Pathway analysis of genome-wide association study data in primary biliary cirrhosisa

Genome-wide association studies (GWAS) have successfully identified several genetic loci associated with inherited predisposition to primary biliary cirrhosis (PBC), the most common autoimmune disease of the liver. Pathway-based tests constitute a novel paradigm for GWAS analysis. By evaluating genetic variation across a biological pathway (gene set), these tests have the potential to determine the collective impact of variants with subtle effects that are individually too weak to be detected in traditional single variant GWAS analysis. To identify biological pathways associated with the risk of development of PBC, GWAS of PBC from Italy (449 cases and 940 controls) and Canada (530 cases and 398 controls) were independently analyzed. The linear combination test (LCT), a recently developed pathway-level statistical method was used for this analysis. For additional validation, pathways that were replicated at the P <0.05 level of significance in both GWAS on LCT analysis were also tested for association with PBC in each dataset using two complementary GWAS pathway approaches. The complementary approaches included a modification of the gene set enrichment analysis algorithm (i-GSEA4GWAS) and Fisher's exact test for pathway enrichment ratios. Twenty-five pathways were associated with PBC risk on LCT analysis in the Italian dataset at P<0.05, of which eight had an FDR<0.25. The top pathway in the Italian dataset was the TNF/stress related signaling pathway (p=7.38×10 -4, FDR=0.18). Twenty-six pathways were associated with PBC at the P<0.05 level using the LCT in the Canadian dataset with the regulation and function of ChREBP in liver pathway (p=5.68×10-4, FDR=0.285) emerging as the most significant pathway. Two pathways, phosphatidylinositol signaling system (Italian: p=0.016, FDR=0.436; Canadian: p=0.034, FDR=0.693) and hedgehog signaling (Italian: p=0.044, FDR=0.636; Canadian: p=0.041, FDR=0.693), were replicated at LCT P<0.05 in both datasets. Statistically significant association of both pathways with PBC genetic susceptibility was confirmed in the Italian dataset on i-GSEA4GWAS. Results for the phosphatidylinositol signaling system were also significant in both datasets on applying Fisher's exact test for pathway enrichment ratios. This study identified a combination of known and novel pathway-level associations with PBC risk. If functionally validated, the findings may yield fresh insights into the etiology of this complex autoimmune disease with possible preventive and therapeutic application.^

Trastuzumab use and risk of congestive heart failure in older breast cancer patients

Trastuzumab is a humanized-monoclonal antibody, developed specifically for HER2-neu over-expressed breast cancer patients. Although highly effective and well tolerated, it was reported associated with Congestive Heart Failure (CHF) in clinical trial settings (up to 27%). This leaves a gap where, Trastuzumab-related CHF rate in general population, especially older breast cancer patients with long term treatment of Trastuzumab remains unknown. This thesis examined the rates and risk factors associated with Trastuzumab-related CHF in a large population of older breast cancer patients. A retrospective cohort study using the existing Surveillance, Epidemiology and End Results (SEER) and Medicare linked de-identified database was performed. Breast cancer patients ≥ 66 years old, stage I-IV, diagnosed in 1998-2007, fully covered by Medicare but no HMO within 1-year before and after first diagnosis month, received 1st chemotherapy no earlier than 30 days prior to diagnosis were selected as study cohort. The primary outcome of this study is a diagnosis of CHF after starting chemotherapy but none CHF claims on or before cancer diagnosis date. ICD-9 and HCPCS codes were used to pool the claims for Trastuzumab use, chemotherapy, comorbidities and CHF claims. Statistical analysis including comparison of characteristics, Kaplan-Meier survival estimates of CHF rates for long term follow up, and Multivariable Cox regression model using Trastuzumab as a time-dependent variable were performed. Out of 17,684 selected cohort, 2,037 (12%) received Trastuzumab. Among them, 35% (714 out of 2037) were diagnosed with CHF, compared to 31% (4784 of 15647) of CHF rate in other chemotherapy recipients (p<.0001). After 10 years of follow-up, 65% of Trastuzumab users developed CHF, compared to 47% in their counterparts. After adjusting for patient demographic, tumor and clinical characteristics, older breast cancer patients who used Trastuzumab showed a significantly higher risk in developing CHF than other chemotherapy recipients (HR 1.69, 95% CI 1.54 - 1.85). And this risk is increased along with the increment of age (p-value < .0001). Among Trastuzumab users, these covariates also significantly increased the risk of CHF: older age, stage IV, Non-Hispanic black race, unmarried, comorbidities, Anthracyclin use, Taxane use, and lower educational level. It is concluded that, Trastuzumab users in older breast cancer patients had 69% higher risk in developing CHF than non-Trastuzumab users, much higher than the 27% increase reported in younger clinical trial patients. Older age, Non-Hispanic black race, unmarried, comorbidity, combined use with Anthracycline or Taxane also significantly increase the risk of CHF development in older patients treated with Trastuzumab. ^

