a cost effectiveness and probabilistic sensitivity analysis of opportunistic screening versus systematic screening for sight threatening diabetic eye disease

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A COST EFFECTIVENESS AND PROBABILISTIC SENSITIVITY ANALYSIS OF OPPORTUNISTIC SCREENING VERSUS SYSTEMATIC

SCREENING FOR SIGHT THREATENING DIABETIC EYE DISEASE

Bryce S Sutton, B.A., M.A

A Dissertation Presented to the Faculty of the Graduate School of Saint Louis University in

Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

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UM! Number: 3102938 ® UMI UMI Microform 3102938

Copyright 2003 by ProQuest Information and Learning Company All rights reserved This microform edition is protected against

unauthorized copying under Title 17, United States Code

ProQuest Information and Learning Company 300 North Zeeb Road

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A COST EFFECTIVENESS AND PROBABILISTIC SENSITIVITY ANALYSIS OF OPPORTUNISTIC SCREENING VERSUS SYSTEMATIC

SCREENING FOR SIGHT THREATENING DIABETIC EYE DISEASE

Bryce S Sutton, B.A., M.A

An Abstract Presented to the Faculty of the Graduate School of Saint Louis University in Partial

Fulfillment of the Requirements for the

Degree of Doctor of Philosophy

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ABSTRACT

According to the American Diabetes Association,

diabetic retinopathy or diabetic eye disease is the leading cause of blindness in the United States To begin to

address the problems associated with the adverse economic impact of diabetes, and in particular diabetes related blindness, a cost effective method of identifying patients for treatment must be determined This study addresses the concerns of health care decision makers from a national health care perspective To inform this decision, a

probabilistic sensitivity analysis and hypothesis test of a screening problem for sight threatening diabetic eye

disease is presented

To provide information of relevance to healthcare decision makers, uncertainty in multiple parameters is

characterized and allowed to vary simultaneously These

parameters affect cost effectiveness calculations of screening for diabetic eye disease and the uncertainty surrounding these parameters is explicitly presented for evaluation

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systematic screening program implemented by a national health service Point estimates from the clinical

literature are used to generate distributions for the probabilistic sensitivity analysis The results of the

sensitivity analysis are then used to test the hypothesis that cost effectiveness of systematic screening for sight threatening diabetic eye disease is significantly different from the cost effectiveness of opportunistic screening for sight threatening diabetic eye disease

To allow for the possibility that healthcare decision makers face differing health care objectives and/or

differing budget constraints, results are presented in the form of acceptability curves showing the probability that

systematic screening is more cost effective for differing

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COMMITTEE IN CHARGE OF CANDICACY: Professor Patrick Welch,

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DEDICATION

This dissertation is dedicated to the memory of

Chester Perry Sutton A man who, despite being robbed of his sight, continued to inspire everyone he touched through his courage and independence

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List of List of Chapter Chapter Chapter Chapter TABLE OF CONTENTS Tables uu , Figures 4 42.+2 I Introduction Ii Itt IV

Review of the Literature The Felli and Hazan Approach The Phelps/Mushlin Model

Claxton’s Decision Making Approach Methodology oo

Disease Background and Review of Cost Effectiveness Research Presentation of the Cost

Effectiveness Data

Sensitivity Analysis in the Screening Study

The Role of Sensitivity Analysis in Cost Effectiveness Models Characterizing Parameter

Uncertainty about Probabilities

Estimation of Costs in the

Simulation `

Characterizing Parameter

Uncertainty About QALYs

Using Quality Adjusted Life Years

{QALYS} ,

The Standard Gamble Method for

QALYS 1 8

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TABLE OF CONTENTS (CONT ) Distributions Used in the

Simulation 4 Descriptive Statistics of Distributions from the Baseline Simulation os Modeling Costs of Systematic

and Opportunistic Screening Calculation of the Incremental

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LIST OF TABLES

Table 2.1: Costs and Utilities Associated

13

with Disease Status and Treatment Status

Table 2.2: Expected Benefits and Expected Costs of Treating and Not Treating Patients Table 2.3: Patients Subgroups, Fallback

