E. Modeling

Quantitative modeling is used to evaluate the clinical and economic effects of health care interventions. Models are often used to answer “What if?” questions. That is, they are used to represent (or simulate) health care processes or decisions and their impacts under conditions of uncertainty, such as in the absence of actual data or when it is not possible to collect data on all potential conditions, decisions, and outcomes of interest. For example, decision analytic modeling can be used to represent alternative sequences of clinical decisions for a given health problem and their expected health outcomes and cost effectiveness.

The high cost and long duration of large RCTs and other clinical studies also contribute to the interest in developing alternative methods to collect, integrate, and analyze data to answer questions about the impacts of alternative health care interventions. Indeed, some advanced types of modeling are being used to simulate (and substitute in certain ways for) clinical trials.

By making informed adjustments or projections of existing primary data, modeling can help account for patient conditions, treatment effects, and costs that are not present in primary data. This may include adjusting efficacy findings to estimates of effectiveness, and projecting future costs and outcomes.

Among the main types of techniques used in quantitative modeling are decision analysis; state-transition modeling, including Markov modeling (described below) and Monte Carlo simulation; survival and hazard functions; and fuzzy logic. A Monte Carlo simulation uses sampling from random number sequences to assign estimates to parameters with multiple possible values, e.g., certain patient characteristics (Caro 2002; Gazelle 2003; Siebert 2012). Infectious disease modeling is used to understand the spread, incidence, and prevalence of disease, including modeling those that model the impact health care interventions such as immunizations (Bauch 2010) and insect control (Luz 2011).

Decision analysis uses available quantitative estimates to represent (model or simulate) alternative strategies (e.g., of diagnosis and/or treatment) in terms of the probabilities that certain events and outcomes will occur and the values of the outcomes that would result from each strategy (Pauker 1987; Thornton 1992). As described by Rawlins:

Combining evidence derived from a range of study designs is a feature of decision-analytic modelling as well as in the emerging fields of teleoanalysis and patient preference trials. Decision-analytic modelling is at the heart of health economic analysis. It involves synthesising evidence from sources that include RCTs, observational studies, case registries, public health statistics, preference surveys and (at least in the US) insurance claim databases (Rawlins 2008).

Decision models often are shown in the form of "decision trees" with branching steps and outcomes with their associated probabilities and values. Various software programs may be used in designing and conducting decision analyses, accounting for differing complexity of the strategies, extent of sensitivity analysis, and other quantitative factors.

Decision models can be used in different ways. They can be used to predict the distribution of outcomes for patient populations and associated costs of care. They can be used as a tool to support development of clinical practice guidelines for specific health problems. For individual patients, decision models can be used to relate the likelihood of potential outcomes of alternative clinical strategies (such as a decision to undergo a screening test or to select among alternative therapies) or to identify the clinical strategy that has the greatest utility (preference) for a patient. Decision models are also used to set priorities for HTA (Sassi 2003).

Although decision analyses can take different forms, the basic steps of a typical approach are:

1. Develop a model (e.g., a decision tree) that depicts the set of important choices (or decisions) and potential outcomes of these choices. For treatment choices, the outcomes may be health outcomes (health states); for diagnostic choices, the outcomes may be test results (e.g., positive or negative).
2. Assign estimates (based on available literature) of the probabilities (or magnitudes) of each potential outcome given its antecedent choices.
3. Assign estimates of the value of each outcome to reflect its utility or desirability (e.g., using a HRQL measure or QALYs).
4. Calculate the expected value of the outcomes associated with the particular choice(s) leading to those outcomes. This is typically done by multiplying the set of outcome probabilities by the value of each outcome.
5. Identify the choice(s) associated with the greatest expected value. Based on the assumptions of the decision model, this is the most desirable choice, as it provides the highest expected value given the probability and value of its outcomes.
6. Conduct a sensitivity analysis of the model to determine if plausible variations in the estimates of probabilities of outcomes or utilities change the relative desirability of the choices. (Sensitivity analysis is used because the estimates of key variables in the model may be subject to random variation or based on limited data or simply expert conjecture.)

Box IV-4 shows a decision tree for determining the cost of treatment for alternative drug therapies for a given health problem.

Box IV-4. Decision Analysis Model: Cost per Treatment, DrugEx vs. Drug Why

This decision analysis model compares the average cost per treatment of two drugs for a given patient population. The cost of the new DrugWhy is twice that of DrugEx, the current standard of care. However, the probability (Pr) that using DrugWhy will be associated with an adverse health event, with its own costs, is half of the probability of that adverse event associated with using DrugEx. Also, the response rate of patients (i.e., the percentage of patients for whom the drug is effective) for DrugWhy is slightly higher than that of DrugEx. For patients in whom either drug fails, there is a substantial cost of treatment with other interventions. The model assumes that: the drugs are equally effective when patients respond to them; the cost of an adverse effect associated with either drug is the same; and the cost of treating a failure of either drug is the same. For each drug, there are four potential paths of treatment and associated costs, accounting for whether or not there is an adverse effect and whether or not patients respond to the drug. The model calculates an average cost per treatment of using each drug.