Detecting genetic and nutritional lung cancer risk factors related to folate metabolism using Bayesian generalized linear models

Complex diseases, such as cancer, are caused by various genetic and environmental factors, and their interactions. Joint analysis of these factors and their interactions would increase the power to detect risk factors but is statistically. Bayesian generalized linear models using student-t prior distributions on coefficients, is a novel method to simultaneously analyze genetic factors, environmental factors, and interactions. I performed simulation studies using three different disease models and demonstrated that the variable selection performance of Bayesian generalized linear models is comparable to that of Bayesian stochastic search variable selection, an improved method for variable selection when compared to standard methods. I further evaluated the variable selection performance of Bayesian generalized linear models using different numbers of candidate covariates and different sample sizes, and provided a guideline for required sample size to achieve a high power of variable selection using Bayesian generalize linear models, considering different scales of number of candidate covariates. ^ Polymorphisms in folate metabolism genes and nutritional factors have been previously associated with lung cancer risk. In this study, I simultaneously analyzed 115 tag SNPs in folate metabolism genes, 14 nutritional factors, and all possible genetic-nutritional interactions from 1239 lung cancer cases and 1692 controls using Bayesian generalized linear models stratified by never, former, and current smoking status. SNPs in MTRR were significantly associated with lung cancer risk across never, former, and current smokers. In never smokers, three SNPs in TYMS and three gene-nutrient interactions, including an interaction between SHMT1 and vitamin B12, an interaction between MTRR and total fat intake, and an interaction between MTR and alcohol use, were also identified as associated with lung cancer risk. These lung cancer risk factors are worthy of further investigation.^

Effect of patient accrual patterns on power and size of log-rank test for time-to-event outcome in clinical trials

The determination of size as well as power of a test is a vital part of a Clinical Trial Design. This research focuses on the simulation of clinical trial data with time-to-event as the primary outcome. It investigates the impact of different recruitment patterns, and time dependent hazard structures on size and power of the log-rank test. A non-homogeneous Poisson process is used to simulate entry times according to the different accrual patterns. A Weibull distribution is employed to simulate survival times according to the different hazard structures. The current study utilizes simulation methods to evaluate the effect of different recruitment patterns on size and power estimates of the log-rank test. The size of the log-rank test is estimated by simulating survival times with identical hazard rates between the treatment and the control arm of the study resulting in a hazard ratio of one. Powers of the log-rank test at specific values of hazard ratio (≠1) are estimated by simulating survival times with different, but proportional hazard rates for the two arms of the study. Different shapes (constant, decreasing, or increasing) of the hazard function of the Weibull distribution are also considered to assess the effect of hazard structure on the size and power of the log-rank test. ^

Evaluation of CHIP perinatal program outcomes in Harris County, Texas

This study compared initial year trends in prenatal care and birth outcomes of women enrolled in the Texas Children's Health Insurance Program (CHIP) Perinatal program to trends in Medicaid program women. The study utilized claims data from Community Health Choice (CHC), a health plan in Harris County, Texas that provides coverage to both populations. Quarterly data was analyzed and compared for the first two years of the CHIP Perinatal program (2007-2008) to determine if outcome trends for the CHIP program improved over the outcome trends seen with those enrolled in Medicaid. Study findings indicate an increase in the quarterly prenatal care utilization for the CHIP Perinatal population from 2007 to 2008 and the associated birth weights of babies delivered also had marginal improvements during the same timeframe. Enrollees in Medicaid continued to have overall better outcomes than those enrolled within the CHIP Perinatal program. However, the study showed that the rate of improvement in both prenatal care utilization and birth outcomes were greater for the CHIP Perinatal enrollees than those enrolled in Medicaid. ^ The majority of these improvements were significant when comparing each coverage program and from year to year. Lastly, the study showed that there was a correlation between prenatal care utilization and birth outcomes. However, further analysis of the data could not conclusively indicate that access to prenatal care services provided by the CHIP Perinatal program contributed to the increases observed in utilization and birth outcomes for the study's sample population.^

