Quantifying uncertainty in cost effectiveness analyses

This study compared four alternative approaches (Taylor, Fieller, percentile bootstrap, and bias-corrected bootstrap methods) to estimating confidence intervals (CIs) around cost-effectiveness (CE) ratio. The study consisted of two components: (1) Monte Carlo simulation was conducted to identify characteristics of hypothetical cost-effectiveness data sets which might lead one CI estimation technique to outperform another. These results were matched to the characteristics of an (2) extant data set derived from the National AIDS Demonstration Research (NADR) project. The methods were used to calculate (CIs) for data set. These results were then compared. The main performance criterion in the simulation study was the percentage of times the estimated (CIs) contained the “true” CE. A secondary criterion was the average width of the confidence intervals. For the bootstrap methods, bias was estimated. ^ Simulation results for Taylor and Fieller methods indicated that the CIs estimated using the Taylor series method contained the true CE more often than did those obtained using the Fieller method, but the opposite was true when the correlation was positive and the CV of effectiveness was high for each value of CV of costs. Similarly, the CIs obtained by applying the Taylor series method to the NADR data set were wider than those obtained using the Fieller method for positive correlation values and for values for which the CV of effectiveness were not equal to 30% for each value of the CV of costs. ^ The general trend for the bootstrap methods was that the percentage of times the true CE ratio was contained in CIs was higher for the percentile method for higher values of the CV of effectiveness, given the correlation between average costs and effects and the CV of effectiveness. The results for the data set indicated that the bias corrected CIs were wider than the percentile method CIs. This result was in accordance with the prediction derived from the simulation experiment. ^ Generally, the bootstrap methods are more favorable for parameter specifications investigated in this study. However, the Taylor method is preferred for low CV of effect, and the percentile method is more favorable for higher CV of effect. ^

Theory of uncertainty in illness in patients with cancer of unknown primary origin: Structure providers as antecedents of uncertainty in a population of cancer patients with an unknown primary diagnosis

Uncertainty has been found to be a major component of the cancer experience and can dramatically affect psychosocial adaptation and outcomes of a patient's disease state (McCormick, 2002). Patients with a diagnosis of Carcinoma of Unknown Primary (CUP) may experience higher levels of uncertainty due to the unpredictability of current and future symptoms, limited treatment options and an undetermined life expectancy. To date, only one study has touched upon uncertainty and its' effects on those with CUP but no information exists concerning the effects of uncertainty regarding diagnosis and treatment on the distress level and psychosocial adjustment of this population (Parker & Lenzi, 2003). ^ Mishel's Uncertainty in Illness Theory (1984) proposes that uncertainty is preceded by three variables, one of which being Structure Providers. Structure Providers include credible authority, the degree of trust and confidence the patient has with their doctor, education and social support. It was the goal of this study to examine the relationship between uncertainty and Structure Providers to support the following hypotheses: (1) There will be a negative association between credible authority and uncertainty, (2) There will be a negative association between education level and uncertainty, and (3) There will be a negative association between social support and uncertainty. ^ This cross-sectional analysis utilized data from 219 patients following their initial consultation with their oncologist. Data included the Mishel Uncertainty in Illness Scale (MUIS) which was used to determine patients' uncertainty levels, the Medical Outcomes Study-Social Support Scale (MOSS-SSS) to assess patients, levels of social support, the Patient Satisfaction Questionnaire (PSQ-18) and the Cancer Diagnostic Interview Scale (CDIS) to measure credible authority and general demographic information to assess age, education, marital status and ethnicity. ^ In this study we found that uncertainty levels were generally higher in this sample as compared to other types of cancer populations. And while our results seemed to support most of our hypothesis, we were only able to show significant associations between two. The analyses indicated that credible authority measured by both the CDIS and the PSQ was a significant predictor of uncertainty as was social support measured by the MOSS-SS. Education has shown to have an inconsistent pattern of effect in relation to uncertainty and in the current study there was not enough data to significantly support our hypothesis. ^ The results of this study generally support Mishel's Theory of Uncertainty in Illness and highlight the importance of taking into consideration patients, psychosocial factors as well as employing proper communication practices between physicians and their patients.^

