A generalized health economic and outcomes research model for the evaluation of companion diagnostics and targeted therapies

Abstract

Aims: To present a generalized model to evaluate health and economic outcomes of targeted drug therapies and associated companion diagnostic tests with two applications. Method: An analytical model and derivatives applied to a nonlinear equation representing the costs and benefits of targeted therapy and associated companion diagnostics is developed. Economic analysis is then applied to a breast and colorectal cancer application with a multiparameter sensitivity analysis. Results: The generalized model readily facilitates trade-off analysis between, for example, alternative diagnostic test strategy cost and performance, and accounts for alternative therapy costs and benefits. Example applications demonstrate test performance and therapy costs and benefits are generally more critical parameters relative to diagnostic test cost. Conclusion: While obtaining accurate data on therapy cost and benefits, test performance remains a key challenge in these analyses, the model presents key trade-offs and priorities for research to obtain more accurate clinical and economic information.

Keywords::

• companion diagnostic testing
• cost–benefit analysis
• cost–effectiveness analysis
• targeted cancer therapy

Financial & competing interests disclosure

All of the authors served as paid consultants, through Altarum Institute, to Abbott Molecular in 2011 and 2012. The methods, analysis, results and manuscript were prepared without external financial support and were under the sole control of the authors. The authors have no other relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript apart from those disclosed.

No writing assistance was utilized in the production of this manuscript.

Appendix 1. Developing the generalized companion diagnostic cost–benefit equation and derivatives.

This appendix presents the derivation of the generalized companion diagnostic cost–benefit equation using the symbols presented in Table 2 and probabilities shown in Table 1. The benefit components for true and false positives are presented first for both when the primary test is equivocal and not equivocal and then summed. As previously stated in the ‘Methods’ section, there are no incremental benefits and costs for false- and true-negative outcomes as the benefits and costs of true and false positives are measured relative to the standard of care provided to true-negative patients. The cost components are then presented for both equivocal and nonequivocal results of the primary test. The net benefit, benefits minus cost, is then computed for each of the four outcomes by subtracting their respective cost equation from their benefit equation. The four components are then added. The derivative of net benefit with respect to each model parameter is then computed and presented for all 15 model parameters (Table 2).

Benefits

True Positive, Non-Equivocal: Pr*Se*Bt*$v*(1-Pq)

True Positive, Equivocal: Pr*Se*Bt*$v*Pq

False Positive, Non-Equivocal: (1-Pr)*(1-Sp)*Bf*$v*(1-Pq)

False Positive, Equivocal: (1-Pr)*(1-Sp)*Bf*$v*Pq

Sum: Pr*Se*Bt*$v+(1-Pr)*(1-Sp)*Bf*$v

Costs

True Positive, Non-Equivocal: Pr*Se*(1-Pq)*[$p+Mt*$t]

True Positive, Equivocal: Pr*Se*Pq*[($p+$r)+Mt*$t]

False Positive, Non-Equivocal: (1-Pr)*(1-Sp)*(1-Pq)*($p+Mf*$t)

False Positive, Equivocal: (1-Pr)*(1-Sp)*Pq*($p+$r+Mf*$t)

True Negative, Non-Equivocal: (1-Pr)*(Sp)*(1-Pq)*$p

True Negative, Equivocal: (1-Pr)*(Sp)*Pq*($p+$r)

False Negative, Non-Equivocal: Pr*(1-Se)*(1-Pq)*$p

False Negative, Equivocal: Pr*(1-Se)*Pq*($p+$r)

Biopsy Cost: Pb*$b

Sum: Pr*Se*($p+Pq*$r+Mt*$t)+(1-Pr)*(1-Sp)*($p+Mf*$t+$Pq*r)+(1-Pr)*(Sp)*($p+Pq*$r)+Pr*(1-Se)*($p+Pq*$r)+Pb*$b

The net benefit for each of the four possible outcomes is presented below by aggregating the equivocal and nonequivocal equations and then subtracting the respective cost equation from the benefit equation. Note that biopsy cost and probability is addressed separately versus repeating in each equation.