A simulation study using the hybrid statistic and the meta-analysis t-test for data with matched and unmatched subjects in the interim analysis of clinical trials

An interim analysis is usually applied in later phase II or phase III trials to find convincing evidence of a significant treatment difference that may lead to trial termination at an earlier point than planned at the beginning. This can result in the saving of patient resources and shortening of drug development and approval time. In addition, ethics and economics are also the reasons to stop a trial earlier. In clinical trials of eyes, ears, knees, arms, kidneys, lungs, and other clustered treatments, data may include distribution-free random variables with matched and unmatched subjects in one study. It is important to properly include both subjects in the interim and the final analyses so that the maximum efficiency of statistical and clinical inferences can be obtained at different stages of the trials. So far, no publication has applied a statistical method for distribution-free data with matched and unmatched subjects in the interim analysis of clinical trials. In this simulation study, the hybrid statistic was used to estimate the empirical powers and the empirical type I errors among the simulated datasets with different sample sizes, different effect sizes, different correlation coefficients for matched pairs, and different data distributions, respectively, in the interim and final analysis with 4 different group sequential methods. Empirical powers and empirical type I errors were also compared to those estimated by using the meta-analysis t-test among the same simulated datasets. Results from this simulation study show that, compared to the meta-analysis t-test commonly used for data with normally distributed observations, the hybrid statistic has a greater power for data observed from normally, log-normally, and multinomially distributed random variables with matched and unmatched subjects and with outliers. Powers rose with the increase in sample size, effect size, and correlation coefficient for the matched pairs. In addition, lower type I errors were observed estimated by using the hybrid statistic, which indicates that this test is also conservative for data with outliers in the interim analysis of clinical trials.^

Performance of HbA1c for classifying diabetes and diagnostic threshold for diabetes among the Mexican American border community

Objective. In 2009, the International Expert Committee recommended the use of HbA1c test for diagnosis of diabetes. Although it has been recommended for the diagnosis of diabetes, its precise test performance among Mexican Americans is uncertain. A strong “gold standard” would rely on repeated blood glucose measurement on different days, which is the recommended method for diagnosing diabetes in clinical practice. Our objective was to assess test performance of HbA1c in detecting diabetes and pre-diabetes against repeated fasting blood glucose measurement for the Mexican American population living in United States-Mexico border. Moreover, we wanted to find out a specific and precise threshold value of HbA1c for Diabetes Mellitus (DM) and pre-diabetes for this high-risk population which might assist in better diagnosis and better management of patient diabetes. ^ Research design and methods. We used CCHC dataset for our study. In 2004, the Cameron County Hispanic Cohort (CCHC), now numbering 2,574, was established drawn from randomly selected households on the basis of 2000 Census tract data. The CCHC study randomly selected a subset of people (aged 18-64 years) in CCHC cohort households to determine the influence of SES on diabetes and obesity. Among the participants in Cohort-2000, 67.15% are female; all are Hispanic. ^ Individuals were defined as having diabetes mellitus (Fasting plasma glucose [FPG] ≥ 126 mg/dL or pre-diabetes (100 ≤ FPG < 126 mg/dL). HbA1c test performance was evaluated using receiver operator characteristic (ROC) curves. Moreover, change-point models were used to determine HbA1c thresholds compatible with FPG thresholds for diabetes and pre-diabetes. ^ Results. When assessing Fasting Plasma Glucose (FPG) is used to detect diabetes, the sensitivity and specificity of HbA1c≥ 6.5% was 75% and 87% respectively (area under the curve 0.895). Additionally, when assessing FPG to detect pre-diabetes, the sensitivity and specificity of HbA1c≥ 6.0% (ADA recommended threshold) was 18% and 90% respectively. The sensitivity and specificity of HbA1c≥ 5.7% (International Expert Committee recommended threshold) for detecting pre-diabetes was 31% and 78% respectively. ROC analyses suggest HbA1c as a sound predictor of diabetes mellitus (area under the curve 0.895) but a poorer predictor for pre-diabetes (area under the curve 0.632). ^ Conclusions. Our data support the current recommendations for use of HbA1c in the diagnosis of diabetes for the Mexican American population as it has shown reasonable sensitivity, specificity and accuracy against repeated FPG measures. However, use of HbA1c may be premature for detecting pre-diabetes in this specific population because of the poor sensitivity with FPG. It might be the case that HbA1c is differentiating the cases more effectively who are at risk of developing diabetes. Following these pre-diabetic individuals for a longer-term for the detection of incident diabetes may lead to more confirmatory result.^

