Simplified Methods for Modelling Dependent Parameters in Health Economic Evaluations: A Tutorial

BACKGROUND

In health economic evaluations, model parameters are often dependent on other model parameters. Although methods exist to simulate multivariate normal (MVN) distribution data and estimate transition probabilities in Markov models while considering competing risks, they are technically challenging for health economic modellers to implement. This tutorial introduces easily implementable applications for handling dependent parameters in modelling.

METHODS

Analytical proofs and proposed simplified methods for handling dependent parameters in typical health economic modelling scenarios are provided, and implementation of these methods are illustrated in seven examples along with the SAS and R code.

RESULTS

Methods to quantify the covariance and correlation coefficients of correlated variables based on published summary statistics and generation of MVN distribution data are demonstrated using examples of physician visits data and cost component data. The use of univariate normal distribution data instead of MVN distribution data to capture population heterogeneity is illustrated based on the results from multiple regression models with linear predictors, and two examples are provided (linear fixed-effects model and Cox proportional hazards model). A conditional probability method is introduced to handle two or more state transitions in a single Markov model cycle and applied in examples of one- and two-way state transitions.

CONCLUSIONS

This tutorial proposes an extension of routinely used methods along with several examples. These simplified methods may be easily applied by health economic modellers with varied statistical backgrounds.

Age Differences in Thermal Pain Responses: A Direct Laboratory Comparison

OBJECTIVES

According to a widely cited assertion, older adults are less likely than younger individuals to express pain complaints. Age-related differences in pain responses have been discussed in the literature despite a paucity of research involving direct comparisons of younger and older adults' pain reactions (i.e., verbal, nonverbal) in the context of a single experimental investigation. Our goal was to test the hypothesis that older adults are more stoic than younger adults in their expression of pain.

METHODS

We measured trait stoicism as well as multiple responses to thermal pain.

RESULTS

In contrast to suggestions in the literature, equivalence testing indicated that older and younger adults displayed similar verbal and nonverbal pain responses. Our results suggest that older adults are no more stoic about their pain than are younger persons.

DISCUSSION

This is the first attempt to explore a wide array of age differences in pain expression within the context of a single experimental study.

Evaluating the correlations of cost and utility parameters from summary statistics for probabilistic analysis in economic evaluations

OBJECTIVES

The correlations between economic modeling input parameters directly impact the variance and may impact the expected values of model outputs. However, correlation coefficients are not often reported in the literature. We aim to understand the correlations between model inputs for probabilistic analysis from summary statistics.

METHODS

We provide proof that for correlated random variables X and Y (e.g. inpatient visits and outpatient visits), the Pearson correlation coefficients of sample means and samples are equal to each other (c o r r X , Y = c o r r X - , Y - ). Therefore, when studies report summary statistics of correlated parameters, we can quantify the correlation coefficient between parameters.

RESULTS

We use examples to illustrate how to estimate the correlation coefficient between the incidence rates of non-severe and severe hypoglycemia events, and the common coefficient of five cost components for patients with diabetic foot ulcers. We further introduce three types of correlations for utilities and provide two examples to estimate the correlations for utilities based on published data. We also evaluate how correlations between cost parameters and utility parameters impact the cost-effectiveness results using a Markov model for major depression.

CONCLUSION

Incorporation of the correlations can improve the precision of cost-effectiveness results and increase confidence in evidence-based decision-making. Further empirical evidence is warranted.

Understanding bias in probabilistic analysis in model-based health economic evaluation

Guidelines of economic evaluations suggest that probabilistic analysis (using probability distributions as inputs) provides less biased estimates than deterministic analysis (using point estimates) owing to the non-linear relationship of model inputs and model outputs. However, other factors can also impact the magnitude of bias for model results. We evaluate bias in probabilistic analysis and deterministic analysis through three simulation studies. The simulation studies illustrate that in some cases, compared with deterministic analyses, probabilistic analyses may be associated with greater biases in model inputs (risk ratios and mean cost estimates using the smearing estimator), as well as model outputs (life-years in a Markov model). Point estimates often represent the most likely value of the parameter in the population, given the observed data. When model parameters have wide, asymmetric confidence intervals, model inputs with larger likelihoods (e.g., point estimates) may result in less bias in model outputs (e.g., costs and life-years) than inputs with lower likelihoods (e.g., probability distributions). Further, when the variance of a parameter is large, simulations from probabilistic analyses may yield extreme values that tend to bias the results of some non-linear models. Deterministic analysis can avoid extreme values that probabilistic analysis may encounter. We conclude that there is no definitive answer on which analytical approach (probabilistic or deterministic) is associated with a less-biased estimate in non-linear models. Health economists should consider the bias of probabilistic analysis and select the most suitable approach for their analyses.