Strategies,and Optimal Treatment

Strategies (Cr = $100,000) oe 32 Table 3.1: Baseline values for the Cost

Effectiveness of Opportunistic and

Systematic Screening Programs for Sight Threatening Diabetic Eye - e ~ oe - 55 Disease Cost Effectiveness figures Table 3.2: for Systematic and Opportunistic Screening Programs os we ew 57 Table 3.3: Mean Visual Utility Values in

Patients with Diabetic Retinopathy 79

Table 4.1: Distributions Used in the

Baseline Simulation a 83

Table 4.2: Distributions Representing

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LIST OF FIGURES

Figure 2.1: The Expected Value of

Clinical Information and the Prior Probability of Disease

Figure 3.1: The Cost Effectiveness Plane Figure 3.2: The Standard Gamble for Some

Chronic Health State Preferred to

Death

Figure 4.1: The Frequency Distribution Opportunistic Screening Rate of Compliance ,

Figure 4.2: The Frequency Distribution

Systematic Screening Rate of

Compliance

Figure 4.3: The Frequency Distribution

the Sensitivity of Opportunistic Screening 020+4

Figure 4.4: The Frequency Distribution the Sensitivity of Systematic Screening 4428+4,4 Figure 4.5: The Frequency Distribution

QALYs from Sight Threatening Diabetic Eye Disease

Figure 4.6: The Frequency Distribution

Potential QALYs Gained

Figure 4.7: The Frequency Distribution for the Duration of Disease Figure 4.8: Total Cost of Systematic

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LIST OF FIGURES (CONT.) Figure 4.9: Acceptability Curves for the

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CHAPTER 1: INTRODUCTION

According to the American Diabetes Association, diabetic retinopathy or diabetic eye disease is the leading cause of blindness in the United States Medical and health services related research has determined that the progress of sight threatening diabetic eye disease can be slowed through detection and treatment Early detection of the disease is critical because treatment for sight threatening diabetic eye disease is most effective in the early Stages of the disease[1l] Clinical studies in the United States and elsewhere show that the incidence of

blindness due to the main forms of diabetic eye disease may be dramatically reduced with laser

therapy{2-4]

The economic importance of screening for sight

threatening diabetic eye disease is reinforced by some

astonishing statistics Estimates of the total

economic impact of diabetes are large The estimated

cost of diabetes alone is $14 billion annually while

diabetic blindness alone accounts for $75 million in lost income and public-welfare expense[5] The

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considers the fact that a large percentage of people who have diabetes do not obtain screening exams for diabetic retinopathy regardless of their disease

status[5]

To begin to address the problems associated with the adverse economic impact of diabetes, and in

particular diabetes related blindness, a cost

effective method of identifying patients for treatment must be determined This study addresses the concerns of health care decision makers from a national health care perspective From this perspective the cost effectiveness of screening, identification of disease,

and treatment, must be determined with respect to a

multitude of concurrent competing health care objectives given a national health care budget

constraint To inform this decision, a probabilistic sensitivity analysis and hypothesis test of a

screening problem for sight threatening diabetic eye disease is presented

To provide information of relevance to health care decision makers, uncertainty in multiple parameters is characterized and allowed to vary Simultaneously These parameters affect cost

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eye disease and the uncertainty Surrounding these parameters is explicitly presented for evaluation A hypothesis test is performed to compare the cost

effectiveness of an opportunistic {primary care)

screening program for sight threatening diabetic eye disease to a systematic screening program implemented

by a national health service

For the decision problem, baseline information is gleaned from a study designed to evaluate the cost effectiveness of replacing an existing opportunistic

screening for sight threatening diabetic eye disease

with systematic screening for diabetic patients in the United Kingdom[{6] Point estimates from this study are used to generate distributions fer the

probabilistic sensitivity analysis The results of

the sensitivity analysis are then used to test the

hypothesis that cost effectiveness of systematic screening for sight threatening diabetic eye disease is significantly different from the cost effectiveness of opportunistic screening for sight threatening

diabetic eye disease To allow for the possibility

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curves showing the probability that systematic

screening is more cost effective for differing prices per effectiveness unit relative to Opportunistic

screening

To provide a theoretical framework for the

economic evaluation of diagnostic technologies,

chapter 2 of this study presents a review of the relevant literature The Phelps/Mushlin model

presents a formal theoretical guide in which to

examine competing diagnostic tests{7] This model presents a diagnostic decision problem in which one diagnostic test is compared to a fallback Strategy This model is easily applicable to the present case in

which the fallback strategy is an existing

opportunistic or primary care screening program Next, Claxton’s decision making approach to the stochastic evaluation of health care technologies is presented{8] This approach presents a complimentary

and general approach to statistically test the

incremental cost effectiveness of competing medical interventions In this approach one may adopt a classical/frequentist or Bayesian approach in

