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ORAL ABSTRACTS: QUANTITATIVE METHODS II

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**Purpose:**Cost-effectiveness models increasingly use a modelling approach called partitioned survival analysis. The appropriateness of this approach has been subject to little critique. The purpose of this work is to describe and critique the partitioned survival analysis approach as a decision modelling tool and to provide formal recommendations to assist different stakeholders in determining it’s appropriateness as a modelling approach and basis for informing policy decisions.

**Method(s): ** We reviewed the 30 most recent technology appraisals of cancer treatments published by NICE (covering the period May 2013-February 2016). Manufacturer submissions and reports by academic Evidence Review Groups/Assessment Groups were reviewed to establish the way and contexts in which the method is being used, its key assumptions and the prevalence and relative merits of alternative methods.

**Result(s): ** The use of partitioned survival analysis was highly prevalent and used in 23 out of 30 appraisals. The method was generally incorrectly described and its assumptions rarely documented or justified. Critical appraisal of the method identified a central assumption of independence of clinical events. This assumption has implications for the reliability of extrapolations and in particular extrapolation of overall survival, modelling of decision uncertainty and transparency with respect to mechanisms underpinning model predictions. The most common alternative approach was the (semi-) Markov model which was typically used when overall survival data were immature and/or to reflect subsequent lines of therapy. The (semi-) Markov models frequently included an assumption that extensions to time to intermediate endpoints (e.g. progression-free survival) translated directly to extensions to overall survival. These assumptions are not necessitated by the (semi-) Markov modelling approach and should be subject to scrutiny. Appropriately designed (semi-) Markov models may offer advantages over partitioned survival approaches by allowing information on intermediate endpoints to inform survival predictions, providing greater transparency on the mechanisms underpinning these predictions and by accurately reflecting endpoint correlations. They may, however, struggle to incorporate external data such as treatment effects from indirect comparisons or long-term observational data on mortality rates.

**Conclusion(s): ** More consideration should be given to the selection and justification of alternative modelling approaches. Choice of modelling approach is likely to be most important for the extrapolation period. Assumptions underpinning extrapolations should be subject to greater scrutiny and where possible informed by empirical data.

**Purpose:**CUSUM plots monitoring quality of treatment are not readily applicable to cancer case series with prolonged follow-up. We describe a Bayesian technique for timely detection of inferior results based on observed survival times.

**Method(s): ** Kaplan-Meier 5-year survival curves for children with acute lymphoblastic leukemia treated on the ongoing Nordic 2008 protocol are available, showing “healthy” standard of treatment. The curves are divided in 3-month intervals, and the risk of event (hazard) in each interval calculated from the survival curves. A “sick” hazard function is specified by multiplying the failure:success ratio in each interval by 1.5, and a hypothetical Kaplan-Meier curve for poor treatment constructed by sequentially multiplying the probabilities of surviving each interval without event. For each patient the likelihood ratio of the observed survival time is determined: for event free cases the ratio of survival probabilities on the two curves, for cases with event the same ratio multiplied with the hazard ratio in the time interval. Using Bayes theorem, considering each case a test of good treatment quality, diagnostic odds are calculated by multiplying prior odds sequentially with the likelihood ratios. The accumulated weight of evidence in favour of or against good performance is determined by adding up log to base 2 of the likelihood ratios.

**Result(s): **We have included 35 children on the ongoing protocol; 9 have completed 5-year follow-up and can be considered cured, 2 have had events during follow-up, and 24 are still at risk with survival times 8-59 months. A Kaplan-Meier estimate of 5-year event free survival for all risk groups combined is 90.7%. Using the Bayesian approach, the weight of evidence in favor of good treatment quality is 1.43, corresponding – if prior odds are fifty:fifty – to odds 2 to the power of 1.43 = 2.70 to 1, i.e. probability 73%. Displaying the accumulation of evidence in a CUSUM plot for the sequential case mix reveals a very good run of the first 14 patients accounting for most of the favourable evidence.

**Conclusion(s): **The quality of treatment in small patient series with unfinished follow-up can be assessed from the observed survival times, permitting monitoring of results in a risk-adjusted CUSUM plot and detection of temporal changes that are not apparent in Kaplan-Meier curves or Cox proportional hazard models.

**Purpose:**

The aim of this study is to explore the impact of different methods for modelling multiple endpoints from survival data on health economics’ modelling.

**Method(s): **

Two methods for modelling multiple clinical endpoints from survival data are studied. If these events are combined, assuming that they are completely dependent, then modelling them as a composite endpoint (CEP) is an approach. Alternatively, considering the events as competing risks when modelling the survival data, accounting for the possible interdependence, does not require restrictive assumptions with respect to the interrelation between these events. There are underlying assumptions in each method about the interaction between these endpoints.

The study’s central research component is a comparison of these approaches, together with how these would be applied in a decision model and how this can affect the final outcome. The cost effectiveness analysis, using a simple Markov model, is used as a case study. Using R software, the inversion method is performed to simulate data for two competing events from Weibull distribution and then conducting survival analysis to examine these various outcomes.

