background: identification of disease risk factors can help in the prevention of diseases. in assessing the predictive value of continuous variables, a routine procedure is to categorize the factors. this yield to inability to detect non‑linear relationship, if exist. multivariate fractional polynomial (mfp) modeling is a flexible method to reveal non‑linear associations. we aim to demonstrate ...

Math 394 1 (Almost bullet-proof) Definition of Expectation Assume we have a sample space Ω, with a σ−algebra of subsets F , and a probability P , satisfying our axioms. Define a random variable as a a function X : Ω → R, such that all subsets of Ω of the form {ω |a < X(ω) ≤ b}, for any real a ≤ b are events (belong to F). Assume at first that the range of X is bounded, say it is contained in th...

The complementary log-log is an alternative to logistic model. In many areas of research, the outcome data are continuous. We aim to provide a procedure that allows the researcher to estimate the coefficients of the complementary log-log model without dichotomizing and without loss of information. We show that the sample size required for a specific power of the proposed approach is substantial...

This paper introduces an influence diagram (ID) model that permits continuous decision variables with multiple continuous parents. The marginalization operation for a continuous decision variable first develops a piecewise linear decision rule as a continuous function of the next continuous parent in the deletion sequence. Least squares regression is used to convert this rule to a piecewise lin...