Objectives: To compare the pubertal development, the hormonal profiles and the prevalence of hirsutism and menstrual disorders in obese adolescent girls and adolescent girls with type 1 diabetes mellitus (T1DM). Methods: Data were collected from 96 obese adolescent girls and 78 adolescent girls with T1DM at Tanner stage IV or V, whose ages ranged between 11.9 and 17.9 years. Results: High prevalence of hirsutism and menstrual disorder was found in the obese adolescent girls (36.5 and 42% respectively) and the adolescent girls with T1DM (21 and 44% respectively). The obese girls were significantly younger at pubarche, thelarche and menarche than the girls with T1DM. Hirsutism in the obese girls and those with T1DM was associated with hyperandrogenaemia and a raised free androgen index (FAI). When the cause of the raised FAI was investigated in both the groups of girls with hirsutism, the raised FAI in the obese girls was due to low serum sex hormone-binding globulin (SHBG) levels. In contrast, the raised FAI of the girls with T1DM and hirsutism was due to hyperandrogenaemia. Menstrual disorders in the T1DM girls were associated also with hyperandrogenaemia unlike obese girls. Conclusions: Hirsutism and menstrual disorders are common in obese adolescent girls and adolescent girls with T1DM. Although hyperandrogenaemia is present in both groups of girls, the androgenic profiles of the two groups differ. The hyperandrogenaemia in the obese girls is primarily due to their decreased serum SHBG levels, whereas the hyperandrogenaemia in the girls with T1DM is due to their increased androgen production.

This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a function of its summands as their number tends to infinity. In the large deviation range of the conditioning event it extends the Gibbs conditional principle in the sense that it provides a description of the distribution of the random walk on long subsequences. An approximation of the density of the runs is also obtained when the conditioning event states that the end value of the random walk belongs to a thin or a thick set with a nonempty interior. The approximations hold either in probability under the conditional distribution of the random walk, or in total variation norm between measures. An application of the approximation scheme to the evaluation of rare event probabilities through importance sampling is provided. When the conditioning event is in the range of the central limit theorem, it provides a tool for statistical inference in the sense that it produces an effective way to implement the Rao-Blackwell theorem for the improvement of estimators; it also leads to conditional inference procedures in models with nuisance parameters. An algorithm for the simulation of such long runs is presented, together with an algorithm determining the maximal length for which the approximation is valid up to a prescribed accuracy.Comment: Published in at http://dx.doi.org/10.1214/13-AAP975 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:1010.361

Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events En := (u(X1) + ... + u(Xn)) ∈ An where the summands are i.i.d. and En is a large or moderate deviation event. The approximation of the conditional density of the vector (X1, ..., X kn ) with respect to En on long runs, when kn/n → 1, is handled. The maximal value of kn compatible with a given accuracy is discussed; simulated results are presented, which enlight the gain of the present approach over classical IS schemes. Detailed algorithms are proposed.