Net cost/benefit for each outcome (with biopsy cost addressed separately)

True Positive Sum: Pr*Se*[Bt*$v-($p+Pq*$r+Mt*$t)]

False Positive Sum: (1-Pr)*(1-Sp)*[Bf*$v-($p+Mf*$t+$Pq*r)]

True Negative Sum: (1-Pr)*(Sp)*[0-($p+Pq*$r)]

False Negative Sum: Pr*(1-Se)*[0-($p+Pq*$r)]

Cost of Biopsy: -Pb*$b

Sum: Pr*Se*[Bt*$v-($p+Pq*$r+Mt*$t)]+(1-Pr)*(1-Sp)*[Bf*$v-($p+Mf*$t+$Pq*r)]+(1-Pr)*(Sp)* [0-($p+Pq*$r)]+Pr*(1-Se)*[0-($p+Pq*$r)]-Pb*$b

Each of the derivatives of the net cost/benefit, abbreviated Δ$c, are presented below. These are interpreted as the incremental change in the net benefit given an incremental change in the parameter of interest. For example, using the equation (1) below regarding the sensitivity, a 5% increase in test sensitivity has a net benefit of Pr*(Bt*$v – Mt*$t) x 0.05 × 100.

(1)	Sensitivity (Δ$c/ΔSe) – the impact of an incremental change in sensitivity of test strategy: = Pr*[Bt*$v-($p+Pq*$r+Mt*$t)]-Pr*[0-($p+Pq*$r)] which reduces to = Pr*(Bt*$v - Mt*$t)
(2)	Specificity (Δ$c/ΔSp) – the impact of an incremental change in specificity of test strategy: = -(1-Pr)*[Bf*$v-($p+Mf*$t+$Pq*r)]+(1-Pr)*[0-($p+Pq*$r)] which reduces to = (Pr-1)*(Bf*$v-Mf*$t)
(3)	Prevalence (Δ$c/ΔPr) – the impact of an incremental change in biomarker prevalence: = Se*[Bt*$v-($p+Pq*$r+Mt*$t)]-(1-Sp)*[Bf*$v-($p+Mf*$t+$Pq*r)]- Sp*[0-($p+Pq*$r)]+(1-Se)*[0-($p+Pq*$r)] which reduces to = Se*(Bt*$v-Mt*$t) + (1-Sp)*(Bf*$v+Mf*$t)
(4)	Cost of therapy per period (Δ$c/Δ$t) – the impact of an incremental change in the cost of therapy per period: = -Pr*Se*Mt-(1-Pr)*(1-Sp)*Mf
(5)	Periods of therapy for true-positive patient (Δ$c/Δ$Bt) – the impact of a change in the periods of therapy for a true-positive patient: = -Pr*Se*$t
(6)	Periods of therapy for false-positive patient (Δ$c/Δ$Bf) – the impact of a change in the periods of therapy for a false positive patient: = -(1-Pr)*(1-Sp)*$t
(7)	Value per QALY (Δ$c/Δ$v) – the impact of an incremental change in the value (benefit in local currency) of a QALY: = Pr*Se*Bt+(1-Pr)*(1-Sp)*Bf
(8)	Benefit of therapy for true positive (Δ$c/Δ$Bt)– the impact of a change in the benefit of therapy for a true positive patient: = Pr*Se*$v
(9)	Benefit of therapy for false positive (Δ$c/Δ$Bf)- the impact of a change in the benefit of therapy for a false positive patient: = (1-Pr)*(1-Sp)*$v
(10)	Biopsy cost (Δ$c/Δ$b)– the impact of an incremental change in the cost of a biopsy: = -Pb
(11)	Probability require biopsy (Δ$c/ΔPb)– the impact of an incremental change in probability of requiring a biopsy: = -$b
(12)	Primary test cost (Δ$c/Δ$p) – the impact of an incremental change in the primary test cost: = -Pr*Se-(1-Pr)*(1-Sp)-(1-Pr)*(Sp)-Pr*(1-Se) which reduces to = -1
(13)	Reflex test cost (Δ$c/Δ$r) – the impact of an incremental change in reflex test cost: = (Pq)*[-Pr*Se-(1-Pr)*(1-Sp)-(1-Pr)*(Sp)-Pr*(1-Se)] which reduces to = -Pq
(14)	Primary test equivocal (Δ$c/ΔPq) – the impact of an incremental change in the probability of a primary test being equivocal: = ($r)*[-Pr*Se-(1-Pr)*(1-Sp)-(1-Pr)*(Sp)-Pr*(1-Se)] which reduces to = -$r
(15)	Share of population tested (Δ$c/ΔPt) – the impact of an incremental change in the share of the eligible population tested: = -($b*Pb+ $p + $Pq*r)

A Microsoft Excel spreadsheet of the generalized model and derivatives is available upon request from the corresponding author, Jim Lee, at [email protected].