A Trivariate Weibull Model for Oestradiol Plus Progestrone Treatment Increases Serum Leptin Concentrations in Normal Premenopasual Women

In the previous studies a hypothesis was developed from the results by using trivariate Weibull model that the increase in leptin concentrations during the second half of the menstrual cycle may be related to changes in the steroidal milieu during the pre ovulatory period and the luteal phase. The present study was undertaken to test this hypothesis further by examining the effect of treatment with oestradiol and progesterone on leptine concentrations in normal pre menopausal women. The trivariate Weibull model is used for finding survival functions and log-likelihood functions for corresponding values of oestradiol, LH and Leptin for both untreated and treated with oestradiol and oestradiol plus progesterone respectively. Keyword: Trivariate Weibull, LH, Leptin, oestradiol and progesterone I. Mathematical Model 1.1 Trivariate Weibull Distribution: Lu and Bhattacharya [5] developed a joint survival function by letting h1(x) and h2(y) be two arbitrary failure rate functions on [0,∞), and H1(x) and H2(y) be their corresponding cumulative failure rate. Given the stress S=s > 0, the joint survival function conditioned on s, as they defined is, F (x,y/s)=exp{[H1(x) + H2(y)]s}, where γ measures the conditional association of X and Y. Further, based on the joint survival function, they proved a theorem that a bivariate survival function F (x,y/s) can be derived with the marginals F x and F y given the assumption that the Laplace transform of the stress S exists on [0,∞) and is strictly decreasing. From the theorem, they derived a bivariate Weibull Distribution