31 resultados para Aalen linear regression model
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Background. The parents of a sick child likely experience situational anxiety due to their young child being unexpectedly hospitalized. The emotional upheaval may be great enough that their anxiety inhibits them in providing positive support to their hospitalized child. Because anxiety affects psychological distress as well as behavioral distress, identifying parental distress helps parents improving their coping mechanisms. ^ Purpose. The study compared situational anxiety levels between Taiwanese fathers and mothers and focused on differences between parental anxiety levels at the beginning of the child's unplanned hospitalization and at time of discharge. The study also identified factors related to the parents' distress and use of coping mechanisms. ^ Methods. A descriptive, comparative research design was used to determine the difference between the anxiety levels of 62 Taiwanese father-mother dyads during the situational crisis of their child's unexpected hospitalization. The Mandarin version (M) of Visual Analog Scale (VAS-M), State-Trait Anxiety Inventory (STAI-M), and the Index of Parent Participation/Hospitalized Child (IPP/HC-M) were used to differentiate maternal and paternal anxiety levels and identify factors related to the parents' distress. Questionnaires were completed by parents within 24-36 hours of the child's hospital admission and within 24 hours prior to discharge. A paired t-test, two sample t-test, and linear mixed regression model were used to test and support the study hypothesis. ^ Results. The findings reveal that the mothers' anxiety levels did not significantly differ from the fathers' anxiety level when their child had a sudden admission to the hospital. In particular, parental state anxiety levels did not decrease during the child's hospital stay and subsequent discharge. Moreover, anxiety levels did not differ between parents regardless of whether the child's disease was acute or chronic. The most effective factor related to parental situational anxiety was parental perception of the severity of the child's illness. ^ Conclusions. Parental anxiety was found to be significantly related to changes in their perception of the severity of their child's illness. However, the study was not able to illustrate how parental involvement in the child's hospital care was related to parental perception of the severity of their child's illness. Future studies, using a qualitative approach to gamer more information as to what variables influence parental anxiety during a situational crisis, may provide a richer database from which to modify key variables as well as the instruments used to improve the quality of the data obtained. ^
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Patients who had started HAART (Highly Active Anti-Retroviral Treatment) under previous aggressive DHHS guidelines (1997) underwent a life-long continuous HAART that was associated with many short term as well as long term complications. Many interventions attempted to reduce those complications including intermittent treatment also called pulse therapy. Many studies were done to study the determinants of rate of fall in CD4 count after interruption as this data would help guide treatment interruptions. The data set used here was a part of a cohort study taking place at the Johns Hopkins AIDS service since January 1984, in which the data were collected both prospectively and retrospectively. The patients in this data set consisted of 47 patients receiving via pulse therapy with the aim of reducing the long-term complications. ^ The aim of this project was to study the impact of virologic and immunologic factors on the rate of CD4 loss after treatment interruption. The exposure variables under investigation included CD4 cell count and viral load at treatment initiation. The rates of change of CD4 cell count after treatment interruption was estimated from observed data using advanced longitudinal data analysis methods (i.e., linear mixed model). Using random effects accounted for repeated measures of CD4 per person after treatment interruption. The regression coefficient estimates from the model was then used to produce subject specific rates of CD4 change accounting for group trends in change. The exposure variables of interest were age, race, and gender, CD4 cell counts and HIV RNA levels at HAART initiation. ^ The rate of fall of CD4 count did not depend on CD4 cell count or viral load at initiation of treatment. Thus these factors may not be used to determine who can have a chance of successful treatment interruption. CD4 and viral load were again studied by t-tests and ANOVA test after grouping based on medians and quartiles to see any difference in means of rate of CD4 fall after interruption. There was no significant difference between the groups suggesting that there was no association between rate of fall of CD4 after treatment interruption and above mentioned exposure variables. ^
Whence a healthy mind: Correlation of physical fitness and academic performance among schoolchildren
