* Candidate for the Lee B. Lusted Student Prize Competition
Purpose: Markov models as used in health care economic evaluation normally involve cycle times that are large enough that the issue of timing errors is potentially relevant. It has become standard practice to use half-cycle correction as a means of addressing this issue. This paper questions this practice.
Method: Logical argument and simulation modeling of examples.
Result: The case is made for treating costs and accumulated quality-adjusted life years (QALYs) differently in calculations from Markov models. It is shown that half-cycle correction is often conceptually unjustified in the calculation of cost differences between two treatment options. For QALYs, the following theorem applies: THEOREM: Suppose that a Markov model is used to compare two decision options and (a) the initial probability distribution among Markov states is the same for both options; (b) the quality of life scores for each Markov state are the same for both options; (c) the discount factor applied to each quality of life score is calculated only in terms of the modeled time at which that quality of life score is calculated. Then half-cycle correction will give exactly the same result for the estimated lifetime difference in quality adjusted life years as methods which count the whole of a cycle according to the probability distribution either at the beginning or at the end of the cycle. PROOF: The only difference between the methods is the time by which the initial quality of life difference is multiplied. Since the initial quality of life difference is zero, by conditions (a) and (b), the difference between the methods is also zero. In cases where it is appropriate to make an assumption that costs or QALYs are accumulated continuously in time, it is shown that a method based on Simpson's rule allows increased cycle lengths and hence considerable reduction in overall computational effort with no loss of accuracy.
Conclusion: Half-cycle correction should not be regarded as a standard tool in the analysis of Markov models.
Purpose: Rapid modeling, simulation, and optimization of resource allocation to an annual cohort of incident cancer patients, considering all clinically relevant chemotherapy choices to achieve the maximum overall survival in life years gained (LYG), for patients in each cancer site and stage.
Method: Orpheus is a software tool that uses operations research techniques (linear programming) to optimize the selection of health care resources by maximizing the total LYG, for a cohort of new cancer patients who are candidates for chemotherapy. Data from the Cancer Care Ontario program for evidence based care are the number of new patients with each cancer (e.g., colon, lung, and breast), and the overall survival (OS) for each alternative chemotherapy regimen, drug costs, staff requirements for treatment delivery, and costs per patient per year. Additional data from the literature regarding specific clinical trials are expected survival in life months and incremental survival benefits between drug regimens for each cancer site and stage.
Results: The total cohort is 7,800 colon, 7,000 lung, and 8,100 breast patients in Ontario based on 2007 incidence data. The cohort includes both adjuvant and metastatic patients. The increase in costs is disproportionate to the increase in benefits. Changes in human resources availability such as full-time equivalent (FTE) Oncologists, Nurses, Pharmacists, Daily Clinic chairs (DCC)) and number of beds, affect drug selection, other resource requirements, and outcomes. In order to treat all patients, the minimum mix of resources required is: Drug Budget $51M ($ CDN), 57 FTE Oncologists, 79 FTE Nurses, 33 FTE Pharmacists, 95 DCC, for a total cost of $135 M. This achieves a benefit of 34,464 LYG, 82.5% of the maximum possible OS. Alternatively, in order to achieve 100% of the maximum possible OS benefit (41,778 LYG), the following mix of resources is required: Drug Budget: $672 M, FTE Oncologists: 57 FTE Oncologists, 113 FTE Nurses, 61 FTE Pharmacists, 299 DCC, for a total cost of $856 M. The incremental benefit is 7,314 LYG; incremental cost per LYG is $98,578, and increase in total cost is $721 M. Marginal benefits decline as funding level increases, showing diminishing returns to additional resources.
Conclusion: The results have strong implications for policy makers and health service researchers interested in the best use of health care resources.
Purpose: Compared to white women, African-American women have had a higher breast cancer mortality rate despite the lower incidence rate for almost thirty years now, and this disparity continues to grow. The objective of this study is to evaluate differences in the natural history of breast cancer between African-American and white women using the University of Wisconsin Breast Cancer Simulation Model (UWBCS), a previously validated discrete-event, stochastic simulation model of breast cancer epidemiology in the U.S. female population from 1975 to 2000 developed by our research team as part of Cancer Intervention and Surveillance Modeling Network (CISNET).
