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## Methods for the estimation of incremental cost effectiveness

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Published: | September 8, 2005 |
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### Outline

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#### Introduction and Purpose

Meanwhile therapeutic and diagnostic procedures are not only evaluated from a clinical, but also from a health economic point of view to link their clinical efficacy to the underlying direct costs. Discussions on ressource allocation and the founding of medical supplementation can be based on the results of such cost effectiveness evaluations and therefore provide an objective rationale for decisions.

The estimation of incremental cost effectiveness ratios (ICERs) has earnt increasing attention during this decade. ICERs relate the cost difference between therapeutical alternatives to the corresponding difference in clinical efficacy or utility. Despite the intuitive interpretation of ICERs as additional costs per additional benefit unit, their statistical treatment imposes severe problems because of the necessity to estimate the distribution of a ratio of at least two stochastically dependent distributions [Ref. 1]. Several attempts were made to modify the well-known Fieller theorem for this purpose, other authors suggest the use of multivariate Bootstrap simulation or Bayesian approaches [Ref. 1], [Ref. 2] . Nevertheless, the problems in ratio estimation remain. Therefore, the concept of ICER estimation is contrasted to the idea of net health benefit (NHB) estimation, which transforms the former ratio estimation problem into a linear estimation procedure [Ref. 2].

#### Material and Methods

Model parametrization

The following will consider two therapeutic alternatives 1 and 2, where treatment 1 denotes an established standard procedure and treatment 2 is under discussion concerning possible recommendation for founding by health care insurers. If then the random variables K_{1} and K_{2} denote the treatments’ costs and the corresponding random variables E_{1} and E_{2} the treatments’ respective efficacies, the following will assume K_{2} > K_{1} and E_{2} > E_{1} (such a treatment alternative 2 is usually called “admissable” for ressource allocation). A cost effectiveness comparison of these treatments may then provide a decision on when to found treatment 2 instead of treatment 1, or when to retain ressource allocation to the standard treatment 1.

The ratio K / E is refered to as the cost effectiveness ratio (CER) and describes a treatment’s marginal costs per gained clinical benefit unit. The incremental cost effectiveness ratio (ICER) of a treatment 2 versus the standard treatment 1 is defined as ICER_{21} = (K_{2} – K_{1}) / (E_{2} – E_{1}) and estimates the additional costs, which must be invested to achieve one additional clinical benefit unit under treatment 2 instead of the standard. In this sense, the ICER concept allows for “health economical ranking” of different health care service offers, when being contrasted to the same standard. Ressource allocation rules can now be formulated straigt-forward: If a health care insurer considers treatment 2 for founding, an allocation rule based on the ICER could use a pre-specified benchmark µ, which characterizes the insurer’s maximum willingness to pay (WTP) additional treatment costs per gained benefit unit. Therefore treatment 2 would be founded as soon as µ > ICER_{21}, whereas treatment 1 remains founded for CER_{1} < µ < ICER_{21}.

A different concept for cost effectiveness evaluation is based on net health benefit estimation [3]: The net health benefit (NHB) of a treatment is defined as its clinical benefit after correction for its incremental costs when being contrasted to a standard, NHB = E – K/µ, where µ denotes the above willingness to pay benchmark. Therefore the net health benefit approach directly involves the WTP model parameter into cost effectiveness estimation. In this context the NHB measures a health service’s benefit after correction for the insurer’s willingness to pay philosophy. A new treatment alternative’s incremental net health benefit versus a standard is then defined as INHB_{21} = NHB_{2} – NHB_{1} and measures the additional clinical benefit of treatment 2 after correction for the two treatment alternatives’ relative cost effectiveness. An NHB-based allocation rule suggests founding of treatment 2 as soon as INHB_{21} > 0 (thereby NHB_{2} > NHB_{1}) and founding of treatment 1 otherwise. It is easy to show, that the ICER-based and the INHB-based allocation rules yield the same allocation decisions [Ref. 3].

The cost and benefit parameters K_{i} and E_{i} can be estimated by their population means and imputed into the above allocation rules as follows:

- 1.
- Determine the WTP benchmark µ > 0 and a significance level α > 0.
- 2.
- Estimate the sample cost and efficacy estimates
*K*and*E*and compute the NHB-estimates in terms of*K*and*E*via NHB =*E*–*K*/µ for both therapies. - 3.
- Compute the incremental net health benefit INHB = NHB
_{2}– NHB_{1}of treatment 2 versus the standard treatment 1. - 4.
- Obtain a one-sided (1-α/2) confidence interval for INHB based on the appropriate t-distribution, or perform a one-sided t-test to ensure INHB>0.

#### Cataract Surgery Data

The above will be illustrated by means of the cost effectiveness evaluation of cataract surgery with multifocal intraocular lenses [Ref. 3]. One drawback of monofocal intraocular lenses consists in the frequent ongoing need for seeing aids after surgery, for example when reading or driving. Multifocal lenses often overcome this need; an increase in subjective quality of life can be expected. German health care insurers reimburse the costs of monofocal lens supplementation. However, founding of multifocal cataract surgery is still under discussion. To assess the incremental cost effectiveness of multifocal lens supplementation with respect to its putative quality of life benefit, data of a randomized trial in cataract patients have been re-analysed from a health economic point of view. Quality of life was assessed by means of a questionnaire-based utility value ranging from 0.0 to 1.0. A total of 400 patients were equally assigned to monofocal or multifocal lens supplementation, and a 6 months follow up on complications and post surgical quality of life was performed. The WTP benchmark was pre-specified at 800 € per gained QALY.

#### Results

A remarkable difference in both costs and gained QALYs was found, whereas already the marginal cost effectiveness of supplementation with multifocal lenses (852 € per gained QALY) turned out worse than the corresponding monofocal estimate of 786 € per gained QALY. If only applied to mean point estimates, the ICER-based allocation rule would still decide founding of monofocal intraocular lenses, but no longer consider multifocal supplementation: ICER = 1060 € / QALY > 800 € / QALY = µ. The INHB-based allocation rule would yield the same decision: INHB = NHB(multifocal) – NHB(monofocal) = -0.133 QALYs – 0.028 QALYs = -0.161 QALYs < 0, i.e. multifocal cataract surgery results in a (slight) loss in cost effectiveness when contrasted to the monofocal therapeutic standard.

If the strategy in Section 2.2 is applied at a 5% significance level, a p-value of 0.045 (one-sided two sample t-test) results. Since p>0.025, no statistically significant difference in net health benefits was found between the multifocal and monofocal lens supplementation, where benefit was based on the number of QALYs achieved by the respective treatment. Therefore supplementation of cataract patients with multifocal intraocular lenses cannot be ensured to show a significantly positive net health benefit when compared to the monofocal supplementation standard.

#### Discussion

Whereas the ICER-based approach provides somewhat instructive information, its statistical feasibility has to be based on severe model assumptions. The NHB approach, however, transforms the problem into standard linear estimation. In this context it is overly important, that the allocation rules based on the net health benefit approach yield the same allocation decisions as the ICER-based ones, since interval estimation in the NHB context can be reduced to standard univariate significance testing and interval estimation. Therefore the rather difficult interpretation of (I)NHB estimates becomes weakened by their advantages concerning statistical feasibility. On the other hand, communication of NHB estimates should be handled with care: Note, that the NHB point estimates in the cataract surgery example do not even slightly mirror the order of the underlying willingness to pay parameter µ! This motivates the integration of methodologists into both the planning and evaluation phase of cost effectiveness investigations [Ref. 4].

### References

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