Sufficient Covariate, Propensity Variable and Doubly Robust Estimation

Statistical causal inference from observational studies often requires adjustment for a possibly multi-dimensional variable, where dimension reduction is crucial. The propensity score, first introduced by Rosenbaum and Rubin, is a popular approach to such reduction. We address causal inference within Dawid's decision-theoretic framework, where it is essential to pay attention to sufficient covariates and their properties. We examine the role of a propensity variable in a normal linear model. We investigate both population-based and sample-based linear regressions, with adjustments for a multivariate covariate and for a propensity variable. In addition, we study the augmented inverse probability weighted estimator, involving a combination of a response model and a propensity model. In a linear regression with homoscedasticity, a propensity variable is proved to provide the same estimated causal effect as multivariate adjustment. An estimated propensity variable may, but need not, yield better precision than the true propensity variable. The augmented inverse probability weighted estimator is doubly robust and can improve precision if the propensity model is correctly specified

Semiparametric theory and empirical processes in causal inference

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss estimation and inference for causal effects under semiparametric models, which allow parts of the data-generating process to be unrestricted if they are not of particular interest (i.e., nuisance functions). These models are very useful in causal problems because the outcome process is often complex and difficult to model, and there may only be information available about the treatment process (at best). Semiparametric theory gives a framework for benchmarking efficiency and constructing estimators in such settings. In the second part of the paper we discuss empirical process theory, which provides powerful tools for understanding the asymptotic behavior of semiparametric estimators that depend on flexible nonparametric estimators of nuisance functions. These tools are crucial for incorporating machine learning and other modern methods into causal inference analyses. We conclude by examining related extensions and future directions for work in semiparametric causal inference

A review of spatial causal inference methods for environmental and epidemiological applications

The scientific rigor and computational methods of causal inference have had great impacts on many disciplines, but have only recently begun to take hold in spatial applications. Spatial casual inference poses analytic challenges due to complex correlation structures and interference between the treatment at one location and the outcomes at others. In this paper, we review the current literature on spatial causal inference and identify areas of future work. We first discuss methods that exploit spatial structure to account for unmeasured confounding variables. We then discuss causal analysis in the presence of spatial interference including several common assumptions used to reduce the complexity of the interference patterns under consideration. These methods are extended to the spatiotemporal case where we compare and contrast the potential outcomes framework with Granger causality, and to geostatistical analyses involving spatial random fields of treatments and responses. The methods are introduced in the context of observational environmental and epidemiological studies, and are compared using both a simulation study and analysis of the effect of ambient air pollution on COVID-19 mortality rate. Code to implement many of the methods using the popular Bayesian software OpenBUGS is provided

The reproductive biology of Euchaeta antarctica Giesbrecht (Copepoda: Calanoida) at South Georgia

The reproductive biology of the predatory calanoid copepod Euchaeta antarctica Giesbrecht was investigated in two interconnected fjord systems at South Georgia. Counts of the number of spermatophores attached to adult females and the number of egg sacs encountered, indicated probable peaks of reproduction in summer and winter. Patterns of spermatophore placement were examined and compared with data for E. norvegica (Boeck) from boreal waters. Elemental analysis indicated a high proportion of carbon and a low proportion of nitrogen in adult females and egg sacs from both sites. High winter carbon levels in adults seem related to their predatory feeding habits allowing high food intake throughout the year whereas in egg sacs it probably reflects extended development times and/or non-feeding naupliar stages. Mean adult female and egg clutch dry weights were higher in Cumberland East Bay during winter than in Moraine Fjord during summer. These differences are discussed in the context of relationships between fjord morphology and production levels

Immunoflow cytometry and cell block immunohistochemistry in the FNA diagnosis of lymphoma: a review of 73 consecutive cases

Aims—To review the results of 73 consecutive fine needle aspirations (FNAs) that were collected by a pathologist and analysed by immunoflow cytometry. Material for a cell block was also collected from some of these lesions. Methods—The setting was a large general hospital in rural New Zealand. The FNAs were performed by a pathologist, or a radiologist for image guided localisations. Material for immunoflow cytometry was collected into RPMI and, when required, material for a cell block was collected into formalin. Results—Of the 73 samples collected by FNA nine were inadequate. Light chain restriction could be demonstrated in most FNA samples from B cell lymphomas (28 of 30 adequate samples). The exceptions were two cases of T cell rich B cell lymphoma. Artefactual light chain restriction was seen occasionally in T cell lymphomas, presumably as a result of autoantibodies binding to the cell surfaces. It was possible to subtype most (18 of 30 adequate samples) B cell lymphomas as chronic lymphocytic leukaemia (CLL), follicle centre cell lymphoma (FCCL), or mantle cell lymphoma. The CD4 to CD8 ratio was not usually restricted in T cell lymphomas and coexpression of CD4 and CD8 was not usually found. Loss of pan-T cell antigens was seen in some T cell lymphomas. Four of the six T cell lymphomas and three of the four non-lymphoid malignancies were diagnosed with the aid of cell block immunohistochemistry. Only one of the four cases of Hodgkin's lymphoma showed Reed-Sternberg cells in the FNA smears. Conclusions—It is not always possible to characterise lymphomas as fully with FNA and immunoflow cytometry as is possible with biopsy histology and a full battery of modern investigations. Nevertheless, in the setting of a large rural general hospital immunoflow cytometry on FNA samples is a highly effective method of diagnosing and typing B cell lymphomas. Immunoflow cytometry is of little use for T cell lymphomas or Hodgkin's lymphomas. We advocate the use of cell block immunohistochemistry in preference to immunoflow cytometry for cases in which the cytological appearance of the specimen is overtly malignant but the differential diagnosis includes non-lymphoid malignancy. Key Words: lymphoma • flow cytometry • cell blocks • immunolabelling • fine needle aspiratio