The subgroup commutativity degree sd(G) of a finite group G was introduced almost ten years ago and deals with the number of commuting subgroups in the subgroups lattice L(G) of G. The extremal case sd(G) = 1 detects a class of groups classified by Iwasawa in 1941 (in fact sd(G) represents a probabilistic measure which allows us to understand how far is G from the groups of Iwasawa). Among them we have sd(G) = 1 when L(G) is distributive, that is, when G is cyclic. The characterization of a cyclic group by the distributivity of its lattice of subgroups is due to a classical result of Ore in 1938. Therefore sd(G) is strongly related to structural properties of L(G). Here we introduce a new notion of probability gsd(G) in which two arbitrary sublattices S(G) and T(G) of L(G) are involved simultaneously. In case S(G) = T(G) = L(G), we find exactly sd(G). Upper and lower bounds in terms of gsd(G) and sd(G) are among our main contributions, when the condition S(G) = T(G) = L(G) is removed. Then we investigate the problem of counting the pairs of commuting subgroups via an appropriate graph. Looking at the literature, we noted that a similar problem motivated the permutability graph of non–normal subgroups ΓN (G) in 1995, that is, the graph where all proper non– normal subgroups of G form the vertex set of ΓN (G) and two vertices H and K are joined if HK = KH. The graph ΓN (G) has been recently generalized via the notion of permutability graph of subgroups Γ(G), extending the vertex set to all proper subgroups of G and keeping the same criterion to join two vertices. We use gsd(G), in order to introduce the non–permutability graph of subgroups ΓL(G) ; its vertices are now given by the set L(G) − CL(G)(L(G)), where CL(G)(L(G)) is the smallest sublattice of L(G) containing all permutable subgroups of G, and we join two vertices H, K of ΓL(G) if HK 6= KH. We finally study some classical invariants for ΓL(G) and find numerical relations between the number of edges of ΓL(G) and gsd(G).

We define a strong form of subgroup separability, which we call RS separability, and we use this to combine LERF and Agol’s RFRS condition on groups into a property called LVRSS. We show that some infinite classes of groups that are known to be both subgroup separable and virtually RFRS are also LVRSS. We also provide evidence for the naturalness of RS separability and LVRSS by showing that they are preserved under various operations on groups. / text

Geographic access to cancer care is an important dimension of quality of cancer care. Previous studies have shown that the more uncertain medical evidence is, the more geographic variation is observed in the medical care utilization that is attributable to local care health care system capacity and local area patient/physician preferences. Chemotherapy for metastatic breast cancer (MBC) is such a case. Although clinical trials have proven the efficacy of chemotherapy in treating MBC, whether to treat elderly MBC patients with chemotherapy is uncertain because of the underrepresentation of elderly patients in the clinical trials. As age advances, uncertainties increase due to competing causes of death, limited life expectancy, and higher risk of toxicities. As a result, geographic access may matter more in chemotherapy choice for older patients than for younger patients. Literature has shown that older patients are less likely to be treated with chemotherapy. In this study, we examined the effect of access to cancer care on age-related difference in chemotherapy use for elderly MBC patients. Access to cancer care is measured by four variables, including travel time to the nearest oncologist practice, local area per capita number of oncologists among stage IV cancer patients, local area per capita number of hospices among stage IV cancer patients, and local area chemotherapy percentage among stage IV cancer patients. The retrospective cohort study used the 1992-2002 SEER-Medicare database. Chemotherapy use was defined as at least one chemotherapy-related claim within 6 months post diagnosis. To examine the age variant effect of access on chemotherapy choice, the analysis adopted both interaction term approach and subgroup analysis. In interaction term analysis, product term between age and access dummy variables were specified in the multivariate logistic regression model controlling for other covariates; in subgroup analysis, age subgroups were specified consistently with interaction term approach. For each age subgroup, we used multivariate logistic regression to estimate the effect of access to cancer care on immediate chemotherapy use controlling for covariates. Among 4533 elderly patients with MBC, 30.16% used chemotherapy. Chemotherapy rate decreased with age. Interaction term approach did not show significant interaction between age and access in each specification. Both interaction term and subgroup analysis showed that the local area treatment rate was positively associated with immediate chemotherapy use across patient age. In addition, subgroup analysis showed among patients who were 85+ years old, the local area oncologist supply was negatively associated with chemotherapy use. This effect was not observed among younger age groups. Our results suggest that estimating all patients in one equation with dummies and interactions can hide results. By estimating each group separately, subgroup analysis showed that provider access is paramount for age subgroup 85 years or older. Our access measures suggest that access to cancer care affects chemotherapy choice among elderly patients whose clinical evidence is uncertain. This can be attributable to local practice style and physician concern of real benefits of chemotherapy. The local area chemotherapy practice styles affect chemotherapy choice for patients across age except patients aged between 80 to 84 years old; provider access plays an important role for patients 85 years or older. The more certain the evidence with age, the more access may affect chemotherapy choice.

No description available.

