For any vector let and

For any vector , let , and . For , let The information matrix for the partial likelihood at Eq. (2.2) can be expressed as It is well known that Ciclopirox receptor under certain regularity conditions such as (A)–(D) in Andersen and Gill (1982), where and denote the maximum likelihood estimator from Eq. (2.2) and the true value of , respectively. Thus, an asymptotic 100% confidence region for can be constructed as follows, where is an empirical estimator of at Eq. (2.3) by plugging in for and is the th quantile of the chi-square distribution with degrees of freedom.
Simulation studies and applications
Discussions The proposed bias-corrected empirical likelihood method is developed under the framework of the sparse Cox regression model, and thus its performance relies on the proportional hazards assumption. The method should not be considered unless the Cox model is deemed as appropriate for real data. In case that the proportional hazards assumption is violated, one may use model-free selection approaches, such as those recently proposed by He et al. (2013) and Li et al. (2016). The current work is limited to dealing with a fixed number of parameters and further efforts may be taken to extend the methods when the dimensionality diverges. One potential way is to generalize the general multivariate model that was firstly proposed by Chen et al. (2009) and applied by Tang and Leng (2010) for linear regression with the diverging dimensionality.
Acknowledgments We are grateful to the Editor, the Associate Editor and the Reviewers for their constructive comments and insightful suggestions, which lead to significant improvement of the manuscript. Wu’s research was partly supportedby NIH, United States grants 2R01HLI9058-03A1, 4P30AI078498-09, and 4R01MH075017-09. Zhao was supported by NSA, United States Grant (H98230-12-1-0209) and NSF Grant (DMS-1613176).
Introduction One of the major genital disorders is erectile dysfunction which can be defined as an impairment of the ability to achieve and maintain a tone of erection sufficient for satisfactory sexual intercourse [1]. The prevalence of erectile dysfunction worldwide is estimated to be 1–10% for men below 40 years old, 20–40% for those of 60–70 years old and above 50% for those of 70–80 years old. In 2011, the prevalence of erectile dysfunction in Middle East has been reported to be almost 47% for those above 18 years old [2,3]. The penis in different species mostly consists of three corpora; two corpora cavernosa which are placed dorsally and a corpus spongiosum which is placed ventrally and surrounds the urethra [4]. The corpus cavernosum is composed of a sponge-like tissue which consists of a meshwork of interconnected spaces lined by a vascular endothelium and separated by trabecular smooth muscles [5]. In order to induce erection, the rate of blood flow into the corpus cavernosum must exceed the rate of drainage. The smooth muscles of the corpus cavernosum are relaxed resulting in increasing the blood flow into the corpus cavernosum and expansion of the sinusoids. This distension forms a mechanical pressure on the wall of the veins and impedes their drainage ability resulting in penile rigidity [6]. These events are mainly under central control, where different sorts of stimulation cause generation of nerve impulses and release of relaxant mediators peripherally which are balanced by contractant ones [7]. One of the major relaxant mediators involved is nitric oxide (NO), it is synthesized and released from the cavernous nerve and endothelium and is reported to be the main mediator involved in both neuronal and endothelial-dependent relaxation of corpus cavernosum [8]. The corpus cavernosal relaxation is mainly mediated through intracellular cyclic nucleotides; cyclic guanosine monophosphate (cGMP) and cyclic adenosine monophosphate (cAMP) and the subsequent activation of protein kinases through different pathways. Among these pathways is guanylyl cyclase (GC)/cGMP pathway. NO activates soluble GC (sGC) which in turn activates cGMP and subsequently cGMP-dependent protein kinase (PKG). As previously reported, PKG- by different mechanisms- reduces the availability of intracellular calcium (Ca2+) which in turn results in smooth muscle relaxation and penile erection [4].