A limitation of modeling with decision trees is representing recurrent health states (i.e., complications or stages of a chronic disease that may come and go, such as in multiple sclerosis). In those instances, a preferable alternative approach is to use state-transition modeling (Siebert 2012), such as in the form of Markov modeling, that use probabilities of moving from one state of health to another, including remaining in a given state or returning to it after intervening health states.

A Markov model (or chain) is a way to represent and quantify changes from one state of health to another, such as different stages of disease and death. These changes can result from the natural history of a disease or from use of health technologies. These models are especially useful for representing patient or population experience when the health problem of interest involves risks that are continuous over time, when the timing of health states is important, and when some or all these health states may recur. Markov models assume that each patient is always in one of a set of mutually exclusive and exhaustive health states, with a set of allowable (i.e., non-zero) probabilities of moving from one health state to another, including remaining in the same state. These states might include normal, asymptomatic disease, one or more stages of progressive disease, and death. For example, in cardiovascular disease, these might include normal, unstable angina, myocardial infarction, stroke, cardiovascular death, and death from other causes. Patient utilities and costs also can be assigned to each health state or event. In representing recurring health states, time dependence of the probabilities of moving among health states, and patient utility and costs for those health states, Markov models enable modeling the consequences or impacts of health technologies (Sonnenberg 1993). Box IV-5 shows a Markov chain for transitions among disease states for the natural history of cervical cancer.

Box IV-5. Disease States and Allowed Transitions for the Natural History Component of a Markov Model Used in a Decision Analysis of Cervical Cancer Screening

HPV: human papillomavirus; CIN: cervical intraepithelial neoplasia (grades 1, 2, 3)

Transition probabilities among disease states are not shown here.

Source: Kulasingam SL, Havrilesky L, Ghebre R, Myers ER. Screening for Cervical Cancer: A Decision Analysis for the U.S. Preventive Services Task Force. AHRQ Pub. No. 11-05157-EF-1. Rockville, MD: Agency for Healthcare Research and Quality; May 2011.

High-power computing technology, higher mathematics, and large data systems are being used for simulations of clinical trials and other advanced applications. A prominent example is the Archimedes model, a large-scale simulation system that models human physiology, disease, and health care systems. The Archimedes model uses information about anatomy and physiology; data from clinical trials, observational studies, and retrospective studies; and hundreds of equations. In more than 15 diseases and conditions, it models metabolic pathways, onset and progression of diseases, signs and symptoms of disease, health care tests and treatments, health outcomes, health services utilization, and costs. In diabetes, for example, the Archimedes model has been used to predict the risk of developing diabetes in individuals (Stern 2008), determine the cost-effectiveness of alternative screening strategies to detect new cases of diabetes (Kahn 2010), and simulate clinical trials of treatments for diabetes (Eddy 2003).

One of the challenges of decision analysis is accounting for the varying perspectives of stakeholders in a given decision, including what attributes or criteria (e.g., health benefit, avoidance of adverse events, impact on quality of life, patient copayment) are important to each stakeholder and the relative importance or weight of each attribute. Multi-criteria decision analysis (MCDA) has been applied to HTA (Goetghebeur 2012; Thokala 2012). A form of operations research, MCDA is a group of methods for identifying and comparing the attributes of alternatives (e.g., therapeutic options) from the perspectives of multiple stakeholders. It evaluates these alternatives by ranking, rating, or pairwise comparisons, using such stakeholder elicitation techniques as conjoint analysis and analytic hierarchy process.

Models and their results are only aids to decision making; they are not statements of scientific, clinical, or economic fact. The report of any modeling study should carefully explain and document the assumptions, data sources, techniques, and software. Modelers should make clear that the findings of a model are conditional upon these components. The use of decision modeling in cost-effectiveness analysis in particular has advanced in recent years, with development of checklists and standards for these applications (see, e.g., Gold 1996; Philips 2004; Soto 2002; Weinstein 2003).

Assumptions and estimates of variables used in models should be validated against actual data as such data become available, and the models should be modified accordingly. Modeling should incorporate sensitivity analyses to quantify the conditional relationships between model inputs and outputs.

Various computer software packages are available to conduct decision-analytic and other forms of modeling; examples are Decision Analysis, Excel, and TreeAge; no particular recommendation is offered here.