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Background. Public schools are a key forum in the fight for child health because of the opportunities they present for physical activity and fitness surveillance. However, because schools are evaluated and funded on the basis of standardized academic performance rather than physical activity, empirical research evaluating the connections between fitness and academic performance is needed to justify curriculum allocations to physical activity. ^ Methods. Analyses were based on a convenience sample of 315,092 individually-matched standardized academic (TAKS™) and fitness (FITNESSGRAM®) test records collected by 13 Texas school districts under state mandates. We categorized each fitness result in quintiles by age and gender and used a mixed effects regression model to compare the academic performance of the top and bottom fitness groups for each fitness test and grade level combination. ^ Results. All fitness variables except BMI showed significant, positive associations with academic performance after sociodemographic covariate adjustments, with effect sizes ranging from 0.07 (95% CI: 0.05,0.08) in girls trunklift-TAKS reading to 0.34 (0.32,0.35) in boys cardiovascular-TAKS math. Cardiovascular fitness showed the largest inter-quintile difference in TAKS score (32-75 points), followed by curl-ups. After an additional adjustment for BMI and curl-ups, cardiovascular associations peaked in 8th-9 th grades (maximum inter-quintile difference 142 TAKS points; effect size 0.75 (0.69,0.82) for 8th grade girls math) and showed dose-response characteristics across quintiles (p<0.001 for both genders and outcomes). BMI analysis demonstrated limited, non-linear association with academic performance after adjustment for sociodemographic, cardiovascular fitness and curl-up variables. Low-BMI Hispanic high school boys showed significantly lower TAKS scores than the moderate (but not high) BMI group. High-BMI non-Hispanic white high school girls showed significantly lower scores than the moderate (but not low) BMI group. ^ Conclusions. In this study, fitness was strongly and significantly related to academic performance. Cardiovascular fitness showed a distinct dose-response association with academic performance independent of other sociodemographic and fitness variables. The association peaked in late middle to early high school. The independent association of BMI to academic performance was only found in two sub-groups and was non-linear, with both low and high BMI posing risk relative to moderate BMI but not to each other. In light of our findings, we recommend that policymakers consider PE mandates in middle-high school and require linkage of academic and fitness records to facilitate longitudinal surveillance. School administrators should consider increasing PE time in pursuit of higher academic test scores, and PE practitioners should emphasize cardiovascular fitness over BMI reduction.^
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Genome-Wide Association Study analytical (GWAS) methods were applied in a large biracial sample of individuals to investigate variation across the genome for its association with a surrogate low-density lipoprotein (LDL) particle size phenotype, the ratio of LDL-cholesterol level over ApoB level. Genotyping was performed on the Affymetrix 6.0 GeneChip with approximately one million single nucleotide polymorphisms (SNPs). The ratio of LDL cholesterol to ApoB was calculated, and association tests used multivariable linear regression analysis with an additive genetic model after adjustment for the covariates sex, age and BMI. Association tests were performed separately in African Americans and Caucasians. There were 9,562 qualified individuals in the Caucasian group and 3,015 qualified individuals in the African American group. Overall, in Caucasians two statistically significant loci were identified as being associated with the ratio of LDL-cholesterol over ApoB: rs10488699 (p<5 x10-8, 11q23.3 near BUD13) and the SNP rs964184 (p<5 x10-8 11q23.3 near ZNF259). We also found rs12286037 ((p<4x10-7) (11q23.3) near APOA5/A4/C3/A1 with suggestive associate in the Caucasian sample. In exploratory analyses, a difference in the pattern of association between individuals taking and not taking LDL-cholesterol lowering medications was observed. Individuals who were not taking medications had smaller p-value than those taking medication. In the African-American group, there were no significant (p<5x10-8) or suggestive associations (p<4x10-7) with the ratio of LDL-cholesterol over ApoB after adjusting for age, BMI, and sex and comparing individuals with and without LDL-cholesterol lowering medication. Conclusions: There were significant and suggestive associations between SNP genotype and the ratio of LDL-cholesterol to ApoB in Caucasians, but these associations may be modified by medication treatment.^
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This study described the relationship of sexual maturation and blood pressure in a sample (n = 361) of white females, ages seven through 18, attending public schools in a defined area of Central Texas during October through December, 1984. Other correlates of blood pressure were also described for this sample.^ A survey was performed to obtain the data on height, weight, body mass, pulse rate, upper arm circumference and length, and blood pressure. Each subject self-assessed her secondary sex characteristics (breast and pubic hair) according to drawings of the Tanner stages of maturation. The subjects were interviewed to obtain data on personal health habits and menstrual status. Student age, ethnic group and place of residence were abstracted from school records. Parents or guardians of the subjects responded to a questionnaire pertaining to parental and subject health history and parents' occupation and educational attainment.