm_care_C",
                     cost_lami_cycle = "define_comb_cost(markov_cycle,cost_lami)",
                     cost_drug = "cost_zido + cost_lami_cycle")
```


```{r}
# Combine the health states
health_states <- combine_state(A,B,C,D)
#The current strategy i.e. control or intervention - here it is combination 
#therapy
comb_strategy <- strategy(tm, health_states, "comb")

```
We run the model with strategy mono_strategy for 20 cycles with initial state 
values 1,0,0,0 corresponding to A,B, C and D. Costs and qualys are discounted following the values given in discount. Parameter values will have any parameter defined as health state values or transition probabilities, but not their 
values were assigned
```{r}
comb_markov <- markov_model(comb_strategy, 20, c(1, 0,0,0), discount = c(0.06,0.0),comb_params,FALSE,FALSE)
``` 
 Now we combine the Markov models given by \code{mono_Markov} and 
 \code{comb_Markov} and  Estimate ICER and NMB for the list of Markov models
 given by lost_Markov using the comparator "mono" and threshold values as 
 1000 GBP. We also plot cost effectiveness acceptability curve using plot_ceac 
 method. The published report suggests that  for mono therapy the accumulated 
 cost is £44,663 while that for the combination therapy is £50,602. The utility
 values for mono therapy and combination therapy are 7.99 and 8.94 respectively.
 This provides the ICER value of £6,276.
```{r}
list_markov <- combine_markov(mono_markov, comb_markov)
icer_nmb <- calculate_icer_nmb(list_markov,20000,"mono")
icer_nmb
```


```{r}
nmb_all <- list()
prob_ce <- list()
for (i in 1:40) {
  threshold = i*1000
  nmb <- calculate_icer_nmb(list_markov,threshold, "mono")
  if (nmb[2,"NMB"] > 0) {
      prob = 1
  }else{
     prob = 0
  }
  prob_ce <- append(prob_ce,prob)
  nmb_all <- append(nmb_all, nmb)
}
threshold_values <- seq(1000,40000,1000)
plot_ceac(list_markov,threshold_values,"mono")
```
