Methods for the analysis of quality-of-life and survival data in health technology assessment

Methods for the analysis of quality-of-life and survival data in health technology assessmen

Flexible parametric joint modelling of longitudinal and survival data

The joint modelling of longitudinal and survival data is a highly active area of biostatistical research. The submodel for the longitudinal biomarker usually takes the form of a linear mixed effects model. We describe a flexible parametric approach for the survival submodel that models the log baseline cumulative hazard using restricted cubic splines. This approach overcomes limitations of standard parametric choices for the survival submodel, which can lack the flexibility to effectively capture the shape of the underlying hazard function. Numerical integration techniques, such as Gauss-Hermite quadrature, are usually required to evaluate both the cumulative hazard and the overall joint likelihood; however, by using a flexible parametric model, the cumulative hazard has an analytically tractable form, providing considerable computational benefits. We conduct an extensive simulation study to assess the proposed model, comparing it with a B-spline formulation, illustrating insensitivity of parameter estimates to the baseline cumulative hazard function specification. Furthermore, we compare non-adaptive and fully adaptive quadrature, showing the superiority of adaptive quadrature in evaluating the joint likelihood. We also describe a useful technique to simulate survival times from complex baseline hazard functions and illustrate the methods using an example data set investigating the association between longitudinal prothrombin index and survival of patients with liver cirrhosis, showing greater flexibility and improved stability with fewer parameters under the proposed model compared with the B-spline approach. We provide user-friendly Stata software

Bayesian multi-parameter evidence synthesis to inform decision-making: a case study in metastatic hormone-refractory prostate cancer

In health technology assessment, decisions are based on complex cost-effectiveness models which require numerous input parameters. When not all relevant estimates are available the model may have to be simplified. Multi-parameter evidence synthesis combines data from diverse sources of evidence which results in obtaining estimates required in clinical decision-making that otherwise may not be available. We demonstrate how bivariate meta-analysis can be used to predict an unreported estimate of a treatment effect enabling implementation of a multi-state Markov model, which otherwise needs to be simplified. To illustrate this, we used an example of cost-effectiveness analysis for docetaxel in combination with prednisolone in metastatic hormone-refractory prostate cancer. Bivariate meta-analysis was used to model jointly available data on treatment effects on overall survival and progression-free survival (PFS) to predict the unreported effect on PFS in a study evaluating docetaxel with prednisolone. The predicted treatment effect on PFS enabled implementation of a three-state Markov model comprising of stable disease, progressive disease and dead states, whilst lack of the estimate restricted the model to a two-state model (with alive and dead states). The two-state and three-state models were compared by calculating the incremental cost-effectiveness ratio (which was much lower in the three-state model: £22,148 per QALY gained compared to £30,026 obtained from the two-state model) and the expected value of perfect information (which increased with the three-state model). The three-state model has the advantage of distinguishing surviving patients who progressed from those who did not progress. Hence, the use of advanced meta-analytic techniques allowed obtaining relevant parameter estimates to populate a model describing disease pathway more appropriately, whilst helping to prevent valuable clinical data from being discarded

Adjusting for measurement error in baseline prognostic biomarkers included in a time-to-event analysis: a joint modelling approach.

Background: Methodological development of joint models of longitudinal and survival data has been rapid in recent years; however, their full potential in applied settings are yet to be fully explored. We describe a novel use of a specific association structure, linking the two component models through the subject specific intercept, and thus extend joint models to account for measurement error in a biomarker, even when only the baseline value of the biomarker is of interest. This is a common occurrence in registry data sources, where often repeated measurements exist but are simply ignored. Methods: The proposed specification is evaluated through simulation and applied to data from the General Practice Research Database, investigating the association between baseline Systolic Blood Pressure (SBP) and the time-to-stroke in a cohort of obese patients with type 2 diabetes mellitus. Results: By directly modelling the longitudinal component we reduce bias in the hazard ratio for the effect of baseline SBP on the time-to-stroke, showing the large potential to improve on previous prognostic models which use only observed baseline biomarker values. Conclusions: The joint modelling of longitudinal and survival data is a valid approach to account for measurement error in the analysis of a repeatedly measured biomarker and a time-to-event. User friendly Stata software is provided

Uncertainty in the Bayesian meta-analysis of normally distributed surrogate endpoints