^ In the simple linear regression analysis, sexual maturation and variables of body size were significantly (p < 0.001) and positively associated with systolic and fourth- and fifth-phase diastolic blood pressure. The demographic and socioeconomic variables were not sufficiently variant in this population to have differential effects on the relation between blood pressure and maturation. Stepwise multiple regression was used to assess the contribution of sexual maturation to the variance of blood pressure after accounting for the variables of body size. Sexual maturation (breast stage) along with weight, height and body mass remained in the multiple regression models for fourth- and fifth-phase diastolic blood pressure. Only height and body mass remained in the regression model for systolic blood pressure; sexual maturation did not contribute more to the explanation of the systolic blood pressure variance.^ The association of sexual maturation with blood pressure level was established in this sample of young white females. More research is needed first, to determine if this relationship prevails in other populations of young females, and second, to determine the relationship of sexual maturation sequence and change with the change of blood pressure during childhood and adolescence. ^
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Traditional comparison of standardized mortality ratios (SMRs) can be misleading if the age-specific mortality ratios are not homogeneous. For this reason, a regression model has been developed which incorporates the mortality ratio as a function of age. This model is then applied to mortality data from an occupational cohort study. The nature of the occupational data necessitates the investigation of mortality ratios which increase with age. These occupational data are used primarily to illustrate and develop the statistical methodology.^ The age-specific mortality ratio (MR) for the covariates of interest can be written as MR(,ij...m) = ((mu)(,ij...m)/(theta)(,ij...m)) = r(.)exp (Z('')(,ij...m)(beta)) where (mu)(,ij...m) and (theta)(,ij...m) denote the force of mortality in the study and chosen standard populations in the ij...m('th) stratum, respectively, r is the intercept, Z(,ij...m) is the vector of covariables associated with the i('th) age interval, and (beta) is a vector of regression coefficients associated with these covariables. A Newton-Raphson iterative procedure has been used for determining the maximum likelihood estimates of the regression coefficients.^ This model provides a statistical method for a logical and easily interpretable explanation of an occupational cohort mortality experience. Since it gives a reasonable fit to the mortality data, it can also be concluded that the model is fairly realistic. The traditional statistical method for the analysis of occupational cohort mortality data is to present a summary index such as the SMR under the assumption of constant (homogeneous) age-specific mortality ratios. Since the mortality ratios for occupational groups usually increase with age, the homogeneity assumption of the age-specific mortality ratios is often untenable. The traditional method of comparing SMRs under the homogeneity assumption is a special case of this model, without age as a covariate.^ This model also provides a statistical technique to evaluate the relative risk between two SMRs or a dose-response relationship among several SMRs. The model presented has application in the medical, demographic and epidemiologic areas. The methods developed in this thesis are suitable for future analyses of mortality or morbidity data when the age-specific mortality/morbidity experience is a function of age or when there is an interaction effect between confounding variables needs to be evaluated. ^
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In regression analysis, covariate measurement error occurs in many applications. The error-prone covariates are often referred to as latent variables. In this proposed study, we extended the study of Chan et al. (2008) on recovering latent slope in a simple regression model to that in a multiple regression model. We presented an approach that applied the Monte Carlo method in the Bayesian framework to the parametric regression model with the measurement error in an explanatory variable. The proposed estimator applied the conditional expectation of latent slope given the observed outcome and surrogate variables in the multiple regression models. A simulation study was presented showing that the method produces estimator that is efficient in the multiple regression model, especially when the measurement error variance of surrogate variable is large.^
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Numerous harmful occupational exposures affect working teens in the United States. Teens working in agriculture and other heavy-labor industries may be at risk for occupational exposures to pesticides and solvents. The neurotoxicity of pesticides and solvents at high doses is well-known; however, the long term effects of these substances at low doses on occupationally exposed adolescents have not been well-studied. To address this research gap, a secondary analysis of cross-sectional data was completed in order to estimate the prevalence of self-reported symptoms of neurotoxicity among a cohort of high school students from Starr County, Texas, a rural area along the Texas-Mexico border. Multivariable linear regression was used to estimate the association between work status (i.e., no work, farm work, and non-farm work) and symptoms of neurotoxicity, while controlling for age, gender, Spanish speaking preference, inhalant use, tobacco use, and alcohol use. The sample included 1,208 students. Of these, the majority (85.84%) did not report having worked during