presentation to: may 22, 2012 by harry j. smolen, president and ceo medical decision modeling inc....

presentation to:

May 22, 2012by Harry J. Smolen, President and CEOMedical Decision Modeling Inc.Indianapolis, IN, USA

2012 Midwest Biopharmaceutical Statistics Workshop

Discussion Agenda

General background on pharmacoeconomic (PE) models

Types of models commonly used in healthcare technology assessment

Methods for selecting modeling method

Cost-effectiveness analysis - Overview

General PE Modeling Background

What is a model?

A model is a hypothetical description of a system


Why not experiment with the actual system?

If it is possible to experiment with the actual system, do it!

However, especially in healthcare, it is frequently too expensive, too disruptive, too slow, and/or unethical to experiment with the actual system


Example “experiment”: How many life years would be saved if every other person in the US >65 years had a one-time colonoscopy, with polypectomy and surveillance every three to five years for positive findings?

Expensive – (1/2) x 40.3M persons x $1,714 ≈$34,537,100,000 + follow-up costs

Disruptive – a day of inconvenience per patient for prep and exam; also disruption to gastroenterologists, is there enough capacity?

Slow – Many years to get results Possibly Unethical – though uncommon,

perforations occur (≈0.9/1000 colonoscopies) with unknown benefit to patients

Computational vs. Physical Models

When most people think of models they envision physical models, e.g., clay cars in wind tunnels or life-size layouts of an emergency room for workflow analysis

The types of models used to evaluate the effectiveness and cost-effectiveness of healthcare technologies are computational models

Computational models represent a system in terms of logical and quantitative relationships that are manipulated to examine how the model reacts, and thus how the system would react if the model is valid1

1. Law and Kelton, Simulation Modeling and Analysis, 2nd edition, 1991.

Simulation vs. Analytical Solution

A simple computational model:d = rt, where

d = distance traveledr = rate of travelt = time spent traveling

In this simple model it is possible to get an exact, analytical solution

This equation may apply to a single car on a test track, but …

Is of little use to determining distance traveled on a busy highway with varying speeds and levels of congestion

Simulation vs. Analytical SolutionIn this simple d = rt model it is possible to get an exact,

analytical solution Some analytical solutions can become extraordinarily

complex, e.g., inverting a non-sparse matrix, and require substantial computing power

If an analytical solution to a computational model is available and computationally efficient, study the model in this manner

However, many systems are highly complex so that valid computational models of them are themselves complex, precluding the possibility of an analytical solution

Such models must be analyzed by simulation, i.e., numerically varying the relevant model inputs to determine how they affect the output measures of interest1

1. Law and Kelton, Simulation Modeling and Analysis, 2nd edition, 1991.

Evidence from RCTs

Evidence from randomized controlled trials (RCTs) remain the highest-quality data source for evaluating the efficacy of health care interventions

However, evidence from RCTs alone can be uninformative if the RCT endpoints are not translated into measures that are valued by patients, providers, insurers, and policy makers1

1. Weinstein MC, et al. Value Health. 2003 Jan-Feb;6(1):9-17.

Evidence from RCTs

For example, in patients with osteoporosis, fracture risk evolves over a lifetime from the development of peak bone mass to subsequent bone loss and the age-related increase in the likelihood of falling, among other factors1

It may takes decades to determine the effects of osteoporosis interventions

Hence, the most informative osteoporosis intervention RCTs would potentially last for decades2

1. NIH Osteoporosis Prevention, Diagnosis and Therapy Consensus Statement 2000.

2. Vanness DJ. Osteoporos Int. 2005 Apr;16(4):353-8.

Evidence from RCTs

A similar situation exists for many other chronic diseases such as diabetes, colorectal and prostate cancer, and Alzheimer's disease

The lengthy clinical trials needed to properly evaluate interventions for these chronic diseases would require financial and time opportunity costs that would make them infeasible1

1. Vanness DJ. Osteoporos Int. 2005 Apr;16(4):353-8.

Evidence from RCTs

Very few epidemiological studies or clinical trials are able to measure disease progression and the impact of interventions on costs, quality of life, and health outcomes over a lifetime1

In the absence of such information, the most practical method to evaluate the health outcomes and costs of interventions is to develop models that integrate relevant data and extrapolate to long-term time horizons

1. Brändle M, et al. Curr Med Res Opin. 2004 Aug;20 Suppl 1:S1-3.

Evidence from Models vs. RCTs

Models that evaluate health care interventions synthesize evidence on health consequences and costs from many different sources, including data from clinical trials, observational studies, insurance claim databases, case registries, public health statistics, and preference surveys1


Evidence from Models vs. RCTs

Even when the disease does not require a long-term evaluation period, models can prove valuable by: Using results from indirect comparisons of

individual RCTs to compare treatments not studied head-to-head and estimate outcomes not consistently measured

Allowing the extrapolation of effects to populations not studied in a particular RCT

Allowing sensitivity analysis of assumptions addressing treatment efficacy, health state utilities, costs, etc.