Fasting blood glucose and 8-year mortality in the hypertension detection follow-up program population

This study analyzed the relationship between fasting blood glucose (FBG) and 8-year mortality in the Hypertension Detection Follow-up Program (HDFP) population. Fasting blood glucose (FBG) was examined both as a continuous variable and by specified FBG strata: Normal (FBG 60–100 mg/dL), Impaired (FBG ≥100 and ≤125 mg/dL), and Diabetic (FBG>125 mg/dL or pre-existing diabetes) subgroups. The relationship between type 2 diabetes was examined with all-cause mortality. This thesis described and compared the characteristics of fasting blood glucose strata by recognized glucose cut-points; described the mortality rates in the various fasting blood glucose strata using Kaplan-Meier mortality curves, and compared the mortality risk of various strata using Cox Regression analysis. Overall, mortality was significantly greater among Referred Care (RC) participants compared to Stepped Care (SC) {HR = 1.17; 95% CI (1.052,1.309); p-value = 0.004}, as reported by the HDFP investigators in 1979. Compared with SC participants, the RC mortality rate was significantly higher for the Normal FBG group {HR = 1.18; 95% CI (1.029,1.363); p-value = 0.019} and the Impaired FBG group, {HR = 1.34; 95% CI (1.036,1.734); p-value = 0.026,}. However, for the diabetic group, 8-year mortality did not differ significantly between the RC and SC groups after adjusting for race, gender, age, smoking status among Diabetic individuals {HR = 1.03; 95% CI (0.816,1.303); p-value = 0.798}. This latter finding is possibly due to a lack of a treatment difference of hypertension among Diabetic participants in both RC and SC groups. The largest difference in mortality between RC and SC was in the Impaired subgroup, suggesting that hypertensive patients with FBG between 100 and 125 mg/dL would benefit from aggressive antihypertensive therapy.^

Impact of donor-recipient gender and race mismatching on patient survival in patients with end-stage liver diseases undergoing liver transplantation

Background. End-stage liver disease (ESLD) is an irreversible condition that leads to the imminent complete failure of the liver. Orthotopic liver transplantation (OLT) has been well accepted as the best curative option for patients with ESLD. Despite the progress in liver transplantation, the major limitation nowadays is the discrepancy between donor supply and organ demand. In an effort to alleviate this situation, mismatched donor and recipient gender or race livers are being used. However, the simultaneous impact of donor and recipient gender and race mismatching on patient survival after OLT remains unclear and relatively challenging to surgeons. ^ Objective. To examine the impact of donor and recipient gender and race mismatching on patient survival after OLT using the United Network for Organ Sharing (UNOS) database. ^ Methods. A total of 40,644 recipients who underwent OLT between 2002 and 2011 were included. Kaplan-Meier survival curves and the log-rank tests were used to compare the survival rates among different donor-recipient gender and race combinations. Univariate Cox regression analysis was used to assess the association of donor-recipient gender and race mismatching with patient survival after OLT. Multivariable Cox regression analysis was used to model the simultaneous impact of donor-recipient gender and race mismatching on patient survival after OLT adjusting for a list of other risk factors. Multivariable Cox regression analysis stratifying on recipient hepatitis C virus (HCV) status was also conducted to identify the variables that were differentially associated with patient survival in HCV + and HCV − recipients. ^ Results. In the univariate analysis, compared to male donors to male recipients, female donors to male recipients had a higher risk of patient mortality (HR, 1.122; 95% CI, 1.065–1.183), while in the multivariable analysis, male donors to female recipients experienced an increased mortality rates (adjusted HR, 1.114; 95% CI, 1.048–1.184). Compared to white donors to white recipients, Hispanic donors to black recipients had a higher risk of patient mortality (HR, 1.527; 95% CI, 1.293–1.804) in the univariate analysis, and similar result (adjusted HR, 1.553; 95% CI, 1.314–1.836) was noted in multivariable analysis. After the stratification on recipient HCV status in the multivariable analysis, HCV + mismatched recipients appeared to be at greater risk of mortality than HCV − mismatched recipients. Female donors to female HCV − recipients (adjusted HR, 0.843; 95% CI, 0.769–0.923), and Hispanic HCV + recipients receiving livers from black donors (adjusted HR, 0.758; 95% CI, 0.598–0.960) had a protective effect on patient survival after OLT. ^ Conclusion. Donor-recipient gender and race mismatching adversely affect patient survival after OLT, both independently and after the adjustment for other risk factors. Female recipient HCV status is an important effect modifier in the association between donor-recipient gender combination and patient survival.^

