Model structure

The analysis uses a decision tree to describe the options being compared and the possible pathways following them (Figure 1). This is a commonly used approach in cost-effectiveness studies of health care programmes [10]. The nodes of a decision tree are points where more than one event is possible. The branches are mutually exclusive events following each node. Decision nodes, represented by squares, show the different options that might be chosen by decision-makers based on the costs and benefits they produce (e.g., to choose diagnostic laparoscopy or direct laparotomy). Chance nodes, represented by circles, show uncertain events, each of which is associated with a probability that it will occur (e.g., whether the diagnostic laparoscopy will show that the cancer is resectable or not). Terminal nodes, represented by triangles, are the endpoints of a decision tree, beyond which no further pathways are available. Each terminal node has costs and QALYs associated with it, summarising the sequence of decisions and events on a unique path leading from the initial decision node to that terminal node. These costs and QALYs are expected values, based on the probability of each event on the pathway occurring up to that point and the costs and QALYs associated with each event.

Patients enter the model with pancreatic or periampullary cancer that has been identified as being resectable following CT scanning. If they undergo diagnostic laparoscopy this may be adequate for determining resectability if histologic confirmation of metastatic disease is possible. If the diagnostic laparoscopy is adequate then it will indicate whether or not the tumour is resectable and if it is, the patient will have a laparotomy. During the laparotomy the tumour may be resected or not. If it is not resected, the patient receives palliative treatment. The laparotomy may result in complications, in some cases an additional laparotomy may be required to treat the complications, and the patient may die perioperatively. If the laparoscopy identifies the tumour as not being resectable then curative surgery is not undertaken and the patient will receive palliative treatment.

For patients undergoing direct laparotomy, it was assumed that the pathway was the same as for resectable disease being identified after adequate laparoscopy, but the probabilities, costs and QALYs associated with each pathway may be different. If the diagnostic laparoscopy was inadequate for histologic confirmation of metastatic disease, the diagnostic laparoscopy was considered to be non-informative and the subsequent pathway was assumed to be as for direct laparotomy but also incurring the costs of the diagnostic laparoscopy procedure.

Probabilities

The probabilities associated with mutually exclusive events at each chance node were obtained from published sources (Additional file 1) [8,14,15]. The probability of non-resectable disease with direct laparotomy was 0.403, calculated in the Cochrane Review as the median pre-test prevalence after CT scan of unresectable disease due to distant metastases or local infiltration [8]. Values in the individual studies included in the Cochrane Review ranged from 0.17 to 0.82 [8]. The Cochrane Review also calculated a post-test probability of unresectable disease of 0.173 (95% CI 0.12 to 0.24), meaning that if a patient is said to have resectable disease after diagnostic laparoscopy, there is a 0.173 probability that their cancer will be unresectable. The difference in the probability that the tumour is unresectable following adequate diagnostic laparoscopy compared with direct laparotomy is therefore 0.403-0.173 = 0.230, meaning that on average using diagnostic laparoscopy prior to laparotomy would avoid 230 unnecessary laparotomies in 1000 patients in whom laparotomy is planned for curative resection of pancreatic cancers [8] and 770 patient would have a laparotomy. The probability of undergoing laparotomy is 1–0.230 = 0.770, and the probability the tumour is unresectable among those who have a laparotomy is 0.173/0.770 = 0.225. Put another way, with direct laparotomy, 403 patients in 1000 would have unresectable disease. With diagnostic laparoscopy 230 of these patients would avoid an unnecessary laparotomy, 770 would have a laparotomy and 770*0.225 = 173 of these would have unresectable disease. The probabilities of complications with laparotomy, of relaparotomy, and of perioperative death were taken from a cohort study of 366 patients with pancreatic cancer [14]. The probability of inadequate laparoscopy was taken from one of the studies included in the Cochrane Review which reported this information [15].

Outcomes

QALYs combine length of life and quality of life, where the latter is measured by utility scores. A utility score of 1 represents full health and a utility of 0 death; negative values represent states worse than death. A review of the NHS Economic Evaluations Database [9] was undertaken using the search terms (pancrea* OR ampullary OR periampullary) AND (QALY) [23 February 2014] to identify studies reporting relevant utility scores. After reviewing the reference lists of the identified studies and removing duplicates, 5 studies containing potentially relevant utility data were identified [16-20]. The utility scores used in the model were from one study [19], selected because values were presented for different points over time, because utility scores for all the health states in the model were included in this study enabling better comparability between values, and the values reported also reflected trends in disease-specific quality of life measures found in other studies [11-13] (Additional file 1). Utility scores were measured at 2 weeks, 3 months and 6 months. QALYs were estimated using the trapezium rule for calculating the area under the curve.

