Accounting for parameter uncertainty in the definition of parametric distributions used to describe individual patient variation in health economic models
Abstract:BackgroundParametric distributions based on individual patient data can be used to represent both stochastic and parameter uncertainty. Although general guidance is available on how parameter uncertainty should be accounted for in probabilistic sensitivity analysis, there is no comprehensive guidance on reflecting parameter uncertainty in the (correlated) parameters of distributions used to represent stochastic uncertainty in patient-level models. This study aims to provide this guidance by proposing appropria… Show more
“…A previously developed DES model 5 was implemented in R Statistical Software version 3.3.2, 19 according to the structure of the CAIRO3 study: postinduction, reintroduction, salvage, and death (Figure 1b). Model state postinduction refers to observation (control) or CAP-B maintenance treatment (intervention) after 6 cycles of CAPOX-B.…”
Section: Methodsmentioning
confidence: 99%
“…Uncertainty in parametric distributions’ parameters can be accounted for in probabilistic sensitivity analyses, so that both stochastic uncertainty (i.e., first-order uncertainty) and parameter uncertainty (i.e., second-order uncertainty) are reflected. 5 Although parametric distributions can also be used to populate STMs, this requires an additional discretization step, that is, evaluation of the cumulative density functions at fixed time points, to obtain discrete-time transition probabilities.…”
Background. Different strategies toward implementing competing risks in discrete-event simulation (DES) models are available. This study aims to provide recommendations regarding modeling approaches that can be defined based on these strategies by performing a quantitative comparison of alternative modeling approaches. Methods. Four modeling approaches were defined: 1) event-specific distribution (ESD), 2) event-specific probability and distribution (ESPD), 3) unimodal joint distribution and regression model (UDR), and 4) multimodal joint distribution and regression model (MDR). Each modeling approach was applied to uncensored individual patient data in a simulation study and a case study in colorectal cancer. Their performance was assessed in terms of relative event incidence difference, relative absolute event incidence difference, and relative entropy of time-to-event distributions. Differences in health economic outcomes were also illustrated for the case study. Results. In the simulation study, the ESPD and MDR approaches outperformed the ESD and UDR approaches, in terms of both event incidence differences and relative entropy. Disease pathway and data characteristics, such as the number of competing risks and overlap between competing time-to-event distributions, substantially affected the approaches’ performance. Although no considerable differences in health economic outcomes were observed, the case study showed that the ESPD approach was most sensitive to low event rates, which negatively affected performance. Conclusions. Based on overall performance, the recommended modeling approach for implementing competing risks in DES models is the MDR approach, which is defined according to the general strategy of selecting the time-to-event first and the corresponding event second. The ESPD approach is a less complex and equally performing alternative if sufficient observations are available for each competing event (i.e., the internal validity shows appropriate data representation).
“…A previously developed DES model 5 was implemented in R Statistical Software version 3.3.2, 19 according to the structure of the CAIRO3 study: postinduction, reintroduction, salvage, and death (Figure 1b). Model state postinduction refers to observation (control) or CAP-B maintenance treatment (intervention) after 6 cycles of CAPOX-B.…”
Section: Methodsmentioning
confidence: 99%
“…Uncertainty in parametric distributions’ parameters can be accounted for in probabilistic sensitivity analyses, so that both stochastic uncertainty (i.e., first-order uncertainty) and parameter uncertainty (i.e., second-order uncertainty) are reflected. 5 Although parametric distributions can also be used to populate STMs, this requires an additional discretization step, that is, evaluation of the cumulative density functions at fixed time points, to obtain discrete-time transition probabilities.…”
Background. Different strategies toward implementing competing risks in discrete-event simulation (DES) models are available. This study aims to provide recommendations regarding modeling approaches that can be defined based on these strategies by performing a quantitative comparison of alternative modeling approaches. Methods. Four modeling approaches were defined: 1) event-specific distribution (ESD), 2) event-specific probability and distribution (ESPD), 3) unimodal joint distribution and regression model (UDR), and 4) multimodal joint distribution and regression model (MDR). Each modeling approach was applied to uncensored individual patient data in a simulation study and a case study in colorectal cancer. Their performance was assessed in terms of relative event incidence difference, relative absolute event incidence difference, and relative entropy of time-to-event distributions. Differences in health economic outcomes were also illustrated for the case study. Results. In the simulation study, the ESPD and MDR approaches outperformed the ESD and UDR approaches, in terms of both event incidence differences and relative entropy. Disease pathway and data characteristics, such as the number of competing risks and overlap between competing time-to-event distributions, substantially affected the approaches’ performance. Although no considerable differences in health economic outcomes were observed, the case study showed that the ESPD approach was most sensitive to low event rates, which negatively affected performance. Conclusions. Based on overall performance, the recommended modeling approach for implementing competing risks in DES models is the MDR approach, which is defined according to the general strategy of selecting the time-to-event first and the corresponding event second. The ESPD approach is a less complex and equally performing alternative if sufficient observations are available for each competing event (i.e., the internal validity shows appropriate data representation).
