Category Reference | |||
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BEC | Behavioral Economics | ESP | Applied Health Economics, Services, and Policy Research |

DEC | Decision Psychology and Shared Decision Making | MET | Quantitative Methods and Theoretical Developments |

* Candidate for the Lee B. Lusted Student Prize Competition

**Purpose: **Population contact networks, such as sexual and drug injection networks, play an important role in the dynamics of Human Immunodeficiency Virus (HIV) and hepatitis C virus (HCV) transmission. We built a complex network model that includes heterosexual, homosexual men, and drug injection networks to provide better understanding of the dynamics of HIV and HCV transmission. This network model facilitates the forecast of HIV and HCV epidemic growth, and thus enhances the accuracy of future cost-effectiveness analyses for HIV and HCV.

**Method: **By combining multi-agent systems and complex networks, we developed a complex agent network model that accommodates differential selectivity, behavior, and network properties to explain the HIV and HCV epidemic. In our model, agents represent individuals who can have interactions with other individuals. We simulated the entire Canadian population, stratified by age groups, sex, sexual orientation, and immigrant status. Each individual has his/her own injection and sexual behavior. Drug injection behavior was characterized by the injection frequency, and the rate of sharing injecting equipment. Sexual behavior was characterized by sexual activity rate, condom usage rate, the number of sexual partners, and the type of partnership (casual or regular). Heterosexual networks, homosexual men networks, and injection networks were created to describe the contact patterns between individual. We estimated parameters from literature-derived estimates of Canadian demographic, epidemiological, sexual and injection behavior data. Historical Canadian HIV and HCV data were used for validation.

**Result: **The simulated number of new HIV and HCV infections were compared with the historical reported cases in Canada. Our initial results showed a similar trend to the reported cases in Canada. In the next 10 years, our model projected that a total of 41,900 individuals would be newly infected with HIV, of whom 30.8% were infected through the heterosexual contact, 59.2% through homosexual contact, and 10.0% through sharing of injection drug paraphernalia. The model also projected that 85,300 individuals would be newly infected with HCV through the drug injection network in the next 10 years.

**Conclusion: **Our network model showed good calibration between historical Canadian HIV and HCV data and the simulation results. This complex network model reflects dynamics of HIV and HCV transmission, which enables forecasting of the epidemiology of HIV and HCV for policy-level decision making in Canada.

**Purpose: **Cost-effectiveness analyses (CEA) may use RCTs to maximise internal validity. However, when RCTs include patients and centres atypical of those in routine clinical practice, CEA results may be subject to sample selection bias. To reduce this bias, observational data can be used to reweight the trial-based estimates. We present an approach to assess the assumptions behind any reweighting strategy, illustrated with a case study of high policy-relevance.

**Method: **We decompose sample selection bias into observable or unobservable differences between the RCT and the setting of interest. We consider alternative ways of reweighting the RCT estimates, to the population’s characteristics. The first estimation strategy, reweights according to Inverse Probability of Treatment Weighting (IPW), where ‘treatment’ is inclusion in the RCT. The second strategy uses maximum entropy (MaxEnt) weighting along with matching. Either approach makes the identifying assumption that selection into the RCT is conditional on observable characteristics. We consider this critical underlying assumption with novel placebo tests. These test the non-equivalence of reweighted outcomes following treatment in the RCT, versus outcomes after treatment in the population. Passing these tests implies that the identifying assumption holds, and there is sufficient power to detect outcome differences across settings. We consider this approach in a UK CEA of Pulmonary Artery Catherization (PAC) using an RCT (n=1,014), and observational data on PAC use in routine practice (n=1,000). Across both settings, 40 baseline covariates were identically recorded. Differences across settings were reported, for example in the proportion admitted to non-teaching hospitals (RCT: 80%; population: 60%). We used IPW and MaxEnt to reweight the RCT estimates. We report cost-effectiveness overall, and for subgroups defined *a priori.*

**Result: **The overall incremental net benefit (INB) of PAC from the RCT was -£7,900 (95% CI from -£18,500 to £2,600), the corresponding estimates reweighted for the general population were, -£10,000 (-18,500 to -£2000) [IPW] and £1,500 (-£6,700 to £9,900) [MaxEnt]. For non-teaching hospitals, the INBs were £900 (-£12,100 to £14,000) [RCT], £200 (-£9,900 to £10,300) [IPW] and £18,800 (£8,400 to £29,200) [MaxEnt]. IPW failed placebo tests both overall and for the non-teaching hospital subgroup, whereas MaxEnt passed the corresponding tests.