Regression with autocorrelated data: A study of time trend of global infant mortality rate

The infant mortality rate (IMR) is considered to be one of the most important indices of a country's well-being. Countries around the world and other health organizations like the World Health Organization are dedicating their resources, knowledge and energy to reduce the infant mortality rates. The well-known Millennium Development Goal 4 (MDG 4), whose aim is to archive a two thirds reduction of the under-five mortality rate between 1990 and 2015, is an example of the commitment. ^ In this study our goal is to model the trends of IMR between the 1950s to 2010s for selected countries. We would like to know how the IMR is changing overtime and how it differs across countries. ^ IMR data collected over time forms a time series. The repeated observations of IMR time series are not statistically independent. So in modeling the trend of IMR, it is necessary to account for these correlations. We proposed to use the generalized least squares method in general linear models setting to deal with the variance-covariance structure in our model. In order to estimate the variance-covariance matrix, we referred to the time-series models, especially the autoregressive and moving average models. Furthermore, we will compared results from general linear model with correlation structure to that from ordinary least squares method without taking into account the correlation structure to check how significantly the estimates change.^

Analysis of life expectancy using linear and nonlinear models

Life expectancy has consistently increased over the last 150 years due to improvements in nutrition, medicine, and public health. Several studies found that in many developed countries, life expectancy continued to rise following a nearly linear trend, which was contrary to a common belief that the rate of improvement in life expectancy would decelerate and was fit with an S-shaped curve. Using samples of countries that exhibited a wide range of economic development levels, we explored the change in life expectancy over time by employing both nonlinear and linear models. We then observed if there were any significant differences in estimates between linear models, assuming an auto-correlated error structure. When data did not have a sigmoidal shape, nonlinear growth models sometimes failed to provide meaningful parameter estimates. The existence of an inflection point and asymptotes in the growth models made them inflexible with life expectancy data. In linear models, there was no significant difference in the life expectancy growth rate and future estimates between ordinary least squares (OLS) and generalized least squares (GLS). However, the generalized least squares model was more robust because the data involved time-series variables and residuals were positively correlated. ^

Bayesian adaptive designs in early phase clinical trials

There are two practical challenges in the phase I clinical trial conduct: lack of transparency to physicians, and the late onset toxicity. In my dissertation, Bayesian approaches are used to address these two problems in clinical trial designs. The proposed simple optimal designs cast the dose finding problem as a decision making process for dose escalation and deescalation. The proposed designs minimize the incorrect decision error rate to find the maximum tolerated dose (MTD). For the late onset toxicity problem, a Bayesian adaptive dose-finding design for drug combination is proposed. The dose-toxicity relationship is modeled using the Finney model. The unobserved delayed toxicity outcomes are treated as missing data and Bayesian data augment is employed to handle the resulting missing data. Extensive simulation studies have been conducted to examine the operating characteristics of the proposed designs and demonstrated the designs' good performances in various practical scenarios.^

