Estimating optimal treatment regimes in survival contexts using an instrumental variable

In survival contexts, substantial literature exists on estimating optimal treatment regimes, where treatments are assigned based on personal characteristics for the purpose of maximizing the survival probability. These methods assume that a set of covariates is sufficient to deconfound the treatment-outcome relationship. Nevertheless, the assumption can be limiting in observational studies or randomized trials in which noncompliance occurs. Thus, we advance a novel approach for estimating the optimal treatment regime when certain confounders are not observable and a binary instrumental variable is available. Specifically, via a binary instrumental variable, we propose two semiparametric estimators for the optimal treatment regime, one of which possesses the desirable property of double robustness, by maximizing Kaplan-Meier-like estimators within a pre-defined class of regimes. Because the Kaplan-Meier-like estimators are jagged, we incorporate kernel smoothing methods to enhance their performance. Under appropriate regularity conditions, the asymptotic properties are rigorously established. Furthermore, the finite sample performance is assessed through simulation studies. We exemplify our method using data from the National Cancer Institute's (NCI) prostate, lung, colorectal, and ovarian cancer screening trial

Partial Replacement Imputation Estimation Method for Complex Missing Covariates in Additive Partially Linear Models

Missing data is a common problem in clinical data collection, which causes difficulty in the statistical analysis of such data. In this article, we consider the problem under a framework of a semiparametric partially linear model when observations are subject to missingness with complex patterns. If the correct model structure of the additive partially linear model is available, we propose to use a new imputation method called Partial Replacement IMputation Estimation (PRIME), which can overcome problems caused by incomplete data in the partially linear model. Also, we use PRIME in conjunction with model averaging (PRIME-MA) to tackle the problem of unknown model structure in the partially linear model. In simulation studies, we use various error distributions, sample sizes, missing data rates, covariate correlations, and noise levels, and PRIME outperforms other methods in almost all cases. With an unknown correct model structure, PRIME-MA has satisfactory performance in terms of prediction, while slightly worse than PRIME. Moreover, we conduct a study of influential factors in Pima Indians Diabetes data, which shows that our method performs better than the other models.Comment: 28 pages, 8 figures and 6 table

Engineering the Phases and Heterostructures of Ultrathin Hybrid Perovskite Nanosheets

Low-dimensional perovskites have gained increasing attention recently, and engineering their material phases, structural patterning and interfacial properties is crucial for future perovskite-based applications. Here a phase and heterostructure engineering on ultrathin perovskites, through the reversible cation exchange of hybrid perovskites and efficient surface functionalization of low-dimensional materials, is demonstrated. Using PbI2 as precursor and template, perovskite nanosheets of varying thickness and hexagonal shape on diverse substrates is obtained. Multiple phases, such as PbI2, MAPbI3 and FAPbI3, can be flexibly designed and transformed as a single nanosheet. A perovskite nanosheet can be patterned using masks made of 2D materials, fabricating lateral heterostructures of perovskite and PbI2. Perovskite-based vertical heterostructures show strong interfacial coupling with 2D materials. As a demonstration, monolayer MoS2/MAPbI3 stacks give a type-II heterojunction. The ability to combine the optically efficient perovskites with versatile 2D materials creates possibilities for new designs and functionalities

Engineering the Phases and Heterostructures of Ultrathin Hybrid Perovskite Nanosheets

Low-dimensional perovskites have gained increasing attention recently, and engineering their material phases, structural patterning and interfacial properties is crucial for future perovskite-based applications. Here a phase and heterostructure engineering on ultrathin perovskites, through the reversible cation exchange of hybrid perovskites and efficient surface functionalization of low-dimensional materials, is demonstrated. Using PbI2 as precursor and template, perovskite nanosheets of varying thickness and hexagonal shape on diverse substrates is obtained. Multiple phases, such as PbI2, MAPbI3 and FAPbI3, can be flexibly designed and transformed as a single nanosheet. A perovskite nanosheet can be patterned using masks made of 2D materials, fabricating lateral heterostructures of perovskite and PbI2. Perovskite-based vertical heterostructures show strong interfacial coupling with 2D materials. As a demonstration, monolayer MoS2/MAPbI3 stacks give a type-II heterojunction. The ability to combine the optically efficient perovskites with versatile 2D materials creates possibilities for new designs and functionalities