**Conclusion: **This approach can help maximise the external validity of RCT-based CEA. The placebo tests presented are useful for choosing amongst competing weighting strategies.

**Purpose: ** To show how continuous-time Markov and semi-Markov models can be analyzed without simulation, based on matrix algebra and stochastic process methods.

**Method: ** Markov and semi-Markov decision models are widely used for cost-effectiveness analysis in health-economic evaluation. These models are often evaluated in discrete time using cohort analysis or in continuous time using microsimulation. However, both approaches have limitations. Cohort analysis is based on the assumption that at most 1 event can occur per cycle and requires ad-hoc methods to avoid biased cost-effectiveness estimates. Microsimulation introduces simulation error and can be computationally intensive, especially when used for model calibration and probabilistic sensitivity analysis. We use matrix algebra and stochastic process methods to derive analytical solutions for continuous-time Markov models. We also show how semi-Markov models can be approximated by Markov models, so that semi-Markov models can also be analyzed without microsimulation.

**Result: ** Using Kolmogorov’s differential equations, we find analytical solutions for the expected distribution of patients over the health states in Markov chain models, and the expected time spent in each state. These mathematical results enable us to analytically calculate the expected costs and health effects of continuous-time Markov chain models. This method can be interpreted as a continuous-time version of the fundamental matrix solution. This method can also be used to account for age-specific transition rates and discounting, which was not possible using the original fundamental matrix solution. Finally, we show how the concept of tunnel states can be generalized so that semi-Markov models (i.e., with any type of sojourn time distribution) can be approximated by Markov models with any degree of accuracy. Computational tests confirm that this approach is feasible; it is possible to compute the costs and health effects in continuous-time Markov models with hundreds of states within a few seconds.

**Conclusion: ** Continuous-time Markov and semi-Markov models are a versatile tool for estimating the health and economic effects of medical interventions. Currently, these models are almost always evaluated using microsimulation. However, analytical solution methods exist and can easily be implemented. Analytical solutions can simplify the optimization methods used for model calibration and can reduce the computation time needed for probabilistic sensitivity analyses.

** Purpose: ** The widely used formula

*â*1-(1-

_{i }=*p*)

_{i}

^{s}*for converting a probability*

^{/t}*p*over time interval

_{i}*t*into a transition probability

*â*for a Markov model with cycle length

_{i}*s*ignores competing risks. We demonstrate anomalies with this approach and derive formulas that take into account the dynamics of competing risks and compute the bias resulting from using the traditional approach in a liver disease Markov model.

** Methods: ** The three-state model with competing risks consists of patients starting at decompensated-cirrhosis (DeCirr), and moving to either hepatocellular carcinoma (HCC) or "Death"—competing risk (Figure 1). Using the relationship between the transition probability and rate matrices, we derived formulas to convert

*t-*interval probabilities into transition probabilities for the model with a fixed cycle length

*s*. Setting

*s*= 1/52.18 (1 week) and

*t*=1 (1 year), and assuming specific values for inputs (Figure 1a), we estimated the cumulative incidence of HCC and "Death", total discounted (at an annual rate of 0.03) cost and quality-adjusted life years (QALYs) using the corrected formula and the traditional approach.

** Results: ** The formulas for converting

*t-*interval probabilities into cycle-length

*s*transition probabilities are shown in Figure 1b. The "uncorrected" approach gave

*â*

_{1}=0.0013,

*â*

_{2}=0.0029, and

*â*

_{3}=0.0106, whereas the "corrected" approach yielded

*ã*

_{1}=0.0019,

*ã*

_{2}=0.0025, and

*ã*

_{3}=0.0106. The

*n*-step (

*n*=52.18) transition probability matrix (TPM) of weekly cycle-length did not yield back the original annual TPM with the "uncorrected" approach. The estimated total cost using the "uncorrected" and "corrected" approach were $45,870 and $53,594, respectively (bias= – 17%), and QALYs were 2.69 and 2.68, respectively (bias=1%) (Table 1).

