Model input

Input parameters for the model were obtained from the published literature. When published evidence was not available, relevant information was obtained from expert opinion. Parameters and values used in the model, in terms of disease progression, costs and quality of life are described below.

4.4.2.A. Disease progression

Information on disease progression, in the form of Kaplan-Meier survival and time-to-progression curves for each treatment was obtained from the only study comparing Gem+Cisp against Gem+Carb²⁰⁸. These curves formed the basis for fitting Weibull models, which were used to derive estimates of the probability of a patient being at in any of the three model states at any given cycle. Weibull models are commonly used to describe the distribution of time-dependent events such as cancer survival and progression and are characterised by two parameters: the shape parameter alpha ( ) and the scale parameter beta ( )^218;219.

In fitting a Weibull model to existing survival curves, the task is to determine the values of the parameters and . This can be done by manipulating the survival function of the Weibull distribution

[ ( ) ]

where represents time (here, in discrete 21-day cycles) and , represent the parameters of the Weibull model, to give

[ ]

This expression shows that the [ ] is a linear function of . Regressing [ ] against gives ordinary least square estimates of the model intercept and coefficients, which can be used to obtain the and parameters for the Weibull model, as

Once the parameters of the Weibull models for disease progression and death were estimated, the resulting progression-free survival and survival functions were used to calculate the probability of a patient staying at the ‘Progression-free’ state, being at the

‘Progression’ state or being dead. This gave the number of patients in the ‘Progression-free’

and ‘Death’ states throughout the model. In turn, the number of patients in the ‘Progression’

state was calculated as the difference between the total number of patients in the cohort (i.e. 1000) and the sum of the patients in the remaining states (i.e. Patients in the

‘Progression’ state = total number of patients in the cohort – (patients in ‘Progression-free’

state + patients in ‘Death’ state). For example, at cycle 10, 468 out of 1000 patients had not progressed and were in the ‘Progression-free’ state and 400 patients had died, leaving 132 patients in the ‘Progression’ state.

In the first two cycles for Gem+Cisp, the calculated sum of patients in the ‘Progression-free’

and ‘Death’ states exceeded the number of patients in the cohort (by ten patients in cycle 1 and six patients in cycle 2). This resulted in observing negative numbers of patients in

‘Progression’ state at cycles 1 and 2. In order to correct for this minor inconsistency, the number of patients in each of the states at cycles 1 and 2 were re-calculated by scaling the values down to 1000. Tables with the output of the regression model for disease progression and survival, the estimated and parameters as well as graphs of the fitted Weibull

models for each treatment are given in Appendix 3.C, Table 3.d to Table 3.k and Figure 3.b to Figure 3.e.

4.4.2.B. Resource use and costs

Costs associated with each treatment were estimated according to use of health care resource due to:

a. drug acquisition and administration;

b. adverse events;

c. other medical resources, and

d. terminal care.

In estimating these costs, health care resource use derived from published studies was multiplied by unit cost estimates taken from national published sources^220-222. Costs were converted to 2004 prices using the Hospital and Community Health Services pay and price inflation indices²²⁰, to reflect the relevant values in the year when the research funding decision was considered.

Drug acquisition costs were calculated according to the standard treatment schedule of two administrations of gemcitabine on days 1 and 8 of a 21-day cycle, and one administration of platinum analogue (either cisplatin or carboplatin) on day 1 of the treatment cycle¹⁹⁸. For these calculations, chemotherapy doses were multiplied by unit costs of drugs published in the British National Formulary²²². The body surface area of an ‘average’ NSCLC patient (1.7

square metres) was taken from the literature²⁰¹. Required doses, constituent parts and unit costs can be found in Table 4.3.

Table 4.3: Unit costs of drug acquisition and administration (NSCLC)

Resource Dose

Gemcitabine (1250mg/m²) 2125mg £295

British National

administration (outpatient) £142 NHS Reference Cost

Schedules 2009-2010²²¹

According to the literature, chemotherapy administrations for NSCLC typically take place in an outpatient setting213;223;224. Outpatient chemotherapy administration cost was obtained from the NHS Reference Costs Schedules²²¹. Different possibilities regarding the split between patients receiving chemotherapy in an inpatient and outpatient setting were explored in sensitivity analyses. The total cost of drug acquisition and administration per treatment cycle for Gem+Cisp and Gem+Carb are given in Table 4.4.

Table 4.4: Cost of drug acquisition and administration for a treatment cycle (NSCLC)

Treatment

Day 1 of treatment cycle Day 8 of treatment cycle Total cost per

Separate calculations were carried out to obtain estimates of the expected cost of adverse events. In line with the literature, the focus was on significant toxicities which would typically lead to hospitalisation^214;224. The probability of a patient in the cohort experiencing a serious adverse event was estimated from data on adverse event occurrence reported in the Zatloukal et al.²⁰⁸ study. This probability was combined with the unit cost of resolving each type of adverse event taken from the NHS Reference Costs Schedules²²¹, using the formula:

∑ ( )

Here, ( ) is the probability of a patient on treatment experiencing adverse event and is the unit cost for resolving the adverse event . An alternative, fixed value for the cost of adverse events (£544 in 2004 prices) obtained from the literature²⁰¹ was used in deterministic sensitivity analysis. The expected cost of experiencing an adverse event is given in Table 4.5.

Table 4.5: Expected cost of adverse events (NSCLC)

Adverse event

An estimate of the expected cost of other medical resources (additional outpatient visits and examinations) associated with Gem+Cisp was taken from Schiller and colleagues²¹² (£728 in 2004 prices). In the absence of estimates of other medical cost specific to Gem+Carb, and in view of the fact that such costs are not expected to differ significantly between treatments²²⁵, the above value was used for both treatments. Last, an estimate of the costs associated with terminal care for cancer patients was obtained from Clegg et al.²⁰¹ (£1460 in 2004 prices).

4.4.2.C. Health-related quality of life

Although estimates of health-related quality of life (HRQoL) were reported in most of the trials identified in the search for effectiveness and cost-effectiveness evidence, these were non-preference-based measures, such as the EORTC-QLQ C30 and LC13206;226-231

. In view of the fact that such instruments have limited applicability to economic evaluations^130;232, a separate search for based quality of life values was carried out. No preference-based quality of life (utility) scores for advanced NSCLC were identified in the pre-2004 literature. Therefore, utility scores were obtained from expert opinion (Professor L.

Billingham, Professor of Biostatistics, University of Birmingham, 10-05-2011). The employed utility scores are given in Table 4.6.

Table 4.6: Preference-based health-related quality of life scores by health state (NSCLC)

Health state Mean Standard error Source

Progression-free 0.65 0.08

Uncertainty in the model was propagated through probabilistic sensitivity analysis. Key parameters were represented by probability distributions, from which 5000 sets of values were drawn through Monte Carlo simulations^169;171 to give 5000 estimates of the costs and effects associated with each treatment.

As mentioned earlier, transition probabilities for the model were drawn from fitted Weibull time-to-progression and survival curves. Each curve is characterised by a shape parameter and a scale parameter , which are derived from the intercepts and coefficients obtained from the fitted linear regression model. Thus varying the transition probabilities required varying and , through varying the coefficients of the linear regression model. The latter were given normal distributions with mean and standard errors taken directly from the linear model. Parameter values and assigned distributions are given in Appendix 3.D, Table 3.l.

Cost parameters were also varied in probabilistic sensitivity analysis. Drug acquisition and administration costs were assigned gamma distributions using the method of moments⁵¹. Owing to lack of information on the standard error of the cost of drug acquisition and