Abstract
Objective:
Model validation is important, but seldom applied in chronic schizophrenia. Validation consists of verifying the model itself for face validity (i.e., structure and inputs), cross-validation with other models assessing the same issue, and comparison with real-life outcomes. The primary purpose was to cross-validate a recent pharmacoeconomic model comparing long-acting injectable (LAI) antipsychotics for treating chronic schizophrenia in Sweden. The secondary purpose was to provide external validation.
Methods:
The model of interest was a decision tree analysis with a 1-year time horizon with costs in 2011 Swedish kroner. Drugs analyzed included paliperidone palmitate (PP-LAI), olanzapine pamoate (OLZ-LAI), risperidone (RIS-LAI), haloperidol (HAL-LAI), and oral olanzapine (oral-OLZ). Embase and Medline were searched from 1990–2012 for models examining LAIs. Articles were retrieved, with data extracted for all drugs compared including: expected costs, rates of hospitalization, proportion of time not in relapse, and associated QALYs. Outcomes from the model of interest were compared with those from other articles; costs were projected to 2012 using the consumer price index.
Results:
Twenty-six studies were used for validation; 14 of them provided evidence for cross-validation, 13 for external validation, and four for cost. In cross-validation, cost estimates varied −1.8% (range: −12.4–20.1%), hospitalizations 5.2% (−12.1–3.1%), stable disease 2.5% (−5.6–1.5%), QALYs 9.0% (4.3% after removing outliers). All estimates of clinical outcomes were within 15%. In external validation, hospitalization rates varied by 6.3% (−0.7–11.3%). The research was limited by data availability and validity of the original results.
Conclusion:
Other models validated the outputs of our model very well.
Introduction
Modeling has become an integral part of pharmacoeconomic analysis. However, little attention has been paid to validating these models. A recent paper by Graham et al.Citation1 has pointed out the importance of such validation. The joint ISPOR−SMDM Modeling Good Research Practices Task Force has defined validation as ‘a set of methods for judging a model’s accuracy in making relevant predictions’Citation2. They identified five types of validity that in three areas where validation was needed. The three areas included (1) the model itself, (2) cross-validation with other models and (3) validation with clinical practice.
The model itself should be subject to two types of validation, which are face validity and internal validity. The former involves a process in which experts (i.e., both clinical and economic experts, in the case of economic analyses) assess the structure of the model as well as appropriateness of data sources, assumptions made, and results generated. Internal validity entails verification of data inputs such as coding accuracy or data entry. These validations are normally conducted as a routine part of the model development.
A further type is the predictive validity of the model through cross-validation which is done after results have been generated. This process involves comparing the results from the model with those from other models that address the same research question. Having similar results produced by independent groups using different models provides increased confidence in the results and enhances model credibilityCitation2,Citation3. This type of validation is encouraged by the Good Research Practices Task Force, who have incorporated these views into their recommendations as item VII-5 of Best PracticesCitation2.
The final area (also done post hoc) involves comparing model results with results from clinical practice. Such data are sometimes available from databasesCitation4, patient registriesCitation5, or large observational cohortsCitation6. Another option is the pragmatic trial, such as the CATIECitation7. It should be noted that, in a different publication, Barnett et al.Citation8 reported that clinical trial participants compared very well to other patients with schizophrenia, thereby lending support to the validation process. The problem with the latter option is that a great deal of time, resources, and effort are required to generate the data.
Our group has recently developed a model to determine the cost-effectiveness of long-acting injectable (LAI) antipsychotics in SwedenCitation9. The drugs examined included paliperidone palmitate (PP-LAI), risperidone (RIS-LAI), olanzapine pamoate (OLZ-LAI), haloperidol (HAL-LAI), and oral olanzapine (oral-OLZ). The model itself was fully examined and validated by clinical and economic experts and each input was verified by a team of investigators. Since two of the drugs involved (i.e., PP-LAI and OLZ-LAI) have only been available since 2010, inadequate time has elapsed for long-term follow-up, making external validation not possible for all drugs at this time. The primary objective of this study was therefore to validate our model using cross-validation. A secondary objective was to gather other available evidence that may provide some degree of external validation.
Methods
In order to validate the outcomes of our model, it was necessary to identify all similar studies that have been published. Only peer-reviewed full research articles were considered acceptable. Those studies must have examined the use of any of the five drugs (i.e., PP-LAI, RIS-LAI, OLZ-LAI, HAL-LAI, and oral-OLZ) for a 1-year period in patients having chronic relapsing schizophrenia. Articles must have reported at least one outcome for one drug of interest. Outcomes we estimated included the cost of treatment, days in remission (i.e., not in relapse), rates of hospitalizations and relapses not requiring hospitalization, and quality adjusted life-years (QALYs). For the examination of costs, we further restricted the articles to those that conducted their research within the Swedish healthcare system. The rationale was that differences in healthcare systems, patterns of care, and costs in other countries may not carry over to the system in SwedenCitation10. On the other hand, outcomes that are observable such as hospitalization or those that are measurable, such as QALYs, should be consistent across countries.
