Motivated by a recent tuberculosis (TB) study, this paper is concerned with covariates missing not at random (MNAR) and models the potential intracluster correlation by a frailty. We consider the regression analysis of right‐censored event times from clustered subjects under a Cox proportional hazards frailty model and present the semiparametric maximum likelihood estimator (SPMLE) of the model parameters. An easy‐to‐implement pseudo‐SPMLE is then proposed to accommodate more realistic situations using readily available supplementary information on the missing covariates. Algorithms are provided to compute the estimators and their consistent variance estimators. We demonstrate that both the SPMLE and the pseudo‐SPMLE are consistent and asymptotically normal by the arguments based on the theory of modern empirical processes. The proposed approach is examined numerically via simulation and illustrated with an analysis of the motivating TB study data. 相似文献
High population growth in the tropics is driving urbanisation, removing diverse natural ecosystems. This is causing native species to suffer while introduced synanthropes flourish. City planners are developing urban greenspace networks, in part trying to address this issue. Architects contribute to these greenspace networks by designing elevated and ground level green spaces on large-scale buildings. However, little evidence is available on whether building green spaces support native fauna. This is true for birds in tropical Singapore that support important ecosystem services and have existence value. Therefore, in this study, we conducted bird surveys and statistical analyses to determine, if and how vegetation on three building green space types (ground gardens, roof gardens and green walls) have a positive impact on native or introduced bird species. We found that elevated greenery (roof gardens and green walls) on large-scale buildings supported a higher richness of birds and abundance of urban native birds than control roofs and walls without vegetation. Ground gardens supported similar levels of native species as roof gardens but also a larger proportion of generalist synanthropes. However, we found no tropical forest habitat specialists across any space type. Therefore, we recommend roof gardens and ground gardens as a potential space for urban natives outside of a less competitive ground-level urban environment. Our study also found certain building design elements (height of elevated space, presence of specific plants) supported different species groups. Therefore, we suggest that these ecological requirements for different species groups are considered when designing a building’s green space.