the prior nine months compared to 4.80% who did only farm work, 6.21% who did only non-farm work, and 3.15% who did both types of work. On average, students reported 3.26 symptoms with a range from 0-16. The most commonly endorsed items across work status were those related to memory impairment. Adolescents employed in non-farm work jobs reported more neurotoxicity symptoms than those who reported that they did not work (Mean 4.31; SD 3.97). In the adjusted multivariable regression model, adolescents reporting non-farm work status reported an average of 0.77 more neurotoxicity symptoms on the Q16 than those who did not work (P = 0.031). The confounding variables included in the final model were all found to be factors significantly associated with report of neurotoxicity symptoms. Future research should examine the relationship between these variables and self-report of symptoms of neurotoxicity.^
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Background Past and recent evidence shows that radionuclides in drinking water may be a public health concern. Developmental thresholds for birth defects with respect to chronic low level domestic radiation exposures, such as through drinking water, have not been definitely recognized, and there is a strong need to address this deficiency in information. In this study we examined the geographic distribution of orofacial cleft birth defects in and around uranium mining district Counties in South Texas (Atascosa, Bee, Brooks, Calhoun, Duval, Goliad, Hidalgo, Jim Hogg, Jim Wells, Karnes, Kleberg, Live Oak, McMullen, Nueces, San Patricio, Refugio, Starr, Victoria, Webb, and Zavala), from 1999 to 2007. The probable association of cleft birth defect rates by ZIP codes classified according to uranium and radium concentrations in drinking water supplies was evaluated. Similar associations between orofacial cleft birth defects and radium/radon in drinking water were reported earlier by Cech and co-investigators in another of the Gulf Coast region (Harris County, Texas).50, 55 Since substantial uranium mining activity existed and still exists in South Texas, contamination of drinking water sources with radiation and its relation to birth defects is a ground for concern. ^ Methods Residential addresses of orofacial cleft birth defect cases, as well as live births within the twenty Counties during 1999-2007 were geocoded and mapped. Prevalence rates were calculated by ZIP codes and were mapped accordingly. Locations of drinking water supplies were also geocoded and mapped. ZIP codes were stratified as having high combined uranium (≥30μg/L) vs. low combined uranium (<30μg/L). Likewise, ZIP codes having the uranium isotope, Ra-226 in drinking water, were also stratified as having elevated radium (≥3 pCi/L) vs. low radium (<3 pCi/L). A linear regression was performed using STATA® generalized linear model (GLM) program to evaluate the probable association between cleft birth defect rates by ZIP codes and concentration of uranium and radium via domestic water supply. These rates were further adjusted for potentially confounding variables such as maternal age, education, occupation, and ethnicity. ^ Results This study showed higher rates of cleft births in ZIP codes classified as having high combined uranium versus ZIP codes having low combined uranium. The model was further improved by adding radium stratified as explained above. Adjustment for maternal age and ethnicity did not substantially affect the statistical significance of uranium or radium concentrations in household water supplies. ^ Conclusion Although this study lacks individual exposure levels, the findings suggest a significant association between elevated uranium and radium concentrations in tap water and high orofacial birth defect rates by ZIP codes. Future case-control studies that can measure individual exposure levels and adjust for contending risk factors could result in a better understanding of the exposure-disease association.^
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The tobacco-specific nitrosamine 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK) is an obvious carcinogen for lung cancer. Since CBMN (Cytokinesis-blocked micronucleus) has been found to be extremely sensitive to NNK-induced genetic damage, it is a potential important factor to predict the lung cancer risk. However, the association between lung cancer and NNK-induced genetic damage measured by CBMN assay has not been rigorously examined. ^ This research develops a methodology to model the chromosomal changes under NNK-induced genetic damage in a logistic regression framework in order to predict the occurrence of lung cancer. Since these chromosomal changes were usually not observed very long due to laboratory cost and time, a resampling technique was applied to generate the Markov chain of the normal and the damaged cell for each individual. A joint likelihood between the resampled Markov chains and the logistic regression model including transition probabilities of this chain as covariates was established. The Maximum likelihood estimation was applied to carry on the statistical test for comparison. The ability of this approach to increase discriminating power to predict lung cancer was compared to a baseline "non-genetic" model. ^ Our method offered an option to understand the association between the dynamic cell information and lung cancer. Our study indicated the extent of DNA damage/non-damage using the CBMN assay provides critical information that impacts public health studies of lung cancer risk. This novel statistical method could simultaneously estimate the process of DNA damage/non-damage and its relationship with lung cancer for each individual.^