Examining the correlation between treatment effects in clinical trials and economic modelling

INTRODUCTION

Many diseases have a sequential treatment pathway. Compared with patients without previous treatment, patients who fail initial treatment may have lower success rates with a second treatment. This phenomenon can be explained by a correlation between treatment effects.

METHODS

We developed a statistical model of covariance for the underlying unobserved correlation between treatments and established a mathematical expression for the magnitude of the latent correlation term. We conducted a simulation study of clinical trials to investigate the correlation between two treatments and explored clinical examples based on published literature to illustrate the identification and evaluation of these correlations.

RESULTS

Our simulation study confirmed that a treatment correlation reduces the probability of success for the second treatment, compared with no correlation. We found that treatment correlations may be observable in clinical trials, such as for depression and lung cancer, and the magnitude of correlation may be estimated. We illustrated that treatment correlations can be incorporated into an economic model, with possible impacts on cost-effectiveness results. Additional applications of correlation concepts are also discussed.

CONCLUSIONS

We evaluated the correlation between treatment effects and our approach can be applied to clinical trial design and economic modelling of sequential clinical treatment pathways.

Review and estimation of disutility for joint health states of severe and nonsevere hypoglycemic events in diabetes

Aim: Many economic evaluations used linear or log-transformed additive methods to estimate the disutility of hypoglycemic events in diabetes, both nonsevere (NSHEs) and severe (SHEs). Methods: We conducted a literature search for studies of disutility for hypoglycemia. We used additive, minimum and multiplicative methods, and the adjusted decrement estimator to estimate the disutilities of joint health states with both NSHEs and SHEs in six scenarios. Results: Twenty-four studies reported disutilities for hypoglycemia in diabetes. Based on construct validity, the adjusted decrement estimator method likely provides less biased estimates, predicting that when SHEs occur, the additional impact from NSHEs is marginal. Conclusion: Our proposed new method provides a different perspective on the estimation of quality-adjusted life-years in economic evaluations of hypoglycemic treatments.

The work function of few-layer graphene

A theoretical and experimental study of the work function of few-layer graphene is reported. The influence of the number of layers on the work function is investigated in the presence of a substrate, a molecular dipole layer, and combinations of the two. The work function of few-layer graphene is almost independent of the number of layers with only a difference between monolayer and multilayer graphene of about 60 meV. In the presence of a charge-donating substrate the charge distribution is found to decay exponentially away from the substrate and this is directly reflected in the work function of few-layer graphene. A dipole layer changes the work function only when placed in between the substrate and few-layer graphene through a change of the charge transfer between the two.

Field Effect and Strongly Localized Carriers in the Metal-Insulator Transition Material VO(2)

The intrinsic field effect, the change in surface conductance with an applied transverse electric field, of prototypal strongly correlated VO(2) has remained elusive. Here we report its measurement enabled by epitaxial VO(2) and atomic layer deposited high-κ dielectrics. Oxygen migration, joule heating, and the linked field-induced phase transition are precluded. The field effect can be understood in terms of field-induced carriers with densities up to ∼5×10(13)  cm(-2) which are trongly localized, as shown by their low, thermally activated mobility (∼1×10(-3)  cm(2)/V s at 300 K). These carriers show behavior consistent with that of Holstein polarons and strongly impact the (opto)electronics of VO(2).

A study of Joule heating-induced breakdown of carbon nanotube interconnects

We investigate breakdown of carbon nanotube (CNT) interconnects induced by Joule heating in air and under high vacuum conditions (10(-5) mbar). A CNT with a diameter of 18 nm, which is grown by chemical vapor deposition to connect opposing titanium nitride (TiN) electrodes, is able to carry an electrical power up to 0.6 mW before breaking down under vacuum, with a corresponding maximum current density up to 8 × 10(7) A cm(-2) (compared to 0.16 mW and 2 × 10(7) A cm(-2) in air). Decoration with electrochemically deposited Ni particles allows protection of the CNT interconnect against oxidation and improvement of the heat release through the surrounding environment. A CNT decorated with Ni particles is able to carry an increased electrical power of about 1.5 mW before breaking down under vacuum, with a corresponding maximum current density as high as 1.2 × 10(8) A cm(-2). The Joule heating produced along the current carrying CNT interconnect is able to melt the Ni particles and promotes the formation of titanium carbon nitride which improves the electrical contact between the CNT and the TiN electrodes.

Probing quantized image-potential states at supported carbon nanotubes

Discrete image-potential states (ISs) are revealed at double-walled carbon nanotubes by means of scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) in the distance-voltage z(V) spectroscopy mode. The nanotubes are supported by flat Au(111) substrates. Due to the high sensitivity of the hot IS electrons to local variations of the surface potential, they can be considered as a sensitive probe to investigate interactions with the supporting substrate and impurities or defects at the nanotube surface. ISs provide information on the local electronic structure as well as on the electron dynamics at supported nanotubes.