Costs

The cost of diagnostic laparoscopy, including histological examination of tissue obtained at laparoscopy was assumed to be £995 (Additional file 1) [21]. This is the average value of the elective inpatient and day case cost, weighted by the proportion of patients in each group. Surgical resection with and without complications was assumed to cost £12 006 and £7083, respectively [21]. Laparotomy without resection was assumed to cost £5378 with complications and £4487 without complications [21]. The cost of repeat laparotomy was assumed to be £7083 [21].

Measuring cost-effectiveness

Cost-effectiveness was measured using monetary net benefits (MNBs). For each treatment the MNB was calculated as the mean QALYs per patient accruing to that treatment multiplied by decision-makers’ maximum willingness to pay for a QALY (also referred to as the cost-effectiveness threshold, which in the UK is approximately £20 000 to 30 000 per QALY gained [22]), minus the mean cost per patient for the treatment. This approach converts the outcomes from each treatment into monetary terms and then subtracts the costs of each treatment from the monetised benefits, calculating the net benefit of each treatment in monetary terms. MNBs were calculated using the base case parameter values shown in Additional file 1; these are referred to as the deterministic results since they do not depend on chance. The treatment with the highest MNB represents good value for money and is preferred on cost-effectiveness grounds.

Sensitivity analyses

One-way sensitivity analysis was undertaken, varying the probabilities, outcomes and costs one at a time within the ranges listed in Additional file 1. The aim was to identify the threshold value for each parameter, where one exists, where the treatment with the highest MNB changed (e.g., the value at which diagnostic laparoscopy was no longer the most cost-effective option).

We undertook a probabilistic sensitivity analysis (PSA) as recommended by the National Institute for Health and Care Excellence (NICE) [22]. Distributions were assigned to parameters (Additional file 1) to reflect the uncertainty with each parameter value. A random value from the corresponding distribution for each parameter was selected. This generated an estimate of the mean cost and mean QALYs and the MNB associated with each treatment. This was repeated 5000 times and the results for each simulation were noted. The mean costs, QALYs and MNBs for each treatment were calculated from the 5000 simulations; these are referred to as the probabilistic results since they depend on chance. Using the MNBs for each of the 5000 simulations the proportion of times each treatment had the highest MNB was calculated for a range of values for the maximum willingness to pay for a QALY. These were summarised graphically using cost-effectiveness acceptability curves [10].

In the PSA we used beta distributions to model uncertainty in the probabilities and utility scores, and gamma distributions to model uncertainty in costs [23]. In cases where standard errors were required for the PSA and these were not reported in the sources used it was assumed the standard error was equal to the mean [23]. For the probability of unresectable disease with direct laparotomy after CT scanning, the parameter values for the beta distribution were based on the numbers of unresectable and resectable cancers pooled across all studies included in the Cochrane Review. For the post-test probability of unresectable disease the parameter values were calculated from the 95% confidence interval reported in the Cochrane Review. For the utilities the variance was calculated assuming a beta distribution based on 97 observations [19,20]. 95% confidence intervals around the base case values were derived using standard deviations calculated from the 5000 simulations in the PSA.

We undertook a further sensitivity analysis to investigate the cost savings associated with diagnostic laparoscopy. We considered a situation where the laparotomy following diagnostic laparoscopy was scheduled for the same admission as the diagnostic laparoscopy. When the diagnostic laparoscopy indicated the tumour was not resectable, so the laparotomy was not required, the cost of the hospital stay was avoided but the cost of the operating theatre time was not. This was assumed to cost £3524, based on 4 hours of theatre time at £881 per hour [24].

Finally, because of jaundice being a relative early presentation of ampullary cancers, the resectability rate of ampullary cancers are believed to be higher than that of pancreatic cancers [25]. We therefore reran our analyses separately based on studies from the Cochrane Review that included only patients with pancreatic cancer and only patients with periampullary cancer. As shown in the Cochrane Review, for patients with pancreatic cancer the sensitivity of diagnostic laparoscopy was 67.9%, the median pre-test probability of unresectability was 0.400 and the post-test probability of unresectable disease after negative diagnostic laparoscopy was 0.180. One study in the Cochrane Review included only patients with periampullary cancer [15]. In this study of 144 patients the sensitivity of diagnostic laparoscopy was 52.0%, the pre-test probability of unresectability was 0.174 and the post-test probability of unresectable disease after negative diagnostic laparoscopy was 0.092. We reran our models using these two sets of values holding all other values constant.