** Conclusions: ** The traditional approach of converting interval probabilities into different cycle lengths ignores competing risk states and results in biased estimates of disease outcomes, cost and QALYs, which can lead to different conclusions. Our method accounts for competing risk and can be generalized to other Markov model structures.

**Purpose: ** To test the practical impact of replacing half-cycle correction with Simpson’s method in Markov models of cost-effectiveness.

**Method: ** Markov models are frequently used in cost-effectiveness modeling, particularly when modeling chronic diseases. In Markov models, time is handled as a series of discrete cycles, where events of interest are counted either at the beginning or end of each cycle. In real life, these events can occur at any time within each cycle, hence, this is best represented as a continuous probability function. This means we are actually interested in the integral of a continuous function even though events are counted either at the start or end of the cycles. Uncorrected, Markov models systematically overestimate (events at cycle start) or underestimate (events at cycle end) event frequency. The most common adjustment in health economic modeling is half-cycle correction; shifting cycle estimates by half a period. While this method reduces model bias, it has been criticized both at the SMDM meeting in 2009, and in an MDM paper for being a poor approximation to the integration problem. Opponents to half-cycle correction suggest using Simpson’s method, an old mathematical approximation to estimating the integral of a continuous line represented by discrete points. We have used three recently developed health economic models to test whether replacing half-cycle correction with Simpson’s method makes a practical difference. All models are Markov models with several events and health states modeling cost-utility in a lifetime perspective. We ran the three models for a number of different scenarios and interventions.

**Result: ** Results varied from -17.2% to 0.19% in terms of incremental costs for Simpson’s method compared to half-cycle correction. In terms of differences in quality-adjusted life-years, results varied between -0.75% and 0.67%. Differences in net health benefit varied between -0.06% and 0.21%, while differences in incremental net health benefit varied between -1.56% and 12.7%. INHB did not change from positive to negative or vice versa in any comparisons.

**Conclusion: ** In our analyses, cost differences varied substantially between half-cycle correction and Simpson’s method. In terms of quality-adjusted life-years, differences were small in our models. Conclusions did not change in any of our analyses, however changes in incremental net health benefit was not negligible, suggesting that conclusions could be altered under specific circumstances.

**Purpose: **To demonstrate the impact and utility of accounting for technology diffusion and uncertainty in calculating the affected population for value of information analysis through a case study in advanced biliary tract cancer.

**Method: **We modified a previously published decision-analytic model to estimate the expected value of perfect information (EVPI) for two treatment strategies in advanced biliary tract cancer: 1) gemcitabine and cisplatin 2) standard care, with all patients receiving gemcitabine alone. The model utilized standard methods to calculate the per-patient EVPI, but incorporated a stochastic method for calculating the population EVPI, representing the uncertainty in the estimated technology lifetime, disease incidence, and technology diffusion rate. Model parameters and uncertainty ranges were derived from the ABC-02 Trial, published literature, and government sources. We used SEER incidence estimates, a 5 to 15% annual diffusion rate, a 5 to 15-year range for technology use, and a willingness-to-pay threshold of $150,000/QALY. We compared three population EVPI estimates, 1) instant technology diffusion (base-case), 2) gradual deterministic diffusion, and 3) gradual diffusion with uncertainty in affected population parameters.

**Result: **The gemcitabine+cisplatin strategy produced greater net-benefit than standard care in 89% of simulations and the average consequence of selecting the wrong strategy was $7,900. In the base case, the population EVPI for an affected population of 67,000 over a 10-year horizon was $58.2 M. Incorporating a gradual deterministic rate of diffusion changed the estimate to $29.6 M. Finally, incorporating uncertainty provided a credible interval to the population EVPI ($29.6 M; CI: $11.1 to $48.8 M).

**Conclusion: **This case study demonstrates the potential impact and utility of incorporating a stochastic method for calculating the affected population in value of research analyses relative to the current deterministic standard and its assumptions regarding technology diffusion. This approach builds on standard methods by representing real world uncertainty about the technology lifetime, incidence estimates, and rate of technology diffusion. This approach may be particularly useful when different study designs may lead to different rates of technology diffusion or when there is substantial variation in annual incidence estimates over the lifetime of the technology (e.g. when changing screening/diagnostic practices may lead to variable disease incidence). These methods can also be applied to other value of information analyses (e.g. value of sample information), and can increase the informational yield of such estimations.