Related Articles

Background

Two distinctly different types of measurement error are Berkson and classical. Impacts of measurement error in epidemiologic studies of ambient air pollution are expected to depend on error type. We characterize measurement error due to instrument imprecision and spatial variability as multiplicative (i.e. additive on the log scale) and model it over a range of error types to assess impacts on risk ratio estimates both on a per measurement unit basis and on a per interquartile range (IQR) basis in a time-series study in Atlanta.

Methods

Daily measures of twelve ambient air pollutants were analyzed: NO2, NOx, O3, SO2, CO, PM10 mass, PM2.5 mass, and PM2.5 components sulfate, nitrate, ammonium, elemental carbon and organic carbon. Semivariogram analysis was applied to assess spatial variability. Error due to this spatial variability was added to a reference pollutant time-series on the log scale using Monte Carlo simulations. Each of these time-series was exponentiated and introduced to a Poisson generalized linear model of cardiovascular disease emergency department visits.

Results

Measurement error resulted in reduced statistical significance for the risk ratio estimates for all amounts (corresponding to different pollutants) and types of error. When modelled as classical-type error, risk ratios were attenuated, particularly for primary air pollutants, with average attenuation in risk ratios on a per unit of measurement basis ranging from 18% to 92% and on an IQR basis ranging from 18% to 86%. When modelled as Berkson-type error, risk ratios per unit of measurement were biased away from the null hypothesis by 2% to 31%, whereas risk ratios per IQR were attenuated (i.e. biased toward the null) by 5% to 34%. For CO modelled error amount, a range of error types were simulated and effects on risk ratio bias and significance were observed.

Conclusions

For multiplicative error, both the amount and type of measurement error impact health effect estimates in air pollution epidemiology. By modelling instrument imprecision and spatial variability as different error types, we estimate direction and magnitude of the effects of error over a range of error types.

Association studies in environmental statistics often involve exposure and outcome data that are misaligned in space. A common strategy is to employ a spatial model such as universal kriging to predict exposures at locations with outcome data and then estimate a regression parameter of interest using the predicted exposures. This results in measurement error because the predicted exposures do not correspond exactly to the true values. We characterize the measurement error by decomposing it into Berkson-like and classical-like components. One correction approach is the parametric bootstrap, which is effective but computationally intensive since it requires solving a nonlinear optimization problem for the exposure model parameters in each bootstrap sample. We propose a less computationally intensive alternative termed the “parameter bootstrap” that only requires solving one nonlinear optimization problem, and we also compare bootstrap methods to other recently proposed methods. We illustrate our methodology in simulations and with publicly available data from the Environmental Protection Agency.

Summary

Estimation of a regression function is a well-known problem in the context of errors in variables, where the explanatory variable is observed with random noise. This noise can be of two types, which are known as classical or Berkson, and it is common to assume that the error is purely of one of these two types. In practice, however, there are many situations where the explanatory variable is contaminated by a mixture of the two errors. In such instances, the Berkson component typically arises because the variable of interest is not directly available and can only be assessed through a proxy, whereas the inaccuracy that is related to the observation of the latter causes an error of classical type. We propose a non-parametric estimator of a regression function from data that are contaminated by a mixture of the two errors. We prove consistency of our estimator, derive rates of convergence and suggest a data-driven implementation. Finite sample performance is illustrated via simulated and real data examples.

In many environmental epidemiology studies, the locations and/or times of exposure measurements and health assessments do not match. In such settings, health effects analyses often use the predictions from an exposure model as a covariate in a regression model. Such exposure predictions contain some measurement error as the predicted values do not equal the true exposures. We provide a framework for spatial measurement error modeling, showing that smoothing induces a Berkson-type measurement error with nondiagonal error structure. From this viewpoint, we review the existing approaches to estimation in a linear regression health model, including direct use of the spatial predictions and exposure simulation, and explore some modified approaches, including Bayesian models and out-of-sample regression calibration, motivated by measurement error principles. We then extend this work to the generalized linear model framework for health outcomes. Based on analytical considerations and simulation results, we compare the performance of all these approaches under several spatial models for exposure. Our comparisons underscore several important points. First, exposure simulation can perform very poorly under certain realistic scenarios. Second, the relative performance of the different methods depends on the nature of the underlying exposure surface. Third, traditional measurement error concepts can help to explain the relative practical performance of the different methods. We apply the methods to data on the association between levels of particulate matter and birth weight in the greater Boston area.