Studies of primary interest (i.e., for cross-validation) were pharmacoeconomic analyses; any model could be used, including decision tree, Markov model, spreadsheet, discrete event simulation, database/registry, or chart review. Studies of secondary interest (i.e., for external validation) included long-term clinical trials or trial extensions, observational studies, database, or registry reports.
We searched Medline and Embase from 1990 to the end of 2012, as they are the primary databases that index economic articles. The start year was selected because it represents the beginning of the era dominated by the atypical antipsychotics. As well, reviews of economic articles were retrieved to locate further potential papers. In addition, the references of retrieved papers and reviews were hand searched.
Data extracted included name of first author, year of publication, year of costing, and reported rates or values of outcomes. All cost outcomes were inflated to 2012 Swedish kroner (SEK) using the Consumer Price Index for SwedenCitation11. Results over a time greater than 1 year were divided by the duration of the study so that all results reflected 1 year of treatment.
Outcomes were then compared using descriptive statistics. Since there are no officially accepted criteria for validity assessment, we constructed an arbitrary scale. For cost of treatment, we used the following definitions: <5% difference = nearly perfect agreement, >5% ≤10% excellent, >10% ≤15% good, >15% ≤20% fair/acceptable, and >20% ≤25% marginal. For the clinical outcomes, we used only first three categories, considering 15% to be the maximum allowable difference.
Results and discussion
Among the outcomes generated in our model, we determined the proportions of patients experiencing relapses not requiring hospitalization; however, the majority of the other studies did not. Most of them reported the average number of relapses per patient as their outcome of interest. Therefore, it was not possible to use that outcome for verification purposes. Therefore, the outcomes that we investigated were cost, hospitalization rate, time in remission, and QALYs.
Our search identified 54 articles that appeared to be suitable; however, 28 of them were rejected, leaving 26 accepted papers. lists the rejected papers and the reasons for their rejectionCitation4,Citation6,Citation12–38. There were 14 articles that provided data for cross-validation and 13 for external validation (one paper provided both types of information). Among those 26 publications, four contained suitable cost information for comparisons.
Table 1. List of rejected studies and reasons.
presents the data from our studyCitation9 as well as the four others identified in the searchCitation38–41. Across the five drugs, total costs varied between −12.4% to +20.1% (average −1.8%). The expected costs for PP-LAI were virtually identical, which is remarkable, since they were produced independently by different groups in different countries using very different models. Also, cost estimates for RIS-LAI, OLZ-LAI, and oral-OLZ are all quite similar between the different models, and (as a group) falling within 15% of our estimate. The greatest individual discrepancy was that by Willis et al.Citation40, who reported a cost that was 23% lower than ours. Their under-estimate may have been due to their omission of fees for psychiatrists or other physician visits outside of the hospital or drugs taken as outpatients, which do not appear to have been included in the total costs. We found that medical care comprised ∼18% of the total cost of RIS-LAI. That would account for the majority of the difference in costs. The other large discrepancy was the 20.1% between cost estimates for HAL-LAI by Hensen et al.Citation39. No explanation could be found for that difference. Overall, these other economic models provided a very good degree of validation for out outputs.
Table 2. Cost verification with other models done in the Swedish healthcare system.
As indicated in , the depot formulations ranked highest in terms of having the lowest cost per patient treated. PP-LAI cost the least of all drugs examined, followed by RIS-LAI, then OLZ-LAI.
Data for the validation of clinical outputs from the model are detailed in Citation5,Citation7,Citation25,Citation38–61. We obtained cross-validation data for all drugs.
Table 3. Clinical output verification.
Our hospitalization rates were very close to those predicted by other economic models, with an average deviation across all estimates of 4% (range: from −12.1% to +3.1%). The greatest difference was for oral-OLZ, with a −12.1% difference. Although our rate for PP-LAI of 25.2% was somewhat different (i.e., 7.8%) from that of Furiak et al.Citation43, those results need to be interpreted with caution. When that study was done, little information was available for PP-LAI. Therefore, those authors assumed that PP-LAI rates were exactly the same as for RIS-LAI, despite the difference in dosing schedules (i.e., monthly vs biweekly). It is well known that frequency of administration can influence adherence. Mehnert and DielsCitation62 estimated that patients would be between 5–10% greater with PP-LAI than with RIS-LAI. Since adherence is most often the major driver in economic models, especially those such as ours dealing with patients having adherence problems, differences in outcomes can be substantial. Therefore, little confidence can be placed in the estimates for PP-LAI made by Furiak et al.Citation43. Note that the other estimate from Edwards et al.Citation44 of 23.6% differs by only 1.6%. Thus, cross-validation was very good for this outcome.