We investigate the effect of the choice of parameterisation of meta-analytic models and related uncertainty on the validation of surrogate endpoints. Different meta-analytical approaches take into account different levels of uncertainty which may impact on the accuracy of the predictions of treatment effect on the target outcome from the treatment effect on a surrogate endpoint obtained from these models. A range of Bayesian as well as frequentist meta-analytical methods are implemented using illustrative examples in relapsing-remitting multiple sclerosis, where the treatment effect on disability worsening is the primary outcome of interest in healthcare evaluation, while the effect on relapse rate is considered as a potential surrogate to the effect on disability progression, and in gastric cancer, where the disease-free survival has been shown to be a good surrogate endpoint to the overall survival. Sensitivity analysis was carried out to assess the impact of distributional assumptions on the predictions. Also, sensitivity to modelling assumptions and performance of the models were investigated by simulation. Although different methods can predict mean true outcome almost equally well, inclusion of uncertainty around all relevant parameters of the model may lead to less certain and hence more conservative predictions. When investigating endpoints as candidate surrogate outcomes, a careful choice of the meta-analytical approach has to be made. Models underestimating the uncertainty of available evidence may lead to overoptimistic predictions which can then have an effect on decisions made based on such predictions

Bayesian methods in health technology assessment: a review

Bayesian methods in health technology assessment: a revie

Bayesian meta-analytical methods to incorporate multiple surrogate endpoints in drug development process

A number of meta-analytical methods have been proposed that aim to evaluate surrogate endpoints. Bivariate meta-analytical methods can be used to predict the treatment effect for the final outcome from the treatment effect estimate measured on the surrogate endpoint while taking into account the uncertainty around the effect estimate for the surrogate endpoint. In this paper, extensions to multivariate models are developed aiming to include multiple surrogate endpoints with the potential benefit of reducing the uncertainty when making predictions. In this Bayesian multivariate meta-analytic framework, the between-study variability is modelled in a formulation of a product of normal univariate distributions. This formulation is particularly convenient for including multiple surrogate endpoints and flexible for modelling the outcomes which can be surrogate endpoints to the final outcome and potentially to one another. Two models are proposed, first using an unstructured between-study covariance matrix by assuming the treatment effects on all outcomes are correlated and second using a structured between- study covariance matrix by assuming treatment effects on some of the outcomes are conditionally independent. While the two models are developed for the summary data on a study level, the individual-level association is taken into account by the use of the Prentice’s criteria (obtained from individual patient data) to inform the within study correlations in the models. The modelling techniques are investigated using an example in relapsing remitting multiple sclerosis where the disability worsening is the final outcome, while relapse rate and MRI lesions are potential surrogates to the disability progression

Methods in health service research: An introduction to bayesian methods in health technology and assessment

Methods in health service research: An introduction to bayesian methods in health technology and assessmen

Risk of esophageal cancer in achalasia cardia: A meta-analysis.

Introduction: The association between cancer of the esophagus and achalasia has long been recognized. However, it has also been recognized that cancers themselves can give rise to achalasia-like syndromes. The risk of developing cancer is also a factor in assessing whether there is a potential role for surveillance in this disease. This paper uses published work to form the basis for a meta-analysis of the risk of developing esophageal cancer among patients with pre-existing achalasia. Methods: This paper considered cancer risk reported in a range of studies of achalasia published over a 50-year period. Twenty-seven potential studies were identified. In 16 reports, it was possible to extract information on both length of follow-up and duration of achalasia so that person-years duration (PYD) could be calculated. The analysis was stratified between cancers identified in the first year after diagnosis of achalasia and cancers identified in subsequent years. Results: From pooling the results of 16 studies, the incidence rate of esophageal cancer in achalasia patients was estimated to be 1.36 (95% CI: 0.56, 2.51) per 1000 person years. This is over 10 times higher than the general population incidence rates as reported by the lARC. Conclusions: Therefore, our meta-analysis shows that achalasia is a major risk factor for the development of esophageal cancer. This is supported by the results from the time-stratified analysis. Incidence of esophageal cancer per 1000 person years was lower in the first year after diagnosis of achalasia than in subsequent years. This is strong evidence against the idea that achalasia may be induced by esophageal cancer instead of vice versa

Accounting for heterogeneity in meta-analysis using a multiplicative model-an empirical study

In meta-analysis, the random-effects model is often used to account for heterogeneity. The model assumes that heterogeneity has an additive effect on the variance of effect sizes. An alternative model, which assumes multiplicative heterogeneity, has been little used in the medical statistics community, but is widely used by particle physicists. In this paper, we compare the two models using a random sample of 448 meta-analyses drawn from the Cochrane Database of Systematic Reviews. In general, differences in goodness of fit are modest. The multiplicative model tends to give results that are closer to the null, with a narrower confidence interval. Both approaches make different assumptions about the outcome of the meta-analysis. In our opinion, the selection of the more appropriate model will often be guided by whether the multiplicative model's assumption of a single effect size is plausible. Copyright © 2016 John Wiley & Sons, Ltd