Random error (misclassification) in exposure measurements usually biases a relative risk, regression coefficient, or other effect measure towards the null value (no association). The most important exception is Berkson type error, which causes little or no bias. Berkson type error arises, in particular, due to use of group average exposure in place of individual values. Random error in exposure measurements, Berkson or otherwise, reduces the power of a study, making it more likely that real associations are not detected. Random error in confounding variables compromises the control of their effect, leaving residual confounding. Random error in a variable that modifies the effect of exposure on health--for example, an indicator of susceptibility--tends to diminish the observed modification of effect, but error in the exposure can create a supurious appearance of modification. Methods are available to correct for bias (but not generally power loss) due to measurement error, if information on the magnitude and type of error is available. These methods can be complicated to use, however, and should be used cautiously as "correction" can magnify confounding if it is present.

 

A primary health concern among residents and evacuees in affected areas immediately after a nuclear accident is the internal exposure of the thyroid to radioiodine, particularly I-131, and subsequent thyroid cancer risk. In Japan, the natural disasters of the earthquake and tsunami in March 2011 destroyed an important function of the Fukushima Daiichi Nuclear Power Plant (F1-NPP) and a large amount of radioactive material was released to the environment. Here we report for the first time extensive measurements of the exposure to I-131 revealing I-131 activity in the thyroid of 46 out of the 62 residents and evacuees measured. The median thyroid equivalent dose was estimated to be 4.2 mSv and 3.5 mSv for children and adults, respectively, much smaller than the mean thyroid dose in the Chernobyl accident (490 mSv in evacuees). Maximum thyroid doses for children and adults were 23 mSv and 33 mSv, respectively.

A population-based case-control study of thyroid cancer was carried out in contaminated regions of Belarus and Russia among persons who were exposed during childhood and adolescence to fallout from the Chernobyl accident. For each study subject, individual thyroid doses were reconstructed for the following pathways of exposure: (1) intake of 131I via inhalation and ingestion; (2) intake of short-lived radioiodines (132I, 133I, and 135I) and radiotelluriums (131mTe, 132Te) via inhalation and ingestion; (3) external dose from radionuclides deposited on the ground; and (4) ingestion of 134Cs and 137Cs. A series of intercomparison exercises validated the models used for reconstruction of average doses to populations of specific age groups as well as of individual doses. Median thyroid doses from all factors for study subjects were estimated to be 0.37 and 0.034 Gy in Belarus and Russia, respectively. The highest individual thyroid doses among the subjects were 10.2 Gy in Belarus and 5.3 Gy in Russia. Iodine-131 intake was the main pathway for thyroid exposure. Estimated doses from short-lived radioiodines and radiotelluriums ranged up to 0.53 Gy. Reconstructed individual thyroid doses from external exposure ranged up to 0.1 Gy, while those from internal exposure due to ingested cesium did not exceed 0.05 Gy. The uncertainty of the reconstructed individual thyroid doses, characterized by the geometric standard deviation, varies from 1.7 to 4.0 with a median of 2.2.

Background: Current knowledge about Chornobyl-related thyroid cancer risks comes from ecological studies based on grouped doses, case–control studies, and studies of prevalent cancers.

Objective: To address this limitation, we evaluated the dose–response relationship for incident thyroid cancers using measurement-based individual iodine-131 (I-131) thyroid dose estimates in a prospective analytic cohort study.

Methods: The cohort consists of individuals < 18 years of age on 26 April 1986 who resided in three contaminated oblasts (states) of Ukraine and underwent up to four thyroid screening examinations between 1998 and 2007 (n = 12,514). Thyroid doses of I-131 were estimated based on individual radioactivity measurements taken within 2 months after the accident, environmental transport models, and interview data. Excess radiation risks were estimated using Poisson regression models.