Decision Model Defined

A decision model is a structured representation of a decision process that allows a person to perform a decision analysis

“… decision analysis is just the systematic articulation of common sense: Any decent doctor [decision maker] reflects on alternatives, is aware of uncertainties, modifies judgments on the basis of accumulated evidence, balances risks of various kinds, considers the potential consequences of his or her diagnoses and treatments, and synthesizes all of this in making a reasoned decision that he or she decrees right for the patient. All that decision analysis is asking the doctor [decision maker] to do is to do this a lot more systematically and in such a way that others can see what is going on and can contribute to the decision process.” 1

1. Raiffa H. Clinical Decision Analysis. Philadelphia:WB Saunders; 1980: ix-x.

Types of Modeling Methods

Types of modeling methods frequently used in health technology assessment:

Decision trees Markov

Cohort Monte Carlo

Microsimulation Fixed-time advance Discrete-event, Time-to-event (without and with

queuing for resources) Agent-based

Decision Trees

A decision tree is a diagrammatic representation of the possible outcomes and events used in decision analysis

The questions to be asked in an analysis of a question are arranged as a series of decision or chance nodes, each node with resulting branches, creating a tree effect

The sequential steps proceed with each step depending on the decision or probability outcome from the preceding step1

1. http://medical-dictionary.thefreedictionary.com/decision+tree

Decision Tree Example

Simple tree fragment modeling complications of anticoagulant therapy1

1. Sonnenberg FA, et al. Med Decis Making. 1993 Oct-Dec;13(4):322-38.

Decision Tree Components

Simple tree decision trees embody the essential paradigm of decision analysis. Specifically, all decisions may be decomposed into three broadly-defined components:

1. Decision node – point in time when a choice is made among competing strategies

2. Decision strategy – set of actions or events consequent to a decision

3. Outcome nodes – terminal branches of tree that represent outcomes of a strategy.1

Multiple outcomes (payoffs) may be assigned.

1. Stahl JE. Pharmacoeconomics. 2008;26(2):131-48.

Calculating Expected Value of a Decision Tree

The expected value of a decision tree is calculated by “averaging out” or “folding back the branches of the tree

The value(s) of each strategy is path probability to the terminal node multiplied by the payoff(s) at the terminal node

Branching probabilities can be deterministic represented by point values (e.g., 0.6) or stochastic represented by probability distributions (e.g., normal, exponential)

Uncertainty around branching probabilities and terminal node values is examined with sensitivity analysis1


Advantages of Decision Trees

Graphical – can diagrammatically represent decision alternatives, chance events, and possible outcomes; visual approach assists with comprehending decision sequences and dependencies

Efficient - can quickly express complex alternatives clearly, and easily modify as new information becomes available

Complementary – can use in conjunction with other methodologies, e.g., append recursive methods to terminal nodes1

1. Olivas R. http://www.stylusandslate.com/decision_trees/download/files/decision-tree_v5_1b.pdf

Disadvantages of Decision Trees

Must assume population being examined can be modeled in the aggregate; if being applied to an individual, assumption is made that aggregate probabilities are relevant to the individual1

Does not specify when events occur Assumes that each event can occur only

once Can address previous two disadvantages with a

recursive tree (see next slide)2



Recursive Decision Tree1


Previous terminal nodes of POST-BLEED, POST-EMBOLUS, AND NO EVENT are replaced by the chance node ANTICOAG which appears at the root of the tree

Note that with only two time periods, there are 17 terminal nodes; five periods would have hundreds of branches

Markov Models

Described as “partially cyclic directed graphs”

Particularly useful when a decision problem involves: exposure to risks or events over time ongoing exposures or situations where the

specific timing of an event is regarded as important or uncertain

or where describing the timing of events is necessary for face validity1


Markov Models

Assumes that the patient is always in one of a finite number of health states called Markov states

