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Truncated Estimate in Log-Binomial Model: Algorithm and Simulation

Problem statement: Relative risk has concrete meanings of comparing two groups and measuring the association between exposures and outcomes in medical and public health studies. Log-binomial model, using a log link function on binary outcomes, is straightforward to estimate risk ratios, whereas generates boundary problems. When the estimates are located near the boundary of constrained parameter space, common approaches or procedures using software such as R or SAS fail to converge. Approach: In this study we proposed a truncated algorithm to estimate relative risk using the log-binomial model. We used simulation studies on both single and multiple covariates models to investigate its performance and compare with other similar methods. Results: Our algorithm was shown to outperform other methods regarding precision, especially in high dimensional predictor space. Conclusion: The truncated IWLS method solves the slow convergence problem and provides valid estimates when previously proposed methods fail.

Measures of Explained Variation and the Base-Rate Problem for Logistic Regression

Problem statement: Logistic regression, perhaps the most frequently used regression model after the General Linear Model (GLM), is extensively used in the field of medical science to analyze prognostic factors in studies of dichotomous outcomes. Unlike the GLM, many different proposals have been made to measure the explained variation in logistic regression analysis. One of the limitations of these measures is their dependency on the incidence of the event of interest in the population. This has clear disadvantage, especially when one seeks to compare the predictive ability of a set of prognostic factors in two subgroups of a population. Approach: The purpose of this article is to study the base-rate sensitivity of several R² measures that have been proposed for use in logistic regression. We compared the base-rate sensitivity of thirteen R² type parametric and nonparametric statistics. Since a theoretical comparison was not possible, a simulation study was conducted for this purpose. We used results from an existing dataset to simulate populations with different base-rates. Logistic models are generated using the covariate values from the dataset. Results: We found nonparametric R² measures to be less sensitive to the base-rate as compared to their parametric counterpart. Logistic regression is a parametric tool and use of the nonparametric R² may result inconsistent results. Among the parametric R²measures, the likelihood ratio R² appears to be least dependent on the base-rate and has relatively superior interpretability as a measure of explained variation. Conclusion/Recommendations: Some potential measures of explained variation are identified which tolerate fluctuations in base-rate reasonably well and at the same time provide a good estimate of the explained variation on an underlying continuous variable. It would be, however, misleading to draw strong conclusions based only on the conclusions of this research only.

A Bayesian Method for Disentangling Dependent Structure of Epistatic Interaction

Problem statement: We propose a Bayesian method (RBP) to recursively infer the independence structure of epistatic interactions in case-control study. Approach: Based on the results of BEAM2, RBP can powerfully detect the marginal and conditional independence within interacting SNPs even in the complicated interaction cases. Results: We did extensive simulations to test RBP and compare it with stepwise logistic regression. Simulation results show that this approach is more powerful than stepwise logistic regression in detecting in marginal independence and conditional independence as well as more complicated dependence structure. We then applied BEAM2 and RBP on dbMHC Type 1 Diabetes (T1D) data and we found in MHC region, genes DRB1 and DQB1 are associated with T1D with saturated interaction structure which is consistent with the current knowledge of haplotype effect of these two genes on T1D. Conclusion: RBP is a powerful method to infer detailed dependence structures in epistatic interactions.

A Novel Technique for Extraction Foetal Electrocardiogram using Adaptive Filtering and Simple Genetic Algorithm

Problem statement: Foetal electrocardiogram (FECG) was the best method used to diagnose Foetal heart problem. Knowledge of the foetal heart signal prevents Foetal problems in the earlier stage. Recently, there has been a growing interest in noninvasive method rather than the old invasive method which was more risky for the mother�s health. The most significant problem in noninvasive method is the extraction of the Foetal signals from maternal signals and many contaminated noises. The problems of extraction of the Foetal signals are the problems that plagued researchers in the field of signal processing. Objective to develop a technique for extracting FECG signals based on adaptive filter and simple Genetic algorithm. Approach: Practical method for extraction using computer simulations was proposed. The proposed method detects Foetal ECG by denoising abdominal ECG (AECG) and lead to the subsequent cancellation of maternal ECG (MECG) by adaptive filtering. The thoracic signal (TECG) which is purely of Mother signal (MECG) was used to cancel MECG in abdominal signal and the Foetal ECG detector extracts the FECG through Simple Genetic algorithm which enters as the editor of unwanted noise. Results: The FECG signal which was obtained appears to agree with the standard Foetal ECG signals. A program for carrying out the calculations was developed in matlab. The testing of the algorithms was done by using real data from SISTA/DAISY and Physionet. Conclusion: the proposed technique for extraction of FECG was useful and the results appear to agree with the mean values of FECG.

Some Test Statistics for Testing the Binomial Parameter: Empirical Power Comparison

Problem statement: The Binomial distribution is one of the most useful probability distributions in the filed of quality control, physical and medical sceinces. Many questions of interest to the health worker related to make inference about the unknown population proportion, parameter of binomial distribution. This study considers the problem of hypotheses testing of the parameter of a binomial distribution. Approach: Different test statistics available in literature are reviewed and compared based on the empirical size and power properties. Since a theoretical comparison is not possible, a simulation study has been conducted to compare the performance of the test statistics. To illustrate the findings of the paper, two real life health related data are analyzed. Results: The simulation study suggests that some methods have better size and power properties than the other test statistics. The performnace of the proposed test statistics also depend on the hypothesized value of the binomial parameter. Conclusions/Recommendations: The practitioners should be careful about the hypothesized value of the binomial parameter p. If the hypothesized value is near 0.5, any test is acceptable for moderate to large sample size. However, for testing the end or small value of p, one might need very large sample size to have a good power and actual size of the test.

