Statistical modeling of causal effects in continuous time

This article studies the estimation of the causal effect of a time-varying treatment on time-to-an-event or on some other continuously distributed outcome. The paper applies to the situation where treatment is repeatedly adapted to time-dependent patient characteristics. The treatment effect cannot be estimated by simply conditioning on these time-dependent patient characteristics, as they may themselves be indications of the treatment effect. This time-dependent confounding is common in observational studies. Robins [(1992) Biometrika 79 321--334, (1998b) Encyclopedia of Biostatistics 6 4372--4389] has proposed the so-called structural nested models to estimate treatment effects in the presence of time-dependent confounding. In this article we provide a conceptual framework and formalization for structural nested models in continuous time. We show that the resulting estimators are consistent and asymptotically normal. Moreover, as conjectured in Robins [(1998b) Encyclopedia of Biostatistics 6 4372--4389], a test for whether treatment affects the outcome of interest can be performed without specifying a model for treatment effect. We illustrate the ideas in this article with an example.Comment: Published in at http://dx.doi.org/10.1214/009053607000000820 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Domestic Violence As A Factor In Custody Determinations In New York State

In 1996, the New York State Legislature mandated that rial courts consider the effect of domestic violence in child custody and visitation disputes. In 1998, the legislature amended the law to provide that, under most circumstances, a person convicted of murdering a child\u27s parent shall be denied custody and visitation. The amendment was in response to a growing national trend to give greater attention to the serious effect domestic violence has on children. While the law now conveys the seriousness with which the legislature view domestic violence, many problems inherent in resolving custody and visitation disputes involving domestic violence still remain. This essay examines the legislation and case law arising out of this issue, identifying remaining problems and judicial responses. Additional interventions are suggested to assist in the appropriate resolution of these cases

The effect of high school rank in English and math on college major choice. ESRI Working Paper No. 650 January 2020

Using unique data on preference rankings for all high school students who apply for college in Ireland, we investigate whether, conditional on absolute achievement, within school-cohort rank in English and math affects choice of college major. We find that higher rank in math increases the likelihood of choosing STEM and decreases the likelihood of choosing Arts and Social Sciences. Similarly, a higher rank in English leads to an increase in the probability of choosing Arts and Social Sciences and decreases the probability of choosing STEM. The rank effects are substantial, being about one third as large as the effects of absolute performance in math and English. We identify subject choice in school as an important mediator – students who rank high in math are more likely to choose STEM subjects in school and this can partly explain their subsequent higher likelihood of choosing STEM for college. We also find that English and math rank have significant explanatory power for the gender gap in the choice of STEM as a college major--they can explain about 36% as much as absolute performance in English and math. Overall, the tendency for girls to be higher ranked in English and lower ranked in math within school-cohorts can explain about 6% of the STEM gender gap in mixedsex schools and about 16% of the difference in the STEM gender gap between mixedsex schools and same-sex schools. Notably, these effects occur even though within-school rank plays no role whatsoever in college admissions decisions

Matrix Roots of Eventually Positive Matrices

Eventually positive matrices are real matrices whose powers become and remain strictly positive. As such, eventually positive matrices are a fortiori matrix roots of positive matrices, which motivates us to study the matrix roots of primitive matrices. Using classical matrix function theory and Perron-Frobenius theory, we characterize, classify, and describe in terms of the real Jordan canonical form the $p$th-roots of eventually positive matrices.Comment: Accepted for publication in Linear Algebra and its Application