REGRESSION ANALYSIS FOR STANDARDIZED MORTALITY RATIOS WITH APPLICATION TO OCCUPATIONAL FOLLOW-UP STUDIES

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. ^

THE IMPROVEMENT REGION IN RIDGE REGRESSION

One of the difficulties in the practical application of ridge regression is that, for a given data set, it is unknown whether a selected ridge estimator has smaller squared error than the least squares estimator. The concept of the improvement region is defined, and a technique is developed which obtains approximate confidence intervals for the value of ridge k which produces the maximum reduction in mean squared error. Two simulation experiments were conducted to investigate how accurate these approximate confidence intervals might be. ^

Logistic regression with Markov chains as covariates

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.^

Immune response to hepatitis B vaccination in drug using populations: A systematic review and meta-regression analysis

Hepatitis B virus (HBV) is a significant cause of liver diseases and related complications worldwide. Both injecting and non-injecting drug users are at increased risk of contracting HBV infection. Scientific evidence suggests that drug users have subnormal response to HBV vaccination and the seroprotection rates are lower than that in the general population; potentially due to vaccine factors, host factors, or both. The purpose of this systematic review is to examine the rates of seroprotection following HBV vaccination in drug using populations and to conduct a meta-analysis to identify the factors associated with varying seroprotection rates. Seroprotection is defined as developing an anti-HBs antibody level of ≥ 10 mIU/ml after receiving the HBV vaccine. Original research articles were searched using online databases and reference lists of shortlisted articles. HBV vaccine intervention studies reporting seroprotection rates in drug users and published in English language during or after 1989 were eligible. Out of 235 citations reviewed, 11 studies were included in this review. The reported seroprotection rates ranged from 54.5 – 97.1%. Combination vaccine (HAV and HBV) (Risk ratio 12.91, 95% CI 2.98-55.86, p = 0.003), measurement of anti-HBs with microparticle immunoassay (Risk ratio 3.46, 95% CI 1.11-10.81, p = 0.035) and anti-HBs antibody measurement at 2 months after the last HBV vaccine dose (RR 4.11, 95% CI 1.55-10.89, p = 0.009) were significantly associated with higher seroprotection rates. Although statistically nonsignificant, the variables mean age>30 years, higher prevalence of anti-HBc antibody and anti-HIV antibody in the sample population, and current drug use (not in drug rehabilitation treatment) were strongly associated with decreased seroprotection rates. Proportion of injecting drug users, vaccine dose and accelerated vaccine schedule were not predictors of heterogeneity across studies. Studies examined in this review were significantly heterogeneous (Q = 180.850, p = 0.000) and factors identified should be considered when comparing immune response across studies. The combination vaccine showed promising results; however, its effectiveness compared to standard HBV vaccine needs to be examined systematically. Immune response in DUs can possibly be improved by the use of bivalent vaccines, booster doses, and improving vaccine completion rates through integrated public programs and incentives.^

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.^

Age -period -cohort analysis: An extension of Cox's lifetable regression with time -dependent covariates

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. ^

The number and timing of time -dependent covariate measurements for the Cox regression model

The problem of analyzing data with updated measurements in the time-dependent proportional hazards model arises frequently in practice. One available option is to reduce the number of intervals (or updated measurements) to be included in the Cox regression model. We empirically investigated the bias of the estimator of the time-dependent covariate while varying the effect of failure rate, sample size, true values of the parameters and the number of intervals. We also evaluated how often a time-dependent covariate needs to be collected and assessed the effect of sample size and failure rate on the power of testing a time-dependent effect.^ A time-dependent proportional hazards model with two binary covariates was considered. The time axis was partitioned into k intervals. The baseline hazard was assumed to be 1 so that the failure times were exponentially distributed in the ith interval. A type II censoring model was adopted to characterize the failure rate. The factors of interest were sample size (500, 1000), type II censoring with failure rates of 0.05, 0.10, and 0.20, and three values for each of the non-time-dependent and time-dependent covariates (1/4,1/2,3/4).^ The mean of the bias of the estimator of the coefficient of the time-dependent covariate decreased as sample size and number of intervals increased whereas the mean of the bias increased as failure rate and true values of the covariates increased. The mean of the bias of the estimator of the coefficient was smallest when all of the updated measurements were used in the model compared with two models that used selected measurements of the time-dependent covariate. For the model that included all the measurements, the coverage rates of the estimator of the coefficient of the time-dependent covariate was in most cases 90% or more except when the failure rate was high (0.20). The power associated with testing a time-dependent effect was highest when all of the measurements of the time-dependent covariate were used. An example from the Systolic Hypertension in the Elderly Program Cooperative Research Group is presented. ^