All events of interest are modeled as transitions

Each state is assigned a utility (and possibly a cost) and the contribution of this utility depends on the length of time in the state1


Markov Models

Common representation of a simple Markov process called a state-transition diagram

Each state represented by a circle

Arrows connecting different states indicate allowed transitions

States with arrows to itself indicate that patient may remain in that state in consecutive cycles

Note no transition from “DISABLED” to “WELL”, nor “DEAD” to any other state

Markov Models – Time Cycles

Time horizon of the analysis divided into equal increments of time called Markov cycles

Assumed that a patient can only make a single state transition during a cycle

Length of cycle chosen to represent a clinically meaningful time interval If time horizon is patient lifetime,

then cycle is usually one year If events occur more frequently,

cycle can be a month or even a week1


Markov Models – Incremental Utility

Evaluation of a Markov process yields the average amount of time spent in each state, patient is “given credit” for time spent in each state (e.g., life years)

Optionally, each state can be associated with a numerical factor representing the quality of life in that state relative to perfect health (e.g., WELL=1.0, DISABLED=0.7, DEAD=0.0)

Utility associated with spending one cycle in a particular state is referred to as the incremental utility1


Markov Models – Costs

Analogous to utilities assigned to particular states, a cost may be specified for each state representing the financial cost of residing in that state for one cycle

Markov Models – Types of

Markov processes are categorized by whether or not state-transition probabilities are constant over time

For example, transition probability from WELL to DEAD may consist of two components:

Probability of dying unrelated to disease in question – changes over time as patient gets older

Probability from disease (e.g., fatal hemorrhage or embolus during cycle) may or may not be constant over time1


Markov Models – Transition Probabilities

For a Markov model of n states, there will be n2

transition probabilities When these probabilities are constant with respect

to time (Markov chains) they can be represented by n x n matrix1


Markov Models – Types of

Most Markov models used in health care are semi-Markov

Unlike Markov chains, in semi-Markov models state transitions may be allowed to vary or be time-variant and usually need to be solved numerically via simulation1


Markov Models – The Markov Property

In Markov processes, the behavior of the process subsequent to any cycle depends only on its description in that cycle, i.e., the process has no memory for earlier cycles

Because of this assumption, the prognosis of a patient cannot depend on events prior to arriving in that state1

For example, patient is WELL after recovering from an osteoporotic forearm fracture

Though WELL, the probability of future fracture is likely higher than for patients in WELL without history of fracture

Build additional states to accurately represent these patients?


Markov Model-Decision Tree Combination1


Markov process used to represent all processes

Markov Cohort Simulation1


In the table above, column 5, sum of number of patients in each state is multiplied by the incremental utility of that state

First row does not contribute to sums

Patients will spend on average 1.5 cycles in the WELL state and 1.25 in the DISABLED state, for a net unadjusted life expectancy of 2.75 cycles

Markov Monte Carlo Simulation1


As an alternative to cohort simulation, analysis performed by individually simulating large numbers of individual patients (e.g., 104)

At the end of each cycle, a random number generator is used together with transition probabilities to determine to which state the patient will transition

Outputs from a large number of individual patients will constitute a distribution of survival values, the mean of which should be similar to expected utility of cohort simulation

Variance measures can also be determined from Monte Carlo simulations

Discounting Utilities and Costs

Costs and benefits occurring immediately are valued more highly than in the future

Discounting formula:

Ut = U0 / (1 + d)t

where

Ut is the incremental utility at time t

U0 is the initial incremental utility

d is discount rate Analogous discounting is done for costs

Advantage of Markov Models

Primary advantage over decision trees is the increased face validity by capturing extended time horizons via Markov cycles1,2



Disadvantages of Markov Models

State transitions can only occur at the start/middle/end (whichever is determined) of a cycle, creating potential biases

Cycle time may force simplifying assumptions regarding transition probabilities1


Microsimulations

In microsimulations, patients are simulated as individuals (as opposed to homogenous cohorts) and represented by software objects called entities

One of the primary advantages of microsimulations is that the patient entities can be assigned attributes and the occurrence and timing of patient events can be determined from these attributes

Microsimulations Microsimulations have the ability to ascribe a

potentially vast number of combinations of characteristics to individually simulated patients

An individual’s health state is defined by its combination of characteristics, not by its assignment among limited pre-defined health states as in Markov cohort simulations

Eliminates the need for excessive number of defined health states, as patient transitions to subsequent health states are dependent upon patient characteristics, not just their current health state

Microsimulations, Types of

Fixed-time advance Patients can only transition to

different health states at fixed time intervals defined by the cycle length

Time-to-event The occurrence (yes/no) and timing of an

event is determined by random sampling of a probability distribution

Microsimulations, Types of Discrete-event simulation (DES)1

Entities (patients) may interact or compete with each other for system resources (e.g., physicians, hospital beds, etc.)