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Objectives. The purpose of this study was to elucidate behavioral determinants (prevailing attitudes and beliefs) of hand hygiene practices among undergraduate dental students in a dental school. ^ Methods. Statistical modeling using the Integrative Behavioral Model (IBM) prediction was utilized to develop a questionnaire for evaluating behavioral perceptions of hand hygiene practices by dental school students. Self-report questionnaires were given to second, third and fourth year undergraduate dental students. Models representing two distinct hand hygiene practices, termed "elective in-dental school hand hygiene practice" and "inherent in-dental school hand hygiene practice" were tested using linear regression analysis. ^ Results. 58 responses were received (24.5%); the sample mean age was 26.6 years old and females comprised 51%. In our models, elective in-dental school hand hygiene practice and inherent in-dental school hand hygiene practice, explained 40% and 28%, respectively, of the variance in behavioral intention. Translation of community hand hygiene practice to the dental school setting is the predominant driver of elective hand hygiene practice. Intended elective in-school hand hygiene practice is further significantly predicted by students' self-efficacy. Students' attitudes, peer pressure of other dental students and clinic administrators, and role modeling had minimal effects. Inherent hand hygiene intent was strongly predicted by students' beliefs in the benefits of the activity and, to a lesser extent, role modeling. Inherent and elective community behaviors were insignificant. ^ Conclusions. This study provided significant insights into dental student's hand hygiene behavior and can form the basis for an effective behavioral intervention program designed to improve hand hygiene compliance.^
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Rabies remains a significant problem in much of the developed world, where canine rabies is not well controlled, and the bite of an infected dog is the most common means of transmission. The Philippines continues to report several hundred cases of human rabies every year, and many more cases go undetected. In recent years, the province of Bohol has been targeted by the Philippine government and the World Health Organization for a rabies eradication program. ^ The primary objective of this dissertation research was to describe factors associated with dog vaccination coverage and knowledge, attitudes, and practices regarding rabies among households in Bohol, Philippines. Utilizing a cross-sectional cluster survey design, we sampled 460 households and 541 dogs residing within dog-owning households. ^ Multivariate linear regression was used to examine potential associations between knowledge, attitudes, and practices (KAPs) and variables of interest. Forty-six percent of households knew that rabies was spread through the bite of an infected dog. The mean knowledge score was 8.36 (SD: ± 3.4; range: 1–24). We found that having known someone with rabies was significantly associated with an almost one point increase in the knowledge score (β = 0.88; p = 0.02). The mean attitudes score was 5.65 (SD: ± 0.63; range: 2–6), and the mean practices score was 7.07 (SD: ± 1.7; range: 2–9). Both the attitudes score and the practices score were positively and significantly associated with only the knowledge score and no other covariates. ^ Multivariate logistic regression was used to examine associations between dog vaccination coverage and variables of interest. Approximately 71% of owned dogs in Bohol were reported as vaccinated at some time during their lives. We found that a dog's age was significantly associated with vaccination, and the odds of vaccination increased in a linear fashion with age. We also found that dogs had approximately twice the odds of being vaccinated if they were confined both day and night to the household premises or if the owner was employed; however, these results were only marginally significant (p = 0.07) in the multivariate model. ^ Finally, a systematic review was conducted on canine rabies vaccination and dog population demographics in the developing world. We found few studies on this topic, especially in countries where the burden of rabies is greatest. Overall, dog ownership is high. Dogs are quite young and do not live very long due to disease and accidents. The biggest deterrent to vaccination is the rapid dog population turnover. ^ It is our hope that this work will be used to improve dog rabies vaccination programs around the world and save lives, both human and canine.^
New methods for quantification and analysis of quantitative real-time polymerase chain reaction data