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calculated in a classical hypothesis test for

Significant differences in the cost effectiveness of

competing screening strategies for Sight threatening diabetic eye disease Alongside the Phelphs/Mushlin and Claxton models, Felli and Hazan'’s approach to the

evaluation of health care technologies under

conditions of uncertainty is reviewed[9] The Felli

and Hazan approach presents logical extensions of the classical hypothesis test and probabilistic

sensitivity analysis examined in this study

In chapter 3, the methodology of the economic evaluation of competing Strategies for detecting sight threatening diabetic eye disease is presented Here a Clinical background of the disease is discussed in which the primary factors affecting the economic

evaluation are examined An in-depth analysis of the baseline data used in the simulation follows with

discussion and calculation of the baseline incremental cost effectiveness ratios Distributions used in the Monte Carlo simulation are given with a brief

discussion of the roll of probabilistic sensitivity

analysis in health care decision making Finally a

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use of quality adjusted life years (QALYs) is presented

Chapter 4 gives the results of the probabilistic sensitivity analysis, hypothesis test, and

acceptability curves Graphs and parameterization of each distribution are given in chapter 4, with a

discussion of the use of each distribution To perform a hypothesis test, a test statistic

incorporating an explicit monetary valuation of the health outcome is given and the results of the test are presented This study supports the conclusion that systematic screening for sight threatening diabetic eye disease is more cost effective than opportunistic or primary care screening for sight threatening diabetic eye disease This result is

highly significant at the standard benchmark price per effectiveness unit of $50,000 per QALY To examine decision sensitivity and the possibility that decision

makers may have alternative valuations of the health outcome, acceptability curves were constructed for the

baseline simulation and alternative simulations The

acceptability curves for the baseline simulation were

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uncertainty in the duration of disease These curves were also discounted at 0%, 3% and 5% and are

presented in the appendix

In chapter 5, a summary of the Study results is given Chapter 5 concludes with Suggestions for further research Overall the Study suggests that Systematic screening, given the baseline data and characterization of parameter uncertainty, should be implemented as the most cost effective method to screen for sight threatening diabetic eye disease for countries with similar disease prevalence, compliance

rates, and patient cohort characteristics These

results are insensitive to changes in the price per effectiveness unit for values far away from the benchmark value of $50,000 per QALY These results also suggest that different training among primary care physicians, specialists, and other medical personnel, leads to large differences in diagnostic

sensitivity These sensitivity differentials complicate the accurate evaluation of any

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CHAPTER 1: REFERENCES

Sculpher, M.J., et al., A Relative Cost-

Effectiveness Analysis of Different Methods of Screening for Diabetic Retinopathy Diabetic Medicine, 1991 8: p 644-650

Diabetic Retinopathy Study Research Group, Photocoagulation Treatment of Proliferative

Diabetic Retinopathy: Clinical Application of the

Diabetic Retinopathy (DRS) Findings - DRS Report

Number 8 Ophthalmology, 1981 88: p 583-600

Early Treatment Diabetic Retinopathy Study Research Group, Photocoagulation for Diabetic Macular Edema: Early Treatment Diabetic

Retinopathy Study Report Number 1 Archives of Opthalmology, 1985 103: p 1796-1806

Early Treatment Diabetic Retinopathy Study Research Group, Early Photocoagulation for Diabetic Retinopathy: ETDRS Report Number 9

Ophthalmology, 1991 98(Supplement): p 766-785

Lairson, D.R., et al., Cost-Effectiveness of Alternative Methods for Diabetic Retinopathy Screening Diabetes Care, 1992 15: p 1369-1377 James, M., et al., Cost Effectiveness Analysis of Screening for Sight Threatening Diabetic Eye