Results: Sixty-five incident thyroid cancers were diagnosed during the second through fourth screenings and 73,004 person-years (PY) of observation. The dose–response relationship was consistent with linearity on relative and absolute scales, although the excess relative risk (ERR) model described data better than did the excess absolute risk (EAR) model. The ERR per gray was 1.91 [95% confidence interval (CI), 0.43–6.34], and the EAR per 104 PY/Gy was 2.21 (95% CI, 0.04–5.78). The ERR per gray varied significantly by oblast of residence but not by time since exposure, use of iodine prophylaxis, iodine status, sex, age, or tumor size.

Conclusions: I-131–related thyroid cancer risks persisted for two decades after exposure, with no evidence of decrease during the observation period. The radiation risks, although smaller, are compatible with those of retrospective and ecological post-Chornobyl studies.

Risk factors for thyroid cancer remain largely unknown except for ionizing radiation exposure during childhood and a history of benign thyroid nodules. Because thyroid nodules are more common than thyroid cancers and are associated with thyroid cancer risk, we evaluated several polymorphisms potentially relevant to thyroid tumors and assessed interaction with ionizing radiation exposure to the thyroid gland. Thyroid nodules were detected in 1998 by ultrasound screening of 2997 persons who lived near the Semipalatinsk nuclear test site in Kazakhstan when they were children (1949-62). Cases with thyroid nodules (n=907) were frequency matched (1:1) to those without nodules by ethnicity (Kazakh or Russian), gender, and age at screening. Thyroid gland radiation doses were estimated from fallout deposition patterns, residence history, and diet. We analyzed 23 polymorphisms in 13 genes and assessed interaction with ionizing radiation exposure using likelihood ratio tests (LRT). Elevated thyroid nodule risks were associated with the minor alleles of RET S836S (rs1800862, p = 0.03) and GFRA1 -193C>G (rs not assigned, p = 0.05) and decreased risk with XRCC1 R194W (rs1799782, p-trend = 0.03) and TGFB1 T263I (rs1800472, p = 0.009). Similar patterns of association were observed for a small number of papillary thyroid cancers (n=25). Ionizing radiation exposure to the thyroid gland was associated with significantly increased risk of thyroid nodules (age and gender adjusted excess odds ratio/Gy = 0.30, 95% confidence interval 0.05-0.56), with evidence for interaction by genotype found for XRCC1 R194W (LRT p value = 0.02). Polymorphisms in RET signaling, DNA repair, and proliferation genes may be related to risk of thyroid nodules, consistent with some previous reports on thyroid cancer. Borderline support for gene-radiation interaction was found for a variant in XRCC1, a key base excision repair protein. Other pathways, such as genes in double strand break repair, apoptosis, and genes related to proliferation should also be pursued.

Background

In epidemiological studies explanatory variables are frequently subject to measurement error. The aim of this paper is to develop a Bayesian method to correct for measurement error in multiple continuous exposures in individually matched case-control studies. This is a topic that has not been widely investigated. The new method is illustrated using data from an individually matched case-control study of the association between thyroid hormone levels during pregnancy and exposure to perfluorinated acids. The objective of the motivating study was to examine the risk of maternal hypothyroxinemia due to exposure to three perfluorinated acids measured on a continuous scale. Results from the proposed method are compared with those obtained from a naive analysis.

Methods

Using a Bayesian approach, the developed method considers a classical measurement error model for the exposures, as well as the conditional logistic regression likelihood as the disease model, together with a random-effect exposure model. Proper and diffuse prior distributions are assigned, and results from a quality control experiment are used to estimate the perfluorinated acids' measurement error variability. As a result, posterior distributions and 95% credible intervals of the odds ratios are computed. A sensitivity analysis of method's performance in this particular application with different measurement error variability was performed.