Key elements of DES are entities, attributes, resources, and queues

When a resource is not available for an entity, the entity is relegated to a queue until a resource is available

Agent-based simulations1

Independent multi-agent DES Agent entities contain information about their

state and decision rules on how to communicate and interact with other agents


Choosing Most Appropriate Modeling Method1

Criteria to be evaluated: Project Type Population Resolution Interdependencies/Feedback Treatment of Time Treatment of Space Resource Constraints Autonomy/Freedom of Action of

Entities/Populations Embedding of Knowledge Availability of Evidential Data



Project Type Model to be used to answer a single

question? KISS, model should only be complex enough to answer the single question

Model to be used programmatically (i.e., long term)? Methods that can handle more complexity usually required

Population Resolution In aggregate? Most simulation methods

can handle Individual level? Microsimulation required



Interdependencies/Feedback Are entity interdependencies important,

e.g., an infectious epidemic involving exposed, unexposed, infected groups? DES or agent-based simulations required

Treatment of Time If time treated cumulatively or

instantaneously, then trees can be used If changes over time are important, e.g.,

time of therapy, surveillance interval, then Markov or microsimulations needed



Treatment of Space Is location important to the study

question, e.g., optimal distribution of mental health professionals in a state, then microsimulations or agent-based simulations needed

Resource Constraints If it is important to model limited

resources and waiting lists, then DES or agent-based simulations required



Autonomy/Freedom of Action of Entities/Populations Are all potential paths through the model

predefined, e.g., idealized RCT? Are absorbing states required, e.g., Markovs? Are multiple paths open to the populations being

modeled?, then DES or agent-based simulations Embedding of Knowledge Treatment of

Space Is the knowledge embedded in the structure of

the model, e.g., decision trees, Markovs? Or is the knowledge embedded in the entities,

e.g., microsimulations?


Algorithm for Choosing a Simulation Method1

CRC = colorectal cancer; AAA = abdominal aortic aneurysm

1. Pickhardt PJ, et al. AJR Am J Roentgenol. 2009 May;192(5):1332-40.

DEEPP = Describe, Evaluate, Explore, Predict, and Persuade; DES = discrete event simulation; KISS – keep it simple stupid


Cost-Effectiveness Analysis (CEA)

CEA is a form of analysis that compares the relative costs and outcomes of competing courses of action

Central measure used in CEA is the cost-effectiveness (CE) ratio

Implicit in the CE ratio is a comparison between alternatives

The CE ratio for comparing these alternatives is the difference in their costs divided by the difference in their effectiveness:

CE ratio = (costA - costB) / (effectivenessA - effectivenessB)


The CE ratio is essentially the incremental cost of obtaining a unit of health effect

Health effects (captured in the CE ratio denominator) can be intermediate (e.g., changes in A1c or bone mineral density) or long term (e.g., lives saved, life years gained, or quality-adjusted life years [QALYS])

QALYS are the most comprehensive outcome measure in CEA in that it incorporates both quality of life and survival information1

1. Gold et al. Cost-effectiveness in health and medicine. Oxford University Press. 1996


CE ratios expressed as “cost per QALY gained” provide a standardization which allows comparisons of incremental value across different outcomes in a particular disease or across different diseases altogether different outcomes in a particular disease: e.g.,

diabetes – comparing value in preventing renal failure vs. lower extremity amputation

different diseases – e.g., stroke outcomes to schizophrenia outcomes

CE Plane1

1. Black WC. Med Decis Making. 1990 Jul-Sep;10(3):212-4.

CE Plane1

1. Black WC. Med Decis Making. 1990 Jul-Sep;10(3):212-4.

Quadrant IV: e>0, c<0, dominant (cost-saving)

Quadrant II: e<0, c>0, dominated

Contact Info

Harry J. SmolenMedical Decision Modeling Inc.8909 Purdue Road, Suite #550Indianapolis, IN [email protected](317) 704-3800 office(317) 716-6650 mobile

presentation to: may 22, 2012 by harry j. smolen, president and ceo medical decision modeling inc....

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