IL -12 inhibits the metastatic potential of osteosarcoma cells and induces tumor regression via a mechanism involving Fas /Fas ligand pathway

Despite multiple changes in the adjuvant chemotherapy regimens used to treat osteosarcoma (OS), the 2-year metastasis-free survival has remained at 65–70% for the past 10 years. Characterizing the molecular determinants that permit metastatic spread of tumor cells is a crucial element in developing new approaches for the treatment of osteosarcoma. Since OS metastasizes almost exclusively to the lung, an organ with constitutive Fas ligand (FasL) expression, we hypothesized that the expression of Fas (CD95, APO-1) by OS cells may play a role in the ability of these cells to form lung metastases. Fas expression was quantified in human SAOS-2 OS cells and selected variants (LM2, LM4, LM5, LM6, LM7). Using northern blot, FACS and RT-PCR analysis, low Fas expression was found to correlate with higher metastatic potential in these cell lines. The highly metastatic LM7 cell line was transfected with the full-length human Fas gene and injected into athymic nude mice. The median number of metastatic nodules per mouse fell from over 200 to 1.1 and the size of the nodules decreased from a range of 0.5–9.0 mm to less than 0.5 mm in the Fas-transfected cell line compared to the native LM7 cell line. Additionally, the subsequent incidence of lung metastases was lower in the Fas-expressing cell line. IL-12 was seen to upregulate Fas expression in the highly metastatic LM sublines in vitro. To visualize the effects of IL-12 in vivo, nude mice were injected with LM7 cells and treated biweekly for 4 weeks with Ad.mIL-12, saline control or Ad.βgal. Lung sections were analyzed via immunchistochemistry for Fas expression. A higher expression of Fas was found in tumors from mice receiving IL-12. To study the mechanism by which IL-12 upregulates Fas, LM7 cells were transfected with a luciferase reporter gene construct containing the full-length human fas promoter. Treatment with IL-12 increased luciferase activity. We therefore conclude that IL-12 influences the metastatic potential of OS cells by upregulating the fas promoter, resulting in increased cell surface Fas expression and susceptibility to Fas-induced cell death. ^

Retinoid -induced regression of human head and neck squamous cell carcinomas is associated with the induction of a pro -inflammatory response

Retinoids are Vitamin A derivatives that are effective chemopreventative and chemotherapeutic agents for head and neck squamous cell carcinomas (HNSCC). Despite the wide application of retinoids in cancer treatment, the mechanism by which retinoids inhibit head and neck squamous cell carcinomas is not completely understood. While in vitro models show that drugs affect cell proliferation and differentiation, in vivo models, such as tumor xenografts in nude mice drugs affect more complex parameters such as extracellular matrix formation, angiogenesis and inflammation. Therefore, we studied the effects of retinoids on the growth of the 22B HNSCC tumors using a xenograft model. In this system, retinoids had no effect on tumor cell differentiation but caused invasion of the tumor by inflammatory cells. Retinoid induced inflammation lead to tumor cell death and tumor regression. Therefore, we hypothesized that retinoids stimulated the 22B HNSCC xenografts to produce a pro-inflammatory signal such as chemokines that in turn activated host inflammatory responses. ^ We used real time quantitative RT-PCR to measure cytokine and chemokine expression in retinoid treated tumors. Treatment of tumors with an RAR-specific retinoid, LGD1550, had no effect on the expression of TNFα, IL-1α, GROα, IP-10, Rantes, MCP-1 and MIP-1α but induced IL-8 mRNA 5-fold. We further characterized the retinoid effect on IL-8 expression on the 22B HNSCC and 1483 HNSCC cells in vitro. Retinoids increased IL-8 expression and enhanced TNFα-dependent IL-8 induction. In addition, retinoids increased the basal and TNFα-dependent expression of MCP-1 but decreased the basal and TNFα dependent expression of IP-10. The effect of retinoids on IL-8 and MCP-1 expression was very rapid with increased levels of mRNA detected within 1–2 hours. This effect did not require new protein synthesis and did not result from mRNA stabilization. Both RAR and RXR ligands increased IL-8 expression whereas only RAR ligands activated MCP-1 expression. ^ We identified a functional retinoid response element in the IL-8 promoter that was located adjacent to the C/EBP-NFkB response element. TNFα treatment of the 22B cells caused rapid, transient and selective acetylation of regions of the IL-8 promoter associated with the NFkB response element. Co-treatment of the cells with retinoids plus TNF increased the acetylation of chromatin in this region without altering the kinetics of acetylation. These results demonstrate that ligand activated retinoid receptors can cooperate with NFkB in histone acetylation and chromatin remodeling. We believe that in certain HNSCC tumors this cooperation and the resulting enhancement of IL-8 expression can induce an inflammatory response that leads to tumor regression. We believe that the induction of inflammation in susceptible tumors, possibly coupled with cytotoxic interventions may be an important component in the use of retinoids to treat human squamous cancers. ^