DUAL ENERGY COMPUTED TOMOGRAPHY FOR PROTON THERAPY TREATMENT PLANNING

Proton radiation therapy is gaining popularity because of the unique characteristics of its dose distribution, e.g., high dose-gradient at the distal end of the percentage-depth-dose curve (known as the Bragg peak). The high dose-gradient offers the possibility of delivering high dose to the target while still sparing critical organs distal to the target. However, the high dose-gradient is a double-edged sword: a small shift of the highly conformal high-dose area can cause the target to be substantially under-dosed or the critical organs to be substantially over-dosed. Because of that, large margins are required in treatment planning to ensure adequate dose coverage of the target, which prevents us from realizing the full potential of proton beams. Therefore, it is critical to reduce uncertainties in the proton radiation therapy. One major uncertainty in a proton treatment is the range uncertainty related to the estimation of proton stopping power ratio (SPR) distribution inside a patient. The SPR distribution inside a patient is required to account for tissue heterogeneities when calculating dose distribution inside the patient. In current clinical practice, the SPR distribution inside a patient is estimated from the patient’s treatment planning computed tomography (CT) images based on the CT number-to-SPR calibration curve. The SPR derived from a single CT number carries large uncertainties in the presence of human tissue composition variations, which is the major drawback of the current SPR estimation method. We propose to solve this problem by using dual energy CT (DECT) and hypothesize that the range uncertainty can be reduced by a factor of two from currently used value of 3.5%. A MATLAB program was developed to calculate the electron density ratio (EDR) and effective atomic number (EAN) from two CT measurements of the same object. An empirical relationship was discovered between mean excitation energies and EANs existing in human body tissues. With the MATLAB program and the empirical relationship, a DECT-based method was successfully developed to derive SPRs for human body tissues (the DECT method). The DECT method is more robust against the uncertainties in human tissues compositions than the current single-CT-based method, because the DECT method incorporated both density and elemental composition information in the SPR estimation. Furthermore, we studied practical limitations of the DECT method. We found that the accuracy of the DECT method using conventional kV-kV x-ray pair is susceptible to CT number variations, which compromises the theoretical advantage of the DECT method. Our solution to this problem is to use a different x-ray pair for the DECT. The accuracy of the DECT method using different combinations of x-ray energies, i.e., the kV-kV, kV-MV and MV-MV pair, was compared using the measured imaging uncertainties for each case. The kV-MV DECT was found to be the most robust against CT number variations. In addition, we studied how uncertainties propagate through the DECT calculation, and found general principles of selecting x-ray pairs for the DECT method to minimize its sensitivity to CT number variations. The uncertainties in SPRs estimated using the kV-MV DECT were analyzed further and compared to those using the stoichiometric method. The uncertainties in SPR estimation can be divided into five categories according to their origins: the inherent uncertainty, the DECT modeling uncertainty, the CT imaging uncertainty, the uncertainty in the mean excitation energy, and SPR variation with proton energy. Additionally, human body tissues were divided into three tissue groups – low density (lung) tissues, soft tissues and bone tissues. The uncertainties were estimated separately because their uncertainties were different under each condition. An estimate of the composite range uncertainty (2s) was determined for three tumor sites – prostate, lung, and head-and-neck, by combining the uncertainty estimates of all three tissue groups, weighted by their proportions along typical beam path for each treatment site. In conclusion, the DECT method holds theoretical advantages in estimating SPRs for human tissues over the current single-CT-based method. Using existing imaging techniques, the kV-MV DECT approach was capable of reducing the range uncertainty from the currently used value of 3.5% to 1.9%-2.3%, but it is short to reach our original goal of reducing the range uncertainty by a factor of two. The dominant source of uncertainties in the kV-MV DECT was the uncertainties in CT imaging, especially in MV CT imaging. Further reduction in beam hardening effect, the impact of scatter, out-of-field object etc. would reduce the Hounsfeld Unit variations in CT imaging. The kV-MV DECT still has the potential to reduce the range uncertainty further.