Results

The proposed Bayesian method to correct for measurement error is feasible and can be implemented using statistical software. For the study on perfluorinated acids, a comparison of the inferences which are corrected for measurement error to those which ignore it indicates that little adjustment is manifested for the level of measurement error actually exhibited in the exposures. Nevertheless, a sensitivity analysis shows that more substantial adjustments arise if larger measurement errors are assumed.

Conclusions

In individually matched case-control studies, the use of conditional logistic regression likelihood as a disease model in the presence of measurement error in multiple continuous exposures can be justified by having a random-effect exposure model. The proposed method can be successfully implemented in WinBUGS to correct individually matched case-control studies for several mismeasured continuous exposures under a classical measurement error model.

Background:

Previous studies showed an increased risk of thyroid cancer among children and adolescents exposed to radioactive iodines released after the Chornobyl (Chernobyl) accident, but the effects of screening, iodine deficiency, age at exposure and other factors on the dose–response are poorly understood.

Methods:

We screened 11 970 individuals in Belarus aged 18 years or younger at the time of the accident who had estimated 131I thyroid doses based on individual thyroid activity measurements and dosimetric data from questionnaires. The excess odds ratio per gray (EOR/Gy) was modelled using linear and linear–exponential functions.

Results:

For thyroid doses <5 Gy, the dose–response was linear (n=85; EOR/Gy=2.15, 95% confidence interval: 0.81–5.47), but at higher doses the excess risk fell. The EOR/Gy was significantly increased among those with prior or screening-detected diffuse goiter, and larger for men than women, and for persons exposed before age 5 than those exposed between 5 and 18 years, although not statistically significant. A somewhat higher EOR/Gy was estimated for validated pre-screening cases.

Conclusion:

10–15 years after the Chornobyl accident, thyroid cancer risk was significantly increased among individuals exposed to fallout as children or adolescents, but the risk appeared to be lower than in other Chornobyl studies and studies of childhood external irradiation.

Summary

Various physiological processes can cause potentially misleading appearances in radioiodine whole body scans; proper understanding of the causes of these can therefore obviate diagnostic errors. Whole-body radioiodine scintigraphy with I131 or I123 is an accurate form of imaging used for management of differentiated thyroid carcinoma. Following thyroidectomy, any residual thyroid tissue or metastatic disease is ablated with high dose I131 and diagnostic images are acquired, demonstrating residual thyroid tissue and metastatic disease. However, atypical physiological uptake of I131 can simulate metastases.

Item response theory (IRT) has a number of potential advantages over classical test theory in assessing self-reported health outcomes. IRT models yield invariant item and latent trait estimates (within a linear transformation), standard errors conditional on trait level, and trait estimates anchored to item content. IRT also facilitates evaluation of differential item functioning, inclusion of items with different response formats in the same scale, and assessment of person fit and is ideally suited for implementing computer adaptive testing. Finally, IRT methods can be helpful in developing better health outcome measures and in assessing change over time. These issues are reviewed, along with a discussion of some of the methodological and practical challenges in applying IRT methods.

While Berkson’s bias is widely recognized in the epidemiologic literature, it remains underappreciated as a model of both selection bias and bias due to missing data. Simple causal diagrams and 2×2 tables illustrate how Berkson’s bias connects to collider bias and selection bias more generally, and show the strong analogies between Berksonian selection bias and bias due to missing data. In some situations, considerations of whether data are missing at random or missing not at random is less important than the causal structure of the missing-data process. While dealing with missing data always relies on strong assumptions about unobserved variables, the intuitions built with simple examples can provide a better understanding of approaches to missing data in real-world situations.

Introduction.

There are scarce data about the optimal increase of L-thyroxine dose during pregnancy in patients with a history of thyroid carcinoma. The first aim of the study was to find out if routine therapeutic measures enable adequate TSH suppression in pregnancy. The other aim was to find out the optimal dose of L-thyroxine for TSH suppression in pregnant women.

Patients and methods.