Cumulative incidence function, derived from the related survivor functions, obtained from the different approaches of modelling the events, was the platform to estimate the transition probabilities. These were the inputs of the Markov cost-effectiveness model, from which the net benefits, generated from the natural disease history, were the main outcome to assess the divergences between the methods.

**Result(s): **

When the events have a constant rate with time, exponentially distributed (a special case of Weibull), the CEP method does not affect the outcome. In the case, where events’ hazards vary with time at the same rate, the estimates obtained from the CEP method are very close to those that the competing risks method generates. However, the situation becomes more challenging if the events have different rates at which they occur. If the events’ rates have two opposite directions, the implications for the decision model that has used the survival modelling outcomes become compounded.

**Conclusion(s): **

The method used for modelling multiple endpoints from survival data can have an impact on the outcome of health economic evaluation that used the transition probabilities derived from these survival data.

** Purpose: ** Little is known about the maximum
achievable life expectancy given a population's unique characteristics, which
is important for estimating actionable population health metrics. Our objective
is to address the question: Given the current state of health science and
technology, what is the difference in the potential life expectancy gain that
could be achieved in the United States and Norway in the idealized scenario where
modifiable risk factors were eliminated and adherence to evidence-based
therapies was perfect.

** Method(s): ** We developed a Monte Carlo
microsimulation model of 19 conditions representing the top causes of mortality
in each age decile and the 28 risk factors associated with their onset that had
consistent directions of effect as well as clinical and statistical
significance. Each month individuals can develop new risk factors and/or new
conditions, have existing risk factors or conditions resolve (e.g. through
treatment), or die. We simulated a birth cohort of one million patients with
characteristics resembling the population of the United States and Norway. We
then compared current health with an idealized scenario where all modifiable
risk factors were eliminated and adherence to evidence-based therapies was
perfect.

** Result(s): ** We estimated that the maximum life
expectancy in the United States would be 84.7 years (a potential increase of 5.9
years) in the idealized scenario. The life expectancy for Norway would be 85.4
years (a potential increase of 3.9 years). Limitations include only capturing
mortality through mortality causing conditions and therefore missing mortality
acting through alternative pathways.

** Conclusion(s): ** With a highest achievable life
expectancy of 84.7 years, an increase of 5.9 years above current life
expectancy (78.8 years), the United States has a greater potential for
improvement than Norway, which has a highest achievable life expectancy of 85.4
years, an increase of 3.9 years above current life expectancy (81.5 years). The
use of mathematical simulations can estimate the maximum achievable life
expectancy in a population and compare the differences in the potential of health
improvement between populations in order to better inform efforts to improve
population health. Through statistically-, rather than projection-based life
expectancy predictions, the use of mathematical modelling holds the potential
to improve the validity of health measures frequently used in health policy
decision making.

**Purpose:**To provide a complete assessment of the cost-effective treatment pathway for patients with hepatitis C virus (HCV) infection with advanced fibrosis.

**Method(s): **

We include three important features of the decision problem ignored in previous economic evaluations internationally. (1) Retreatment if patients do not achieve cure, by comparing all licensed drugs in sequences of one to three lines. (2) Inclusion of watchful waiting followed by treatment at cirrhosis as a relevant comparator. (3) Allowing patients to be treated at more severe disease stages for patients who do not achieve cure with the initial treatment sequence.

We developed a decision-analytic Markov model to estimate lifetime costs and health benefits of all comparators and compared treatment strategies in subgroups defined by viral genotype, prior treatment experience and interferon eligibility. Value of information analysis explored in which patient subgroups it would be most useful to conduct future research. Additionally, we have prepared a tool to recalculate the cost-effective strategies for a given set of prices and thresholds since some health care systems have negotiated discounts.

**Result(s): **

In contrast to previous analyses, and given the current list prices, eligible patients with genotypes 2-4 should be initially offered peginterferon with ribavirin rather than the newer drugs. First-line treatment with sofosbuvir-ledipasvir over 8 weeks is cost-effective in HCV genotype 1 patients. The cost-effective strategies all include multiple lines of therapy prior to cirrhosis (where available), resulting in cure rates of 89%-98% across HCV genotypes. Future research is most valuable in HCV genotypes 3 and 4, with an upper bound of £3 million. The tool can help clinicians and health care systems locally and worldwide decide on the cost-effective strategy given their local context and prices.

**Conclusion(s): **

Health systems should invest in sequential therapy with multiple lines to treat HCV patients with advanced fibrosis. Although current guidance permits first line treatment with the new drugs, we concluded that their use should mostly be reserved to patients who do not achieve cure from first line treatment with peginterferon. This work demonstrates that excluding sequential therapy as a relevant comparator will bias results and ultimately have a detrimental impact to population health. The tool shows how complex economic modelling can be made accessible and adaptable to policy-makers and clinicians needs.