Diagnostik von Regressionsschätzungen bei kleinen Stichproben (mit einem Exkurs zu logistischer Regression)

Wie alle anderen statistischen Verfahren konzentriert sich auch die Methode der Regression nur auf die Analyse ausgewählter Aspekte vorliegenden Datenmaterials. Entsprechend sind zu gegebenen Regressionsergebnissen ganz unterschiedliche Datenkonstellationen denkbar, wovon aber für die Interpretation der Ergebnisse nicht alle unproblematisch sind. So besteht besonders bei kleinen Stichproben die Gefahr, dass die Regressionsschätzung entscheidend von einzelnen Extremwerten abhängt, was die Verlässlichkeit der daraus abgeleiteten Schlussfolgerungen beeinträchtigt. In diesem Beitrag werden deshalb anhand von Beispielen einige einfache grafische und formale Instrumente zur Diagnose einflussreicher Datenpunkte in der linearen und logistischen Regression vorgestellt, die im Prozess der Datenanalyse standardmäßig angewendet werden sollten. Weiterhin werden nach Identifikation „atypischer“ Datenpunkte zu verfolgende Analysestrategien diskutiert.

From regression estimates to document tables: output formatting using -estout-

Postestimation processing and formatting of regression estimates for input into document tables are tasks that many of us have to do. However, processing results by hand can be laborious, and is vulnerable to error. There are therefore many benefits to automation of these tasks while at the same time retaining user flexibility in terms of output format. The estout package meets these needs. estout assembles a table of coefficients, "significance stars", summary statistics, standard errors, t/z statistics, p-values, confidence intervals, and other statistics calculated for up to twenty models previously fitted and stored by estimates store. It then writes the table to the Stata log and/or to a text file. The estimates are formatted optionally in several styles: html, LaTeX, or tab-delimited (for input into MS Excel or Word). There are a large number of options regarding which output is formatted and how. This talk will take users through a range of examples, from relatively basic simple applications to complex ones.

Measuring fixed costs for firms' use of a free trade agreement : threshold regression approach

In this paper, by employing the threshold regression method, we estimate the average tariff equivalent of fixed costs for the use of a free trade agreement (FTA) among all existing FTAs in the world. It is estimated to be 3.2%. This global estimate serves as a reference rate in the evaluation of each FTA’s fixed costs.

Lazy Lasso for local regression

Locally weighted regression is a technique that predicts the response for new data items from their neighbors in the training data set, where closer data items are assigned higher weights in the prediction. However, the original method may suffer from overfitting and fail to select the relevant variables. In this paper we propose combining a regularization approach with locally weighted regression to achieve sparse models. Specifically, the lasso is a shrinkage and selection method for linear regression. We present an algorithm that embeds lasso in an iterative procedure that alternatively computes weights and performs lasso-wise regression. The algorithm is tested on three synthetic scenarios and two real data sets. Results show that the proposed method outperforms linear and local models for several kinds of scenarios

Area-Efficient Linear Regression Architecture for Real-Time Signal Processing on FPGAs

Linear regression is a technique widely used in digital signal processing. It consists on finding the linear function that better fits a given set of samples. This paper proposes different hardware architectures for the implementation of the linear regression method on FPGAs, specially targeting area restrictive systems. It saves area at the cost of constraining the lengths of the input signal to some fixed values. We have implemented the proposed scheme in an Automatic Modulation Classifier, meeting the hard real-time constraints this kind of systems have.

A Generalized Regression Methodology for Bivariate Heteroscedastic Data

We present a methodology for reducing a straight line fitting regression problem to a Least Squares minimization one. This is accomplished through the definition of a measure on the data space that takes into account directional dependences of errors, and the use of polar descriptors for straight lines. This strategy improves the robustness by avoiding singularities and non-describable lines. The methodology is powerful enough to deal with non-normal bivariate heteroscedastic data error models, but can also supersede classical regression methods by making some particular assumptions. An implementation of the methodology for the normal bivariate case is developed and evaluated.