In this retrospective observational study, we analysed 36 pregnancies of 32 women with a history of thyroid carcinoma. Before pregnancy, all of them underwent total thyroidectomy and radioiodine ablation of thyroid remnant, and they were on suppressive doses of L-thyroxine. Thyroid function tests were obtained before, during and after pregnancy.

Results

Mean L-thyroxine dose before pregnancy, in the first, second and, third trimester and after delivery was 149, 147, 155, 165 and 158 micrograms daily, respectively. TSH concentration remained suppressed in 9 pregnancies, it was within normal range in 22 and elevated in 5 pregnancies. The mean dose of L-thyroxine in patients with suppressed TSH before pregnancy, in the first, second and, third trimester and after delivery was 154, 154, 164, 160 and 161 micrograms daily, respectively. When the dose had to be changed, the mean increase of the dose was 31.5 micrograms daily.

Conclusions

The range of changes in TSH concentration during pregnancy in the patients who have been on suppressive L-thyroxine therapy before conception is quite wide. TSH was adequately suppressed in only 25% of pregnancies. The dose of L-thyroxine in patients with suppressed TSH in the first, second and third trimester was 154, 164 and 160 micrograms daily, respectively.

Objective

The purpose of this study is to estimate a patient's organ dose (effective dose) during performance of dual X-ray absorptiometry by using the correlations derived from the surface dose and the depth doses in an anthropomorphic phantom.

Materials and Methods

An anthropomorphic phantom was designed and TLDs (Thermoluminescent Dosimeters) were placed at the surface and these were also inserted at different depths of the thyroid and uterus of the anthropomorphic phantom. The absorbed doses were measured on the phantom for the spine and femur scan modes. The correlation coefficients and regression functions between the absorbed surface dose and the depth dose were determined. The derived correlation was then applied for 40 women patients to estimate the depth doses to the thyroid and uterus.

Results

There was a correlation between the surface dose and depth dose of the thyroid and uterus in both scan modes. For the women's dosimetry, the average surface doses of the thyroid and uterus were 1.88 µGy and 1.81 µGy, respectively. Also, the scan center dose in the women was 5.70 µGy. There was correlation between the thyroid and uterus surface doses, and the scan center dose.

Conclusion

We concluded that the effective dose to the patient's critical organs during dual X-ray absorptiometry can be estimated by the correlation derived from phantom dosimetry.

Objective

The goal of this study was to develop, evaluate, and apply a method to quantify the unknown spatial extent of activation in deep brain stimulation (DBS) of the ventral intermedius nucleus (Vim) of the thalamus.

Methods

The amplitude-distance relationship and the threshold amplitudes to elicit clinical responses were combined to estimate the unknown amplitude-distance constant and the distance between the electrode and the border between the Vim and the ventrocaudal nucleus (Vc) of the thalamus. We tested the sensitivity of the method to errors in the input parameters, and subsequently, applied the method to estimate the amplitude-distance constant from clinically-measured threshold amplitudes.

Results

The method enabled estimation of the amplitude-distance constant with a median squared error of 0.07–0.23 V/mm2 and provided an estimate of the distance between the electrode and the Vc/Vim border with a median squared error of 0.01–0.04 mm. Application of the method to clinically-measured threshold amplitudes to elicit paresthesias estimated the amplitude-distance constant to be 0.22 V/mm2.

Conclusions

The method enabled robust quantification of the spatial extent of activation in thalamic DBS and predicted that stimulation amplitudes of 1–3.5 V would produce a mean effective radius of activation of 2.0–3.9 mm.

Significance

Knowing the spatial extent of activation may improve methods of electrode placement and stimulation parameter selection in DBS.