A strength of this approach is that the models were all different, yet produced quite similar results. Decision trees produce a weighted average outcome based on probabilities for events (e.g., success/fail, relapse, etc.) that occur over time. They calculate the average cost for the average patient. Markov models also calculate the average cost for the average patient, but do so it a different way. They estimate the time spent in different disease states and the associated costs, summing them over time. Discrete event models and micro-simulations are completely different in that they simulate what happens to an individual patient over time, based on probabilities. Costs are then averaged across all patients in the simulation and directly provide a mean and standard deviation for all outputs. Despite these differences in the way they generate patient outcomes, we have found the results agree very well. That adds strength to our model and provides greater confidence in the outcomes.
On the other hand, data for external validation were sparse, with the exception of hospitalization rates RIS-LAI (10 studies); there were also two studies for oral-OLZ and one for HAL-LAI. Similar results were produced for external validation, which varied 6.3% on average (range: −0.7% to −11.3%). Hospitalization rates for RIS-LAI were almost identical, 32.3% vs 33.0%, and very similar to the cross-validation rate of 29.5%. Similarly, the rate for oral-OLZ varied by 6.9%; however, the rate for HAL-LAI was 11.3% lower. Thus, congruence between models was generally quite good.
Stable disease cross-validation rates were very consistent for the three drugs involved, with an average deviation across estimates of 1.2% (range: −5.6% to 1.5%).
Estimates of QALYS varied an average of 0.071 (9.0%) across all drugs. There was one extreme outlier among those results, a QALY score of 0.425 for oral-OLZ produced by Lindström et al.Citation41. In that study, all of the drugs had very low QALY scores compared to those from other economic models. Removal of that value resulted in an overall average QALY score for oral-OLZ of 0.737, which is very similar to the 0.773 in our studyCitation9. The other outlier was the QALY score for PP-LAI reported in the Furiak et al.Citation43 study, which was based on faulty assumptions, as previously discussed. The QALY score reported by Mehnert et al.Citation38 of 0.830 was virtually the same as our 0.817. When both outliers were removed, the average discrepancy among QALY scores decreased to 0.034 or 4.3% difference overall. All of these results support the validity of our model.
Overall, when all QALY scores were averaged, those for PP-LAI and OLZ-LAI were similar, and both were slightly higher than that for RIS-LAI. PP-LAI also had the lowest cost of treatment, suggesting that PP-LAI is the drug of choice among the LAIs and that all LAIs are to be preferred over either the first generation depot (i.e., HAL-LAI) or oral-OLZ. Benefits seem to have accrued from monthly administration and lower hospitalization rates.
As with all research, this paper has some limitations. We were limited by the availability and validity of the results published by ourselves and by other researchers. Our inclusion criteria required that only full peer-reviewed research articles be accepted; however, we did locate a few poster presentations from scientific meetings, which were not considered. Also, we were limited by an absence of official criteria by which to judge the concordance between research results from different studies. Our categorization of validity was done on an ad hoc basis and was quite arbitrary. Readers can decide if they agree with such a system.
Conclusions
This research has established the validity of the outputs of our economic model for both costs and clinical outcomes. We have produced strong evidence for cross-validation and some supporting evidence for its external validation. Estimates from other economic models are generally in very good agreement, as are those from other research models. Thus, we can have some degree of confidence that our model does generate an acceptable representation of clinical practice and resource utilization. Clinically, our results have been strengthened so that practitioners (at least in Sweden) can make selections between these drugs based on total costs of care. However, results may not reflect practice in other countries.
Few published studies have reported the validation of their economic models. For decision makers to have confidence in such results, it is important that researchers undertake this activity and publish their results.
Transparency
Declaration of funding
This research was funded by Janssen Cilag. MH is a co-author and employee of Janssen Cilag. He participated in the design and writing of the paper. Other Janssen personnel edited the final version and approved the content, as per company policy; however, none made substantive changes.
Declaration of financial/other relationships
TE received a fee for conducting and publishing this research. MH is an employee of Janssen Cilag. CMRO peer reviewers may have received honoraria for their review work. The peer reviewers on this manuscript have disclosed that they have no relevant financial relationships.
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