Application of a Statistical Model to Biological Data Analysis: Exclusive Breastfeeding

Problem statement: Breastfeeding is of utmost importance in the maternal life of a woman, particularly exclusive breastfeeding. Exclusive breastfeeding during the first 6 months of life supports optimal growth and development during infancy and reduces the risk of obliterating diseases and problems. Many probability distributions were proposed to model such data such as the mixed Poisson distributions. However, the estimation methodologies based on such mixed Poisson distributions may be complicated and may not yield consistent and efficient regression estimates. Approach: In this study, we proposed a negative-binomial regression model to analyze the local practices of exclusive breastfeeding and factors affecting this practice. Results: The estimation of parameters is carried out using a quasi-likelihood estimation technique based on a marginal approach via Newton-Raphson iterative procedure. Conclusion: The negative binomial distribution is applied on a sample of data on infant feeding practices in 2006 and has yielded reliable estimates of the regression and over-dispersion parameters.

Comparisons of Test Statistics for Noninferiority Test for the Difference between Two Independent Binominal Proportions

Problem statement: Noninferiority tests are frequently used in clinical trials to demonstrate that the response for study drugs is not much worse than the response for reference drugs. Several test statistics exist. However, a detailed comparison of those test statistics is not researched. Moreover, a little complex calculation might be necessary in some of those test statistics. Approach: In this study, we investigated the performance of the existing test statistics and propose new test statistics. Further, we compare them with existing test methods by means of simulation and devise a suitable technique of using of these test statistics. Results: We found that for the proposed test statistics, the actual type I error was close to the nominal level. Further, when the sample size is moderate it is found that, the new test statistics have a little higher power than other test statistics. Conclusion: One of the biggest advantages of our method is that it does not require complicated calculations.

Design Based on Intra-Class Correlation Coefficients

Problem statement: Reliability studies are concerned with the study of �consistency� or �repeatability� of measurements. Often times (but not always) the reliability coefficients are Intra-class Correlation Coefficients (ICC). Depending on the design or the conceptual intent of the study there are three types of intra-class correlation coefficients, termed intra-class correlation coefficients Case 1, 2 and 3, for measuring the reliability of a single interval measure. While methods for sample size calculations for intra-class correlation coefficients in Case 1 are available and implemented in PASS (Power Analysis and Sample Size System); to our knowledge, no methods based on intra-class correlation coefficients in Case 2 and 3 are available. Develop a method for calculating the size of a reliability study based using intra-class correlation coefficients Case 1 and 2. Approach: A practical method for computing sample size using simulations was proposed. We proposed to compute sample size based on the expected width of the confidence interval. For a given target value of the intra-class correlation coefficient, the proposed method chooses the design assures a 95% confidence interval with average length shorter than a pre-specified value. The applicability of the proposed method in practice for intra-class coefficients Case 2 was supported by demonstrating three invariance properties of the proposed confidence intervals. Results: Tables with sample size requirements were derived and displayed. A program for carrying out the calculations was developed in R. The method was used to size a trial aimed to study the reliability of a scale that measures the cleanness of the colon at the time of colonoscopy. Conclusion: A simple method for sample size calculation for intra-class correlation coefficient Case 1 and 2 based on the average length of confidence intervals was proposed. The proposed was implemented by the authors in R (freely available software). Three invariance properties of the confidence intervals for the intra-class correlation coefficients Case 2 were studied by simulations. These properties are an important tool when considering the design of this type of studies.

Measure for No Three-Factor Interaction Model in Three-Way Contingency Tables

Problem statement: For 2�2�K contingency tables, the measure is considered to represent the degree of departure from a log-linear model of No Three-Factor Interaction (NOTFI). We are interested in considering a similar measure for general I�J�K contingency tables. Approach: The present study proposed a measure to represent the degree of departure from the NOTFI model for I�J�K contingency tables. Also the approximate confidence interval for the proposed measure is given. Results: The proposed measure was applied and analyzed (1) for a 3�4�4 cross-classification data of dumping severity, hospital and operation which treat duodenal ulcer patients corresponding to removal of various amounts of the stomach and (2) for a 2�3�4 cross-classification data of experiment of animals (mouse and rat) on cancer (the tumor of leukemia and lymphoma) and tolazamide. Conclusion: The proposed measure is useful for comparing the degrees of departure from the NOTFI model in several tables.

Measure of Departure from Average Cumulative Symmetry for Square Contingency Tables with Ordered Categories

Problem statement: For square contingency tables with ordered categories, we are interested in considering a structure of weak symmetry when Bowker�s symmetry model does not hold and in measuring the degree of departure from weak symmetry. Approach: The present study considered the average cumulative symmetry model that has a weaker restriction than the structure of symmetry. It also gave a measure to represent the degree of departure from average cumulative symmetry. When the conditional symmetry and the cumulative linear diagonals-parameter symmetry holds, the proposed measure can measure what degree of departure from the symmetry is. Results: The proposed model and the measure were applied and analyzed (1) for the data of 4�4 contingency table of unaided distance vision of 7477 women aged 30-39 employed in Royal Ordnance factories in Britain from 1943-1946 and (2) the data of 4�4 contingency table of the 59 matched pairs using from dose levels of conjugated oestrogen. Conclusion: The proposed model is useful when the symmetry model does not hold and the proposed measure is useful for comparing the degree of departure from the weak symmetry model in several tables. Especially the proposed measure is useful to measure the degree of departure from symmetry when the conditional symmetry (the cumulative diagonalsparameter symmetry) model holds.