Point and Interval Estimations of Marginal Risk Difference by Logistic Model

We use logistic model to get point and interval estimates of the marginal risk difference in observational studies and randomized trials with dichotomous outcome. We prove that the maximum likelihood estimate of the marginal risk difference is unbiased for finite sample and highly robust to the effects of dispersing covariates. We use approximate normal distribution of the maximum likelihood estimates of the logistic model parameters to get approximate distribution of the maximum likelihood estimate of the marginal risk difference and then the interval estimate of the marginal risk difference. We illustrate application of the method by a real medical example.     

Circular functional relationships

This paper develops techniques for fitting a circular functional relationship. The model is formulated assuming the centre of the circle is known and taken to be the origin. This incurs some loss of generality, but considerably simplifies the analysis. Methods of estimating the parameters of the relationship, assuming that the co-ordinates have uncorrelated errors with equal variance, are developed and compared by way of simulations. Consistent estimators are obtained from unbiased estimating equations and by maximising the marginal likelihood. Approximate estimators are obtained by approximating the estimating equations and by maximising a modified profile likelihood function. The ideas and methodology are then applied to the relationship with the more realistic assumption of an unknown centre, with an example highlighting the differences between estimation techniques.     

On the Test of Significance of Linear Multiple Regression Coefficients

The t-statistic used in the existing literature for testing the significance of linear multiple regression coefficients has only a limited use in testing the marginal significance of explanatory variables though it is used in testing the partial significance also. This article identifies the t-statistic appropriate for testing the partial significance.     

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