Disease British Medical Journal, 2000 320: p

1627-1633

Phelps, C.E and A.I Mushlin, Focusing

Technology Assessment Using Medical Decision

Theory Medical Decision Making, 1988 8: p 279- 289

Claxton, K., The Irrelevance of Inference: A

Decision-Making Approach to the Stochastic

Evaluation of Health Care Technologies Journal

of Health Economics, 1999 18: p 341-364

Felli, J.C and G.B Hazan, Sensitivity Analysis and the Expected Value of Perfect Information

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CHAPTER 2: REVIEW OF THE LITERATURE

According to Briggs, probabilistic analysis is still not common in health economic evaluation

1iterature[l1, 2] In a study from 1996, only 7 out of

492 studies reviewed contained any probabilistic

analysis, and of the 7, only 2 included discount rates in their probabilistic analysis{3}

Probabilistic sensitivity analysis describes a method in which all uncertainties (probabilities,

costs, utilities) are considered Simultaneously Each

uncertain parameter in a probabilistic sensitivity analysis is assumed to possess a probability

distribution representing the possible values an input parameter may obtain[4] Multiple simulations of the decision problem are run in which each input parameter in the decision problem is randomly assigned a value from its respective distribution

The simulation output contains the mean and

standard deviation for each input parameter and/or any desired statistic over all iterations of the

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Studies suggests that probabilistic sensitivity analysis is still not widely understood

Probabilistic sensitivity analysis is an

essential method in assessing uncertainty inherent in any decision problem While Simple sensitivity

analysis, threshold analysis, and analysis of

extremes, all provide methods for evaluating

uncertainty, probabilistic analysis is well suited in facilitating natural extensions of Bayesian decision- making analysis Acceptability curves anda full Bayesian decision-making approach can be adopted readily once a probabilistic sensitivity analysis has been completed

A current problem in medical decision-making

models is distinguishing between value sensitivity and

decision sensitivity[5] Value sensitivity refers to sensitivity of a model's outcome measure such as a cost~-utility measure, cost-benefit measure, or cost effectiveness measure Whenever an outcome measure Fluctuates dramatically in response to changes in input parameters, the outcome measure is defined as being "sensitive" to changes in those input

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changes in input parameters It is quite possible for medical decision-making models to have @ high degree of value sensitivity while at the same time having little or no decision sensitivity or vice versa[5] For example, during a Sensitivity analysis an

incremental cost effectiveness ratio (ICER) may fluctuate considerably when input parameters are changed but the sign of the ICER does not change This indicates the ICER is value sensitive but not decision sensitive For an ICER to be decision

sensitive, the sign of the ICER must change This

indicates that the optimal action, adopt treatment 1 Or treatment 2 for example, has changed It is argued here that decision uncertainty is the relevant

uncertainty and sensitivity analysis should

effectively address this risk in the decision-making problem

Felli et al have demonstrated that sensitivity analysis (SA) methods based on threshold proximity and

entropy can substantially overestimate sensitivity[5] Threshold proximity measures use an established

threshold value to address decision sensitivity When a measure approaches or crosses the established

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likely to lead to a change in the Optimal alternative This type of analysis becomes difficult as the number of input parameters increases and the effect of

Simultaneous variation in input parameters cannot be

considered as in one- and two-way SA[5] Likewise,

arbitrary definitions of what is the appropriate

threshold, as well as what is an appropriate distance

metric, lead to arbitrary determination of what may or

may not be “sensitive"{6, 7]

Entropy based measures, such as the mutual information index, provide yet another method to assess decision sensitivity[5, 8-10] The mutual

information index represents the information gained

about a distribution B conditioned on a specific value A= a An increase in the index indicates that A

contains information about B, while a small increase indicates A contains little information about B

Critchfield and Willard normalize fas by using the

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I

(2.2) lng = > Py oes}

# P,

The mutual information index for the Optimal action B influenced by the parameter A normalized by the self- information of B is given by[10]:

(2.3) Sự, = «100%,

8

Critchfield and Willard indicate that a mutual

information index could serve as a proxy for decision sensitivity to the parameter A because the magnitude

of Ss3 indicates the degree to which the parameter A

explains the variability in the action B[5, 10]