This dissertation examines the impact of Georgia’s accountability system on both school and student performance. We focus on two components within Georgia’s accountability system – the sanctioning of failing schools and binding subgroup requirements. Schools within Georgia become subject to sanctions upon two consecutive years of failing to show Adequate Yearly Progress (AYP). The subgroup binding requirements, introduced by the No Child Left Behind (NCLB) Act, hold schools independently responsible for the performance of given subgroups contingent upon enrollment. The first question of this dissertation examines the factors that influence a school’s ability to meet assessment standards. We examine the relative importance of school characteristics, as they relate to accountability components, in determining AYP in practice. A binary response model is used as AYP is determined on a pass/fail basis. More specifically, we apply a correlated random effects probit model with a Chamberlain-Mundlak adjustment. The second question of this dissertation examines the impact of binding requirements on subgroup performance, where subgroup performance is defined as the percentage of students scoring at or above proficiency. We employ a regression discontinuity design that compares the performance of bounded and unbounded subgroups to determine the treatment effect. Each question of this dissertation is addressed through evaluating both mean and distributional effects. We find that imposing sanctions on failing schools has a positive impact on future performance. However, increasing the number of binding requirements has a negative impact on a school’s probability of passage. This result suggests that heterogeneous schools, or schools with several large subgroup populations, are negatively impacted by the requirement. While we find that accountability components have a statistically significant impact on probability of AYP passage, factors related to school resources and quality appear to have a greater influence. The mechanism for the negative impact of binding requirements remains unidentified as we also find that binding requirements have a slight positive impact on individual subgroup performance. The magnitude of this impact is dependent upon the subgroup examined, school type, and position of the subgroup within the Meets/Exceeds distribution. Overall, our results suggest the need for re-examination of the binding requirements as a method of targeting disadvantaged populations.

University, Diss., 2005--Bonn.

The subgroup identification field which sometimes is called personalized medicine, tries to group individuals such that the effects of a treatment are the most beneficial for them. One of the methods developed for this purpose is called PSICA. Currently this method works in a setting of multiple treatments and real valued response variables. In this thesis, this methodology is extended to the degree that it can also handle ordinal response variables that can take a finite number of values. It is also compared to a competitor method which results in similar performance but with the added value of a probabilistic output and a model that is interpretable and ready for policy making. This is achieved at the expense of a higher execution time. Finally, this extension is applied to a longitudinal study done in Nicaragua in the los Cuatro Santos population in which some interventions were applied in order to reduce poverty. The results showed which were the most beneficial treatments for different population subgroups.

Indiana University-Purdue University Indianapolis (IUPUI) / Subgroup analyses assess the heterogeneity of treatment effects in groups of patients defined by patients’ baseline characteristics. Identifying subgroup of patients with differential treatment effect is crucial for tailored therapeutics and personalized medicine. Model-based variable selection methods are well developed and widely applied to select significant treatment-by-covariate interactions for subgroup analyses. Machine learning and data-driven based methods for subgroup identification have also been developed. In this dissertation, I consider two different types of subgroup identification methods: one is nonparametric machine learning based and the other is model based. In the first part, the problem of subgroup identification was transferred to an optimization problem and a stochastic search technique was implemented to partition the whole population into disjoint subgroups with differential treatment effect. In the second approach, an integrative three-step model-based variable selection method was proposed for subgroup analyses in longitudinal data. Using this three steps variable selection framework, informative features and their interaction with the treatment indicator can be identified for subgroup analysis in longitudinal data. This method can be extended to longitudinal binary or categorical data. Simulation studies and real data examples were used to demonstrate the performance of the proposed methods. / 2022-05-06

No description available.

The prevalence rate of childhood obesity has increased rapidly worldwide. The childhood obesity epidemic is associated with many adverse health consequences in children as well as a financial burden for a nation’s economy. A meta-analysis was conducted to investigate the effectiveness of school-based childhood obesity prevention programs in preventing childhood obesity. The objectives of this study were to 1) identify the most effective childhood obesity prevention programs through effect size comparison, and 2) identify important program components that affect the effectiveness of the intervention through subgroup analysis. The Comprehensive Meta-Analysis (CMA) program was used for all statistical analyses. Results of the meta-analysis demonstrated that the summary effect size was small (d = 0.039, 95% confidence interval). The school-based program identified in the meta-analysis as the most effective had a d value of 0.368. Subgroup analyses were performed because this meta-analysis study was heterogeneous (Q = 167.774, p = 0.001) with an I2 value of 68.410%. The subgroup moderators were length of program duration, age of participants, nutrition, physical activity, parental involvement, specialist involvement, and theory based versus non-theory based intervention programs. Subgroup analyses demonstrated that significant differences (p < 0.05) occurred among the moderator components. Programs that targeted younger children less than ten years old and programs that were theory based were more effective. The meta-analysis study contained publication bias because the funnel plot was skewed and smaller studies were missing. To further explore the publication bias problem, Classic fail-safe N and Duval and Tweedie’s trim and fill analyses were performed. Classic fail-safe N indicated that two programs were missing from the present study to achieve a non-biased result. The Duval and Tweedie’s trim and fill analysis demonstrated that a small mean effect size difference was detected between the present observed studies and the unbiased effect size. The small mean effect size difference indicated that the results and the reported effect sizes in this meta-analysis study were valid.