Cost-effective treatments are needed to reduce the burden of depression. One way to improve the cost-effectiveness of psychotherapy might be to increase session frequency, but keep the total number of sessions constant.

To evaluate the cost-effectiveness of twice-weekly compared with once-weekly psychotherapy sessions after 12 months, from a societal perspective.

An economic evaluation was conducted alongside a randomised controlled trial comparing twice-weekly versus once-weekly sessions of psychotherapy (cognitive–behavioural therapy or interpersonal psychotherapy) for depression. Missing data were handled by multiple imputation. Statistical uncertainty was estimated with bootstrapping and presented with cost-effectiveness acceptability curves.

Differences between the two groups in depressive symptoms, physical and social functioning, and quality-adjusted life-years (QALY) at 12-month follow-up were small and not statistically significant. Total societal costs in the twice-weekly session group were higher, albeit not statistically significantly so, than in the once-weekly session group (mean difference €2065, 95% CI −686 to 5146). The probability that twice-weekly sessions are cost-effective compared with once-weekly sessions was 0.40 at a ceiling ratio of €1000 per point improvement in Beck Depression Inventory-II score, 0.32 at a ceiling ratio of €50 000 per QALY gained, 0.23 at a ceiling ratio of €1000 per point improvement in physical functioning score and 0.62 at a ceiling ratio of €1000 per point improvement in social functioning score.

Based on the current results, twice-weekly sessions of psychotherapy for depression are not cost-effective over the long term compared with once-weekly sessions.

Cost-effectiveness analyses of empirical participant data are frequently complicated by irregularly distributed and correlated observations, which are not well approximated by normal distributions. Things get even more difficult when observations are clustered within higher level units (for example, hospitals) or the participant (that is, multiple measurements at different timepoints). Therefore, we developed a flexible Bayesian approach to jointly model costs and effects of two competing interventions with a multilevel structure.

Our new model is presented in mathematical form and discussed in detail. We model costs and Quality-Adjusted Life-Years effects through Gamma and Beta distributions, and account for the dependency between costs and effects by adding the effects as a predictor for the costs. We further include hurdle models to account for costs of for the presence of zero costs and perfect health scores.

The full model is implemented in the probabilistic programming language Stan. To compare the performance of our Bayesian model to a frequentist approach (linear mixed model combined with bootstrapping), we simulate 1000 datasets consisting of 400 participants and 20 clusters. Performance of both models is assessed in terms of variance, bias and coverage probability with respect to the costs and effects defined in the simulation.

We ran a preliminary simulation with high intraclass correlation, strong negative correlation for patient-level costs and effects, and positive correlation of cluster effects on both outcomes. The analysis shows that the Bayesian model exhibits a slightly larger bias for estimated costs, but smaller errors and higher coverage probability compared to the frequentist alternative. We will explore different scenarios where we vary the parameters of the simulations and assess whether the results are robust to change.

It is very important that economic evaluations in health care produce precise and reliable results. Our Bayesian approach is able to handle multiple statistical complexities at once and performs better than a comparable frequentist model. Whether this conclusion holds for different simulation scenarios will be explored in further stages of this study.

For the analysis of clinical effects, multiple imputation (MI) of missing data was shown to be unnecessary when using longitudinal linear mixed-models (LLM). It remains unclear whether this also applies to cost estimates from trial-based economic evaluations, that are generally right-skewed. Therefore, this study aimed to assess whether MI is required prior to LLM when analyzing longitudinal cost-effectiveness data.

Two-thousand complete datasets were simulated containing five time points. Incomplete datasets were generated with 10 percent, 25 percent, and 50 percent missing data in costs and effects, assuming a Missing At Random (MAR) mechanism. Statistical performance of six different methodological strategies was compared in terms of empirical bias (EB), root-mean-squared error (RMSE), and coverage rate (CR). Six strategies were compared: (i) LLM (LLM), (ii) MI prior to LLM (MI-LLM), (iii) mean imputation prior to LLM (M-LLM), (iv) complete-case analysis prior to seemingly unrelated regression (CCA-SUR), (v) MI prior to SUR (MI-SUR), and (vi) mean imputation prior to SUR (M-SUR). To evaluate the impact on the probability of cost-effectiveness at different willingness-to-pay [WTPs] thresholds, cost-effectiveness analyses were performed by applying the six strategies to two empirical datasets with 9% and 50% of missing data, respectively.

For costs and effects, LLM, MI-LLM, and MI-SUR performed better than M-LLM, CCA-SUR, and M-SUR, as indicated by smaller EBs and RMSEs, as well as CRs closer to the nominal levels of 0.95. However, even though LLM, MI-LLM, and MI-SUR performed equally well for effects, MI-LLM and MI-SUR were found to perform better than LLM for costs at 10 percent and 25 percent missing data. At 50 percent missing data, all strategies resulted in relatively high EBs and RMSEs for costs. In both empirical datasets, LLM, MI-LLM, and MI-SUR all resulted in similar probabilities of cost-effectiveness at different WTPs.

When opting for using LLM for analyzing trial-based economic evaluation data, researchers are advised to multiply impute missing values first. Otherwise, MI-SUR may also be used.

Patients’ EQ-5D health states are preferably valued using country-specific value sets. If value sets are not available, crosswalks may be used to estimate utility values. However, up until now the impact of using crosswalks instead of value sets on cost-utility outcomes remains unclear.

Trial-based cost-utility data were simulated for four conditions (depression, low back pain, osteoarthritis, and cancer), three levels of disease severity (mild, moderate, and severe), and three treatment effect sizes (small, medium, and large), resulting in 36 scenarios. For all scenarios, utility values were estimated using four scoring methods (EQ-5D-3L value set, EQ-5D-5L value set, 3L-to-5L crosswalk, and 5L-to-3L crosswalk) for three countries (the Netherlands, the United States, and Japan). Mean utility values, quality-adjusted life years (QALYs), incremental QALYs, and cost-utility outcomes (incremental cost-effectiveness ratios [ICER], probabilities of cost-effectiveness at willingness-to-pay [WTP] thresholds) were compared between value sets and crosswalks.

Differences between value sets and crosswalks ranged from -0.33 to 0.13 for mean utility values, from -0.18 to 0.13 for QALYs, and from -0.01 to 0.08 for incremental QALYs. Because of the small differences in incremental QALYs, ICERs between scoring methods were considerably different. For small effect sizes, at a WTP of EUR 20,000/QALY gained, the largest difference in the probability of cost-effectiveness was found for moderate cancer between the 5L value set and 3L-to-5L crosswalk (difference 0.63) using Japanese valuations. For medium effect sizes, the largest difference was found for mild cancer between the 3L value set and the 5L-to-3L crosswalk (difference 0.06) using Japanese valuations. For large effect sizes, the largest difference was found for mild osteoarthritis between the 3L value set and 5L-to-3L crosswalk (difference 0.08) using Japanese valuations.

Our findings indicate that reimbursement decisions may change depending on the use of crosswalks. Crosswalks are justifiable in absence of country-specific value sets but should not be considered a sustainable alternative for value sets.