Repeat-biomarker measurement error models accounting for systematic correlated within-person error can be used to estimate the correlation coefficient (ρ) and deattenuation factor (λ), used in measurement error correction. These models account for correlated errors in the food frequency questionnaire (FFQ) and the 24-hour diet recall and random within-person variation in the biomarkers. Failure to account for within-person variation in biomarkers can exaggerate correlated errors between FFQs and 24-hour diet recalls. For 2 validation studies, ρ and λ were calculated for total energy and protein density. In the Automated Multiple-Pass Method Validation Study (n = 471), doubly labeled water (DLW) and urinary nitrogen (UN) were measured twice in 52 adults approximately 16 months apart (2002–2003), yielding intraclass correlation coefficients of 0.43 for energy (DLW) and 0.54 for protein density (UN/DLW). The deattenuated correlation coefficient for protein density was 0.51 for correlation between the FFQ and the 24-hour diet recall and 0.49 for correlation between the FFQ and the biomarker. Use of repeat-biomarker measurement error models resulted in a ρ of 0.42. These models were similarly applied to the Observing Protein and Energy Nutrition Study (1999–2000). In conclusion, within-person variation in biomarkers can be substantial, and to adequately assess the impact of correlated subject-specific error, this variation should be assessed in validation studies of FFQs.

Within the project “Environmental Modelling for Radiation Safety” (EMRAS) organized by the IAEA in 2003 experimental data of 131I measurements following the Chernobyl accident in the Plavsk district of Tula region, Russia were used to validate the calculations of some radioecological transfer models. Nine models participated in the inter-comparison. Levels of 137Cs soil contamination in all the settlements and 131I/137Cs isotopic ratios in the depositions in some locations were used as the main input information. 370 measurements of 131I content in thyroid of townspeople and villagers, and 90 measurements of 131I concentration in milk were used for validation of the model predictions.

A remarkable improvement in models performance comparing with previous inter-comparison exercise was demonstrated. Predictions of the various models were within a factor of three relative to the observations, discrepancies between the estimates of average doses to thyroid produced by most participant not exceeded a factor of ten.

Background

Limitations in our current knowledge of normative physiologic changes in thyroid function during the periconception window narrow our ability to establish an optimal approach to screening and diagnosis of thyroid disease in pregnant women. The objective of this study was to characterize changes in thyroid function during the transition from the pre-pregnant to pregnant state in normal fertile women.

Methods

Women (N = 60) ages 30-42 years without a history of thyroid disease, who were planning pregnancy, were observed prospectively before and during early pregnancy. Thyroid function (thyroid stimulating hormone, TSH and free thyroxine, FT4) was measured before conception and between 6 and 9 weeks gestation. Pre-pregnancy samples were analyzed for thyroid antibodies. Bivariate analyses and longitudinal curves (general estimating equation models) were used to analyze changes in thyroid function during the periconception window by antibody status.

Results

Pre-pregnancy TSH values were significantly higher than early pregnancy TSH (p < 0.001), but FT4 values did not differ (p = 0.53). TSH declined as gestational age increased (P < 0.01). Thyroid antibody positive women had a higher pre-pregnancy TSH compared to antibody negative women (p < 0.01). Periconceptional change in thyroid function was more variable among women with antibodies (p < 0.001). 50% of women with elevated pre-pregnancy TSH values (TSH > 3.0 mIU/L) had normal TSH values (TSH < 2.5 mIU/L) in pregnancy.

Conclusions

TSH values decline during the transition from pre-pregnancy to early pregnancy. The change in TSH appears to be less predictable in women with thyroid antibodies. Periconceptional changes in thyroid function should be considered in formulating prenatal thyroid screening guidelines.

The presence of low concentrations of perchlorate in some drinking water sources has led to concern regarding potential effects on the thyroid. In a recently published report, the National Academy of Sciences indicated that the perchlorate dose required to cause hypothyroidism in adults would probably be > 0.40 mg/kg-day for months or longer. In this study, we calculated benchmark doses for perchlorate from thyroid-stimulating hormone (TSH) and free thyroxine (T4) serum indicators from two occupational cohorts with long-term exposure to perchlorate, and from a clinical study of volunteers exposed to perchlorate for 2 weeks. The benchmark dose for a particular serum indicator was defined as the dose predicted to cause an additional 5 or 10% of persons to have a serum measurement outside of the normal range. Using the data from the clinical study, we estimated the half-life of perchlorate in serum at 7.5 hr and the volume of distribution at 0.34 L/kg. Using these estimates and measurements of perchlorate in serum or urine, doses in the occupational cohorts were estimated and used in benchmark calculations. Because none of the three studies found a significant effect of perchlorate on TSH or free T4, all of the benchmark dose estimates were indistinguishable from infinity. The lower 95% statistical confidence limits on benchmark doses estimated from a combined analysis of the two occupational studies ranged from 0.21 to 0.56 mg/kg-day for free T4 index and from 0.36 to 0.92 mg/kg-day for TSH. Corresponding estimates from the short-term clinical study were within these ranges.