Method: We used an acceptance sampling process for model calibration. Specifically, we determined biologically plausible ranges for each input parameter and ran the UWBCS for all possible input combinations for white and African-American women separately. From each run's output, we calculated age-adjusted incidence rates for each breast cancer stage and compared them with age-adjusted incidence rates calculated based on stage-specific incidence rates as reported in the SEER database. We selected input vectors that generated incidence rates sufficiently close to the observed ones. The calibrated input parameters included Onset Proportion (the ratio of assumed age-specific biologic onset rate to age-specific incidence rate in the absence of screening), Mean Gamma and Var Gamma (simulated tumors grow according to Gompertz-type function with growth rate for individual tumors having a gamma distribution with mean Mean Gamma and variance Var Gamma expressed in months), Percent 4 Nodes and Percent 5 Nodes (percentage of tumors classified as regional and distant at onset, respectively).
Result: Onset Proportion was 0.88 for African-American and 0.80 for white women. Mean Gamma and Var Gamma were 0.13 and 0.025 for African-American vs. 0.10 and 0.008 for white women, respectively. Percent 4 Nodes and Percent 5 Nodes were 0.02 and 0.04 for African-American vs. 0.01 and 0.02 for white females, respectively.
Conclusion: Our results suggest that breast cancer tumors in African-American women have higher growth rates, higher variation in growth rates and may be more likely to become fatal than those occurring in white women. This raises the question whether the screening guidelines should be adjusted to accommodate those differences in natural history of breast cancer between white and African-American women.
Purpose: Decision makers require evidence on cost-effectiveness when making decisions to reimburse any particular health technology. There may be a great deal of uncertainty with cost and effectiveness data, hence health economic evaluations should also investigate whether collecting additional information may reduce this uncertainty. Value of Information (VoI) methods seek to quantify the existing level of uncertainty in terms of the expected net benefit associated with obtaining perfect information on all model parameters. VoI can be computed using Monte Carlo methods which involve a large number of model evaluations. Practical problems lie in the computational requirements of performing VoI analysis for structurally complex models with large number of factors. This paper demonstrates a new methodological framework for expected value of information analysis from complex health economics models.
Method: Linear regression (LR) and Gaussian process (GP) metamodels have recently been used in a number of cost effectiveness studies but both have limitations. LR assumes linearity which severely limits its applicability while the available software for GP restricts the number of model input parameters to 30. This work-in-progress study introduces a framework, which involves running a factor screening method, based on statistical experimental design approach, to role out unimportant factors from the simulation and then developing a new non-parametric function approximation method, called artificial neural network (ANN) as a simulation metamodel. The framework was explored previously by the first-author in a non-health economics application, which does not require any specific input-output functional relationship and can handle any number of input parameters. The paper illustrates the method through an EVPI analysis from a case study of Total Hip Replacement and reports on the preliminary results.
Result: The factor screening method was able to detect 12 important factors, out of 31, from the Total Hip Replacement model. Using 12 important factors, an ANN simulation metamodel was developed to predict per patient EVPI. The estimated per patient EVPI was then compared with those calculated from the linear regression and Gaussian process metamodels. From preliminary results, an ANN metamodel has showed better predictive capability than its LR and GP counterparts in EVPI analysis.
Conclusion: An ANN metamodel, along with a factor screening method, has a great potential in VoI analysis from a large and complex health economic model.
Purpose: Markov models are widely employed in cost-effectiveness analyses of healthcare interventions. Although nearly all of the models are formulated in discrete time, continuous-time Markov (CTM) models, which evaluate time as a continuous variable and allow transitions to occur at any instance, offer more realistic representation of most medical problems. Wide application of CTM modeling for medical decision making is hampered by theoretical and computational complexities.
Method: We reviewed methods from continuous-time stochastic process literature and implemented time-dependency and cohort methods to continuous-time modeling for this purpose. We considered several real and hypothetical examples, and demonstrated the similarities and differences between CTM and discrete-time Markov (DTM) analytically and numerically. One example was a simple survival model of individuals with constant annual mortality rate. We also applied CTM models to a published cost-effectiveness analysis.
Result: As an approximation of the continuous phenomenon of death, the DTM model always underestimates life-expectancy. For instance, if the cycle length of the DTM model is one year and annual mortality rate is 0.1, the DTM model underestimates life expectancy by almost half a year. Use of 'work-around-methods' such as half-cycle correction or trapezoidal rule improves, but does not eliminate, the approximation. Although the incremental cost per quality-adjusted life year (QALY) calculated from the published study can be close for DTM and CTM models, discrepancies in QALY and costs were often large.
Conclusion: The choice of DTM chain with a long cycle length can lead to misleading conclusions. It is often more natural and accurate to formulate medical problems in continuous time and model them using a CTM. The feasibility of this approach was established.