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Quantitative real-time polymerase chain reaction (qPCR) is a sensitive gene quantitation method that has been widely used in the biological and biomedical fields. The currently used methods for PCR data analysis, including the threshold cycle (CT) method, linear and non-linear model fitting methods, all require subtracting background fluorescence. However, the removal of background fluorescence is usually inaccurate, and therefore can distort results. Here, we propose a new method, the taking-difference linear regression method, to overcome this limitation. Briefly, for each two consecutive PCR cycles, we subtracted the fluorescence in the former cycle from that in the later cycle, transforming the n cycle raw data into n-1 cycle data. Then linear regression was applied to the natural logarithm of the transformed data. Finally, amplification efficiencies and the initial DNA molecular numbers were calculated for each PCR run. To evaluate this new method, we compared it in terms of accuracy and precision with the original linear regression method with three background corrections, being the mean of cycles 1-3, the mean of cycles 3-7, and the minimum. Three criteria, including threshold identification, max R2, and max slope, were employed to search for target data points. Considering that PCR data are time series data, we also applied linear mixed models. Collectively, when the threshold identification criterion was applied and when the linear mixed model was adopted, the taking-difference linear regression method was superior as it gave an accurate estimation of initial DNA amount and a reasonable estimation of PCR amplification efficiencies. When the criteria of max R2 and max slope were used, the original linear regression method gave an accurate estimation of initial DNA amount. Overall, the taking-difference linear regression method avoids the error in subtracting an unknown background and thus it is theoretically more accurate and reliable. This method is easy to perform and the taking-difference strategy can be extended to all current methods for qPCR data analysis.^
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This thesis project is motivated by the potential problem of using observational data to draw inferences about a causal relationship in observational epidemiology research when controlled randomization is not applicable. Instrumental variable (IV) method is one of the statistical tools to overcome this problem. Mendelian randomization study uses genetic variants as IVs in genetic association study. In this thesis, the IV method, as well as standard logistic and linear regression models, is used to investigate the causal association between risk of pancreatic cancer and the circulating levels of soluble receptor for advanced glycation end-products (sRAGE). Higher levels of serum sRAGE were found to be associated with a lower risk of pancreatic cancer in a previous observational study (255 cases and 485 controls). However, such a novel association may be biased by unknown confounding factors. In a case-control study, we aimed to use the IV approach to confirm or refute this observation in a subset of study subjects for whom the genotyping data were available (178 cases and 177 controls). Two-stage IV method using generalized method of moments-structural mean models (GMM-SMM) was conducted and the relative risk (RR) was calculated. In the first stage analysis, we found that the single nucleotide polymorphism (SNP) rs2070600 of the receptor for advanced glycation end-products (AGER) gene meets all three general assumptions for a genetic IV in examining the causal association between sRAGE and risk of pancreatic cancer. The variant allele of SNP rs2070600 of the AGER gene was associated with lower levels of sRAGE, and it was neither associated with risk of pancreatic cancer, nor with the confounding factors. It was a potential strong IV (F statistic = 29.2). However, in the second stage analysis, the GMM-SMM model failed to converge due to non- concaveness probably because of the small sample size. Therefore, the IV analysis could not support the causality of the association between serum sRAGE levels and risk of pancreatic cancer. Nevertheless, these analyses suggest that rs2070600 was a potentially good genetic IV for testing the causality between the risk of pancreatic cancer and sRAGE levels. A larger sample size is required to conduct a credible IV analysis.^
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It is well known that an identification problem exists in the analysis of age-period-cohort data because of the relationship among the three factors (date of birth + age at death = date of death). There are numerous suggestions about how to analyze the data. No one solution has been satisfactory. The purpose of this study is to provide another analytic method by extending the Cox's lifetable regression model with time-dependent covariates. The new approach contains the following features: (1) It is based on the conditional maximum likelihood procedure using a proportional hazard function described by Cox (1972), treating the age factor as the underlying hazard to estimate the parameters for the cohort and period factors. (2) The model is flexible so that both the cohort and period factors can be treated as dummy or continuous variables, and the parameter estimations can be obtained for numerous combinations of variables as in a regression analysis. (3) The model is applicable even when the time period is unequally spaced.^ Two specific models are considered to illustrate the new approach and applied to the U.S. prostate cancer data. We find that there are significant differences between all cohorts and there is a significant period effect for both whites and nonwhites. The underlying hazard increases exponentially with age indicating that old people have much higher risk than young people. A log transformation of relative risk shows that the prostate cancer risk declined in recent cohorts for both models. However, prostate cancer risk declined 5 cohorts (25 years) earlier for whites than for nonwhites under the period factor model (0 0 0 1 1 1 1). These latter results are similar to the previous study by Holford (1983).^ The new approach offers a general method to analyze the age-period-cohort data without using any arbitrary constraint in the model. ^