However, once again, the question arises as to what

constitutes “sensitivity"™ As Felli and Hazan point out concerning mutual information index figures,

“while it is true that the problem is 'more sensitive’ to these parameters than to others, it is not clear

what this means" [5] Additionally, the constructicn of the index and the difficulty in calculating

conditional probability distributions make the use of

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information, toward the value of information to reduce uncertainty

The Felli and Hazan Approach

Felli and Hazan conceptually present the expected value of perfect information (EVPI) as the average improvement in a payoff a decision-maker could expect to receive from perfect information relative to the

payoff associated with the actual decision[5] In any

decision the primary problem facing the decision-maker is the choice of action given parameter uncertainty Following Felli and Hazan we can consider a problem with several possible actions and a4 Single uncertain parameter, 5 The decision-maker seeks to maximize his

or her expected payoff, IF, given the value of most likely to obtain, say đo The decision maker seeks to

choose the action ag among all possible alternatives

such that:

(2.4) EL, |¢ =o) = max, EŒ, lý =ếa)

Whenever we base a decision upon our best estimate of

the uncertain parameter ¢, we face some risk that our estimate is wrong Thus given our estimate of é, the

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payoff Felli and Hazan express this difference

as[5]:

Average Forgone Payoff = E, [max ECV, | 2) — Ef Mis) | = EVPI(Z)

(2.5)

Here the EVPI represents the difference between payoff # from perfect knowledge about parameter uncertainty

prior to the time of decision and the payoff received from the chosen action ag This measure of decision sensitivity provides information not only on parameter

uncertainty, which has the greatest chance of causing a change in the base-optimal action, but also about marginal improvements in payoffs that could be

obtained from reduction in parameter uncertainty{5] Further the EVPI can be expressed in the same units as payoffs in the decision problem, whether they be in effectiveness units, QALYs, or monetary units

Felli and Hazan provide two possible Monte Carlo

Simulation procedures to calculate the EVPI The

procedures are broadly applicable as independence, and

Linearity of parameters is not necessarily required to

calculate the EVPI Again, following Felli and Hazan,

we consider a decision problem which has a payoff /, and depends upon a set of parameters é and an

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EVPI for a set of parameters ¢; = (ớ,Ìl¡ei with the

remaining set of parameters in the problem denoted ¢/

The EVPI for the parameters of interest cr becomes:

EVPHG,)= E, AES 67 a(S )- EW 1S) 57 ‹a*)

(2.6)

= Ee er {Improvement using a *(¢, ) instead of a*]

where:

a* = base optimal action

a*(¢,) = optimal action as a function of ¢,

The suggested Monte Carlo simulation procedure amounts to generating random parameter values for the set of

interest, $,; For every generated set ¢;, the optimal action as a function of that set a*(¢; }), is

determined Then the improvement obtained from using

a*(cr } as opposed to a* is determined The average of

cal

all improvement values gives the estimated EVPI (¢;) The idea of valuing perfect information about a

decision is not new[11-14] However the application of the expected value of perfect information applied

to medical decision making is new Phelphs and

Mushlin provided the general framework utilizing value

of information analysis in a formal model by

considering a simple treat/no treat decision tree for

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The Phelps/Mushlin Model

The Phelps/Mushlin model is a decision analytic

model designed to assess diagnostic technologies [15] The authors consider a simple decision tree in which a diagnostic technology is employed to determine the course of treatment The model simplifies the

possible actions by considering only two alternatives, to either treat or to not treat based on the

diagnostic information The value of the diagnostic technology is compared to a preferred fallback

Strategy, in this case to not treat a patient The

model is instructive in presenting a pragmatic medical

decision problem

When new medical technology is introduced it must be compared to existing technology in current medical use An important question when faced with the task of medical technology evaluation is how to determine what research is necessary to adequately inform the

decision By introducing the concept of the expected

value of imperfect diagnostic information, a cut-off

is established which can eliminate certain types of costly medical research [15]