Summary

We consider functional measurement error models, i.e. models where covariates are measured with error and yet no distributional assumptions are made about the mismeasured variable. We propose and study a score-type local test and an orthogonal series-based, omnibus goodness-of-fit test in this context, where no likelihood function is available or calculated—i.e. all the tests are proposed in the semiparametric model framework. We demonstrate that our tests have optimality properties and computational advantages that are similar to those of the classical score tests in the parametric model framework. The test procedures are applicable to several semiparametric extensions of measurement error models, including when the measurement error distribution is estimated non-parametrically as well as for generalized partially linear models. The performance of the local score-type and omnibus goodness-of-fit tests is demonstrated through simulation studies and analysis of a nutrition data set.

In epidemiological studies for an environmental risk assessment, doses are often observed with errors. However, they have received little attention in data analysis. This paper studies the effect of measurement errors on the observed dose-response curve. Under the assumptions of the monotone likelihood ratio on errors and a monotone increasing dose-response curve, it is verified that the slope of the observed dose-response curve is likely to be gentler than the true one. The observed variance of responses are not so homogeneous as to be expected under models without errors. The estimation of parameters in a hockey-stick type dose-response curve with a threshold is considered on line of the maximum likelihood method for a functional relationship model. Numerical examples adaptable to the data in a 1986 study of the effect of air pollution that was conducted in Japan are also presented. The proposed model is proved to be suitable to the data in the example cited in this paper.

Various studies have demonstrated the safety and efficacy of recombinant human thyroid-stimulating hormone (rhTSH) for radioiodine remnant ablation. On this basis, rhTSH was approved in Europe for the radioiodine ablation of low-risk differentiated thyroid cancer (DTC) during thyroid hormone therapy with L-thyroxine (L-T4). Moreover, in December 2007, the US Federal Drug Administration approved the use of rhTSH for adjuvant treatment with radioiodine in patients with DTC without evidence of metastatic thyroid cancer. Quality of life was found to be better with rhTSH preparation than with L-thyroxine withdrawal, thereby resulting in benefits for society as a whole. Furthermore, rhTSH for radioiodine remnant ablation results in a longer effective radioiodine half-life within remnant thyroid tissue and a lower specific absorbed dose in the blood and exposure of bone marrow to X-rays. More studies are required to establish the amount of radioiodine to be administered especially in high-risk patients.

With rapid improvements in medical treatment and health care, many datasets dealing with time to relapse or death now reveal a substantial portion of patients who are cured (i.e., who never experience the event). Extended survival models called cure rate models account for the probability of a subject being cured and can be broadly classified into the classical mixture models of Berkson and Gage (BG type) or the stochastic tumor models pioneered by Yakovlev and extended to a hierarchical framework by Chen, Ibrahim, and Sinha (YCIS type). Recent developments in Bayesian hierarchical cure models have evoked significant interest regarding relationships and preferences between these two classes of models. Our present work proposes a unifying class of cure rate models that facilitates flexible hierarchical model-building while including both existing cure model classes as special cases. This unifying class enables robust modeling by accounting for uncertainty in underlying mechanisms leading to cure. Issues such as regressing on the cure fraction and propriety of the associated posterior distributions under different modeling assumptions are also discussed. Finally, we offer a simulation study and also illustrate with two datasets (on melanoma and breast cancer) that reveal our framework’s ability to distinguish among underlying mechanisms that lead to relapse and cure.