“…As stated in [51], even when we have abundant, good-quality data to work with and a good model, our parameter estimates are still subject to a standard error. Although general guidance is available on how parameter uncertainty should be accounted for in probabilistic sensitivity analysis, there is no comprehensive guidance on the estimation of uncertainty in the parameters of the distributions used to represent stochastic uncertainty in statistical models [52]. Therefore, to assess the consistency of the theoretical distribution with the empirical distribution, the Kolmogorov-Smirnov (K-S) test was adopted [53].…”
Section: Maximum Annual Daily Precipitation With a Specific Probabilimentioning
The aim of this study was to determine the best probability distributions for calculating the maximum annual daily precipitation with the specific probability of exceedance (Pmaxp%). The novelty of this study lies in using the peak-weighted root mean square error (PWRMSE), the root mean square error (RMSE), and the coefficient of determination (R2) for assessing the fit of empirical and theoretical distributions. The input data included maximum daily precipitation records collected in the years 1971–2014 at 51 rainfall stations from the Upper Vistula Basin, Southern Poland. The value of Pmaxp% was determined based on the following probability distributions of random variables: Pearson’s type III (PIII), Weibull’s (W), log-normal, generalized extreme value (GEV), and Gumbel’s (G). Our outcomes showed a lack of significant trends in the observation series of the investigated random variables for a majority of the rainfall stations in the Upper Vistula Basin. We found that the peak-weighted root mean square error (PWRMSE) method, a commonly used metric for quality assessment of rainfall-runoff models, is useful for identifying the statistical distributions of the best fit. In fact, our findings demonstrated the consistency of this approach with the RMSE goodness-of-fit metrics. We also identified the GEV distribution as recommended for calculating the maximum daily precipitation with the specific probability of exceedance in the catchments of the Upper Vistula Basin.
“…The theory of MLE states that for large sample sizes n and a k-dimensional parameter vector, MLE estimators are approximately distributed as a multivariate normal. Thus, the uncertainties of distribution parameters are then quantified by randomly generating parameters based on the multivariate asymptotic normality assumption (Nixon et al, 2010;Degeling et al, 2017). The detailed process is as follows:…”
Section: Methods For Quantifying the Effects Of Parameter Estimation Ementioning
The standardized precipitation index (SPI) is widely used in drought assessments due to its simple data requirement and multiscale characteristics. However, there are some uncertainties in the process of its calculation. This study, taking the Heihe River basin in northwest of China as the study area, mainly focuses on the uncertainty issues both in SPI calculation and in drought characteristics associated with the probability distributions and parameter estimation errors. Ten probability distributions (two-and three-parameter log-logistic and log-normal, generalized extreme value, Pearson type III, burr, gamma, inverse Gaussian, and Weibull) are employed to estimate the SPI. Maximum likelihood estimation is used to estimate distribution parameters. Randomly generating parameters based on the normality assumption is applied to quantify the uncertainty of parameter estimations. Results show that log-logistic-type distribution presents quite close performance with the benchmark gamma distribution and thus is recommended as an alternative in fitting the precipitation data over the study area. Effects of both uncertainty sources (probability distribution functions and parameter estimation errors) are more reflected on extreme droughts (extremely dry or wet). The more extreme the SPI value, the greater uncertainties caused by both sources. Furthermore, the drought characteristics vary a lot from different distributions and parameter errors. These findings highlight the importance of uncertainty analysis of drought assessments, given that most studies in climatology focus on extreme values for drought analysis.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.