Certain types of medical research must be

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efficacy of medical technology in that technology's ideal use These types of trials ignore the costs of less than ideal use of these technologies across

heterogeneous populations with varying degrees of

disease prevalence [15] Therefore a model which

evaluates medical technology in the less than ideal

state can provide a more accurate assessment of the

technology's cost effectiveness in actual use The model effectively demonstrates the importance of disease prevalence in the assessment of a diagnostic technology's cost effectiveness

The Phelps and Mushlin model considers several prior probabilities and patient states The

clinician's prior probability of disease and wellness

is given by:

m = prior probability that the patient has disease

(prevalence)

{1 ~ m) = prior probability that the patient does not have disease (well)

To characterize the capability of the diagnostic technology we specify the probabilities of true and false diagnoses as:

p = probability of a true positive given the

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(1 - p) = probability of false negative given the patient has disease

q = probability of a false positive given the patient is well

(1 -~ 4ì) = probability of a true negative given the

patient is well (specificity)

Two possible actions are allowed in the model either to treat (tf) or to not treat (n) The costs and

benefits (utilities) of each patient health state are

denoted as C,;, and £;; respectively The subscripts i

and j indicate health status and treatment choice

respectively Thus, the cost associated with a

diseased patient who is receiving treatment would be denoted Cre, while the utility associated with a

patient who is well and not receiving treatment would be denoted by E,y, The costs and utilities associated with all possible states are given by table 2.1[15]

Table 2.1: Costs and Utilities Associated with

Disease Status and Treatment Status Costs Utilities

Came ¡ COSt of sick patient, Emer | Utility of sick

treated patient, treated

Can | cost of sick patient, Emn | Utility of sick

not treated patient, not treated Cwr | cost of well patient, | Ey | utility of well

treated patient, treated

Cun | cost of well patient, Eyn | utility of well

not treated patient, not treated

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Phelps and Mushlin assume that treating sick people and not treating well people provides more benefit than not treating sick people and treating well people

Or: Ene > Eve and Ey, > Eng The fundamental assumption

in decision analysis is that a decision should be based on maximizing expected benefit or utility

Therefore a decision about whether or not to treat a

patient with a prior probability (m) of disease

depends upon expected benefit of treating and not treating patients weighted by the prevalence of disease (m) The expected utility and costs of

treating and not treating patients are given in table

2.2115]

Table 2.2: Expected Benefits and Expected Costs of

Treating and Not Treating Patients m-E,, +(l-m)-E,, Expected benefit of treatment m-E,, +(l-m)-E,, Expected benefit of not treating

m-C,, +(l-m)-C,, Expected cost of treatment

m Ca + (Ì— HC Expected cost of not

treating

Expressing expected benefit in incremental terms from

treating patients versus not treating patients we obtain[{15]:

[m-E,,, +(l-—m)-E,, ]-[m- E,,, +Œ —m)-E „| (2.7)

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where:

AE, = Ent Em

AE, = Ey, ~ Ey,

Similarly, for incremental costs of treating versus

not treating we obtain{15}: [mt -Cy, + -m)-C,, ]-[m-c,, +d—m)-C,, ] (2.8) ` =m-AC, —(l-—m)- AC, where: AC, = Coy — Com AC, = —C

Given we seek to compare the cost effectiveness of treatment versus no treatment, equation (2.8) becomes the numerator in the incremental cost effectiveness

ratio (ICER) while equation (2.7) becomes the

denominator in the ICER A decision-maker is faced

with the problem of comparing the net benefit of

treatment versus no treatment to the net benefit

forgone of expanding the next best "marginal" activity [15] If we let the cost effectiveness of the next

best activity be denoted as 1 / g=$ / Quality

Adjusted Life Year (QALY), then the decision maker must compare the inverse of the ICER of treatment versus no treatment to g or[1i5]:

(2.9) m AE, ~ (=m) AE, vơ

m-AC, —(l-m)- Ac,

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If equation (2.9) is true then the expected benefits

and costs of treating all patients as opposed to not treating exceeds the critical "target" or "ceiling" effectiveness cost ratio The "target" or "ceiling" effectiveness cost ratio is the required effectiveness per unit cost necessary for a diagnostic test or

treatment to be considered "effective" given a medical decision-maker's budget constraint Therefore it is cost effective to undertake treatment for all

patients Once we incorporate g we can express

equation (2.3) in terms of net benefit (conditional on g) or[15]:

(2.10) m-(AE,, ~ gAC,,)>(l-m)-(AE, -g-AC,)

Equation (2.10) illustrates the critical role of both disease prevalence (m) and the ceiling cost

effectiveness ratio (g) Uncertainty about disease prevalence and disagreement on an appropriate level of

g complicate the determination of the optimal course of action As Phelps and Mushlin point out,

"sensitivity analysis across values of g will prove important in many settings."[{15]

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[15] Thus, there is a critical prior probability of disease that leaves a decision-maker indifferent

between treating and not treating Solving equation {2.10) for disease prevalence we obtain[1i5]:

(AE, ~g-AC,)

(2.11) m, =

(AE, ~ g- AC.) +(AE, ~ gAC„)

If the prior probability of disease m is greater than

the critical disease prevalence m,, treatment becomes the optimal action; otherwise the fallback strategy of

no treatment becomes optimal A prior probability of disease close to the critical disease prevalence

indicates substantial uncertainty about the optimal

course of action When the value of information is

assessed, uncertainty about disease prevalence can have a dramatic effect on the expected value of information of diagnostic tests

To begin to assess the value of diagnostic

information the sensitivity and specificity of the

diagnostic test in question must be introduced The

Phelps/Mushlin model determines the value of a

diagnostic test by determining the expected value of

clinical information (EVCI){15] The choice of

whether to use an imperfect diagnostic test depends

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The EVCI for a test depends upon the fallback

Strategy If the fallback Strategy is to not treat patients then an imperfect diagnostic test should be used whenever EVCI yr > gCr, Or the expected gain in clinical information exceeds the re~scaled costs of the test based on g- Evaluation of the value of a diagnostic test relative to a fallback strategy is necessary because in some extreme cases for this example it may make sense to treat all or treat none based on the prior probability of disease m For example, if the prior probability of disease m is quite low, very few patients in the relevant

population have disease This lessens the benefit of Screening programs of all patients In this case it may be cost-effective, conditional upon g, to wait for patients to become Symptomatic before treatment rather

than screen for disease Again, this decision must be

contingent upon a monetary valuation of the health Outcome g If a societal perspective is taken then g may be interpreted as the marginal willingness to pay for a health outcome improvement where the budget

constraint is endogenous (16, 17]

To calculate the EVCI, the sensitivity of an

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imperfect diagnostic test g must be applied to the expected benefits and expected costs of the diagnostic

test If the fallback strategy is to not treat,

expected benefits are[15]:

(2.12)

m-(p- E„ +(1—p)- Eqn) + —m\(l—4)- Eun + 9° Eq, |—[mt- Eng + —m)E., | =m: p- AE, —(l—-m)-q-AE,

The first term on the left-hand side of (2.12) gives the expected benefit of treating true positives and not treating false negatives The second term on the

left-hand side of (2.12) gives the expected benefit of

not treating true negatives and treating false

positives The third term on the left-hand side of

(2.12) subtracts off the benefit of the fallback strategy to not treat everyone Therefore the left- hand side of equation (2.12) can be interpreted as the

net benefit of treatment based on the imperfect diagnostic test less the opportunity cost of not treating all patients The right hand side of (2.12) gives the expected utility in incremental terms

Incorporating g to re-scale costs the EVCI is the

expected incremental benefit less the expected incremental cost or[{15]:

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Equation (2.13) indicates the functional relationship between the value of clinical information for an

imperfect diagnostic test and the test's sensitivity, specificity, and the prior probability of disease or prevalence Given our fallback strategy is to not treat everyone, the choice about whether or not to adopt this diagnostic technology depends on the

correct identification of positives The first term in the right hand side of equation (2.13) is the net

gain from identifying true positives while the second term on the right hand side of (2.13) is the net loss of false positives An assumption of the

Phelps/Mushlin model is that the correct

identification of negatives outweighs the cost of

false negatives Therefore when all patients are not

treated we need only consider the potential gain from

true positives and net losses from false positives to inform the adoption decision

We can see the relationship between disease

prevalence and the EVCI by taking the derivative of EVCIne with respect to m or{15]:

dEVCI

2.14