Source: extracted from pages 30 to 33, Chapter 2 of "Decision Modelling for Health Economic Evaluation" by Briggs, Claxton & Sculpher

A case study in HIV

The details of the Markov model can be illustrated using a case study. This is a cost-effectiveness analysis of zidovudine monotherapy compared with zidovudine plus lamivudine (combination) therapy in patients with HIV infection (Chancelloret al. 1997). This example has been used for didactic purposes before (Drummondet al. 2005), but is further developed here, and in Chapter 4 for purposes of probabilistic analysis.

The structure of the Markov model is shown in Fig. 2.3. This model characterizes a patient's prognosis in terms of four states. Two of these are based on CD4 count: 200-500 cells/mm3 (the least severe disease state - State A) and less than 200 cells/mm3 (State B). The third state is AIDS (State C) and the final state is death (State D). The arrows on the Markov diagram indicate the transitions patients can make in the model. The key structural assumption in this early HIV model (now clinically doubtful, at least in developed countries) is that patients can only remain in the same state or progress; it is not feasible for them to move back to a less severe state. More recent models have allowed patients to move back from an AIDS state to non-AIDS states and, through therapy, to experience an increase in CD4 count. These models have also allowed for the fact that prognosis for these patients is now understood in terms of viral load as well as CD4 count (Sanderset al. 2005).

Fig. 2.3ThestructureoftheMarkovmodelusedinthecasestudy(Chancelloretal.1997).

The transition probabilities governing the direction and speed of transitions between disease states in the model are shown in Table 2.2 where a cycle is taken as 1 year. For monotherapy, these 'baseline' (i.e. control group) probabilities are taken from a longitudinal cohort study where data were collected prior to any use of combination therapy. The zeros indicate that backwards transitions are assumed not to be feasible. The transition probabilities for combination therapy were based on an adjustment to the baseline values

according to the treatment effect of combination therapy relative to monotherapy.

This treatment effect took the form of a relative risk (0.509) which was derived from a meta-analysis of trials. Although the treatment effect in the trials was something rather different, it was assumed that the relative risk

worked to reduce the transition probabilities from one state to any worse state. The calculation of these revised (combination) transition probabilities is shown in Table 2.2. Any probability relating to the movement to a worse state is multiplied by 0.509, and the probability of remaining in a state is correspondingly increased. The separation of baseline probabilities from a relative treatment effect is a common feature of many decision models used for cost effectiveness.

Table 2.2Transition probabilities and costs for the HIV Markov model used in the case study (Chancelloret al. 1997)

State at start of cycle State at end of cycle

1. Annual transition probabilities

(a) Monotherapy

	State A	State B	State C	State D
State A	0.721	0.202	0.067	0.010
State B	0.000	0.581	0.407	0.012
State C	0.000	0.000	0.750	0.250
State D	0.000	0.000	0.000	0.000
(b) Combination	therapy
	State A	State B	State C	State D
State A	0.858 (1 - sum)	0.103 (0.202 RR)	0.034 (0.067 RR)	0.005 (0.010 RR)
State B	0.000	0.787 (1 - sum)	0.207 (0.407 RR)	0.006 (0.012 RR)
State C	0.000	0.000	0.873 (1 - sum)	0.127 (0.25 RR)
State D	0.000	0.000	0.000	1.000
2. Annual costs
Direct medical	1701	1774	6948	-
Community	1055	1278	2059	-
Total	2756	3052	9007	-

RR, relative risk of disease progression. Estimated as 0.509 in a meta-analysis. The drug costs were 2278 (zidovudine) and 2086 (lamivudine).

One advantage of this approach relates to the important task of estimating cost-effectiveness for a particular location and population subgroup. Often it is assumed that baseline event probabilities should be as specific as possible to the location(s) and subgroup(s) of interest, but that the relative treatment effect is assumed fixed.

It can be seen that all the transition probabilities are fixed with respect to time. That is, the baseline annual probability of progressing from, for example, State A to State B is 0.202, and this is the case 1 year after start of therapy and it is also the case, for those remaining in State A, after 10 years. When these time invariant probabilities are used, this is sometimes referred to as a Markov Chain.

Table 2.2 also shows the annual costs associated with the different states. These are assumed identical for both treatment options being compared -excluding the costs of the drugs being evaluated. The drug costs were 2278 (zidovudine) and 2086 (lamivudine). Outcomes were assessed in terms of changes in mean survival duration so no health-related quality of-life weights (utilities) were included.

Your task:

1. Rebuild the Markov model in TreeAge(hint: involving four health states following the Markov node; transition probability zero means there is NO transition possible: e.g., from State B to State C).
2. Estimate the incremental cost-effectiveness ratio for combination therapy compared to monotherapy from the societal perspective (hint: including both direct medical and community costs).