On Bayesian seamless phase I-II designs

Early phase clinical trial designs have long been the focus of interest for clinicians and statisticians working in oncology field. There are several standard phse I and phase II designs that have been widely-implemented in medical practice. For phase I design, the most commonly used methods are 3+3 and CRM. A newly-developed Bayesian model-based mTPI design has now been used by an increasing number of hospitals and pharmaceutical companies. The advantages and disadvantages of these three top phase I designs have been discussed in my work here and their performances were compared using simulated data. It was shown that mTPI design exhibited superior performance in most scenarios in comparison with 3+3 and CRM designs. ^ The next major part of my work is proposing an innovative seamless phase I/II design that allows clinicians to conduct phase I and phase II clinical trials simultaneously. Bayesian framework was implemented throughout the whole design. The phase I portion of the design adopts mTPI method, with the addition of futility rule which monitors the efficacy performance of the tested drugs. Dose graduation rules were proposed in this design to allow doses move forward from phase I portion of the study to phase II portion without interrupting the ongoing phase I dose-finding schema. Once a dose graduated to phase II, adaptive randomization was used to randomly allocated patients into different treatment arms, with the intention of more patients being assigned to receive more promising dose(s). Again simulations were performed to compare the performance of this innovative phase I/II design with a recently published phase I/II design, together with the conventional phase I and phase II designs. The simulation results indicated that the seamless phase I/II design outperform the other two competing methods in most scenarios, with superior trial power and the fact that it requires smaller sample size. It also significantly reduces the overall study time. ^ Similar to other early phase clinical trial designs, the proposed seamless phase I/II design requires that the efficacy and safety outcomes being able to be observed in a short time frame. This limitation can be overcome by using validated surrogate marker for the efficacy and safety endpoints.^

Mixture modeling for joint analysis of survival, discrete, and continuous data

Mixture modeling is commonly used to model categorical latent variables that represent subpopulations in which population membership is unknown but can be inferred from the data. In relatively recent years, the potential of finite mixture models has been applied in time-to-event data. However, the commonly used survival mixture model assumes that the effects of the covariates involved in failure times differ across latent classes, but the covariate distribution is homogeneous. The aim of this dissertation is to develop a method to examine time-to-event data in the presence of unobserved heterogeneity under a framework of mixture modeling. A joint model is developed to incorporate the latent survival trajectory along with the observed information for the joint analysis of a time-to-event variable, its discrete and continuous covariates, and a latent class variable. It is assumed that the effects of covariates on survival times and the distribution of covariates vary across different latent classes. The unobservable survival trajectories are identified through estimating the probability that a subject belongs to a particular class based on observed information. We applied this method to a Hodgkin lymphoma study with long-term follow-up and observed four distinct latent classes in terms of long-term survival and distributions of prognostic factors. Our results from simulation studies and from the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. This flexible inference method provides more accurate estimation and accommodates unobservable heterogeneity among individuals while taking involved interactions between covariates into consideration.^

A comparison of adherence with minocycline treatment in Parkinson's disease and rheumatoid arthritis clinical trials

Background: Little is known about the effects on patient adherence when the same study drug is administered in the same dose in two populations with two different diseases in two different clinical trials. The Minocycline in Rheumatoid Arthritis (MIRA) trial and the NIH Exploratory Trials in Parkinson's disease (NET-PD) Futility Study I provide a unique opportunity to do the above and to compare methods measuring adherence. This study may increase understanding of the influence of disease and adverse events on patient adherence and will provide insights to investigators selecting adherence assessment methods in clinical trials of minocycline and other drugs in future.^ Methods: Minocycline adherence by pill count and the effect of adverse events was compared in the MIRA and NET-PD FS1 trials using multivariable linear regression. Within the MIRA trial, agreement between assay and pill count was compared. The association of adverse events with assay adherence was examined using multivariable logistic regression.^ Results: Adherence derived from pill count in the MIRA and NET-PD FS1 trials did not differ significantly. Adverse events potentially related to minocycline did not appear useful to predict minocycline adherence. In the MIRA trial, adherence measured by pill count appears higher than adherence measured by assay. Agreement between pill count and assay was poor (kappa statistic = 0.25).^ Limitations: Trial and disease are completely confounded and hence the independent effect of disease on adherence to minocycline treatment cannot be studied.^ Conclusion: Simple pill count may be preferred over assay in the minocycline clinical trials to measure adherence. Assays may be less sensitive in a clinical setting where appointments are not scheduled in relation to medication administration time, given assays depend on many pharmacokinetic and instrument-related factors. However, pill count can be manipulated by the patient. Another study suggested that self-report method is more sensitive than pill count method in differentiating adherence from non-adherence. An effect of medication-related adverse events on adherence could not be detected.^