Mathematical Sciences
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Mathematical research at MSU is focused primarily on related topics in pure and applied mathematics. Research programs complement each other and are often applied to problems in science and engineering. Research in statistics encompasses a broad range of theoretical and applied topics. Because the statisticians are actively engaged in interdisciplinary work, much of the statistical research is directed toward practical problems. Mathematics education faculty are active in both qualitative and quantitative experimental research areas. These include teacher preparation, coaching and mentoring for in-service teachers, online learning and curriculum development.
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Item Lifetime alcohol consumption patterns and young-onset breast cancer by subtype among Non-Hispanic Black and White women in the Young Women’s Health History Study(Springer Nature, 2023-10) Hirko, Kelly A.; Lucas, Darek R.; Pathak, Dorothy R.; Hamilton, Ann S.; Post, Lydia M.; Ihenacho, Ugonna; Carnegie, Nicole Bohme; Houang, Richard T.; Schwartz, Kendra; Velie, Ellen M.Purpose. The role of alcohol in young-onset breast cancer (YOBC) is unclear. We examined associations between lifetime alcohol consumption and YOBC in the Young Women’s Health History Study, a population-based case–control study of breast cancer among Non-Hispanic Black and White women < 50 years of age. Methods. Breast cancer cases (n = 1,812) were diagnosed in the Metropolitan Detroit and Los Angeles County SEER registry areas, 2010–2015. Controls (n = 1,381) were identified through area-based sampling and were frequency-matched to cases by age, site, and race. Alcohol consumption and covariates were collected from in-person interviews. Weighted multivariable logistic regression was conducted to calculate adjusted odds ratios (aOR) and 95% confidence intervals (CI) for associations between alcohol consumption and YOBC overall and by subtype (Luminal A, Luminal B, HER2, or triple negative). Results. Lifetime alcohol consumption was not associated with YOBC overall or with subtypes (all ptrend ≥ 0.13). Similarly, alcohol consumption in adolescence, young and middle adulthood was not associated with YOBC (all ptrend ≥ 0.09). An inverse association with triple-negative YOBC, however, was observed for younger age at alcohol use initiation (< 18 years vs. no consumption), aOR (95% CI) = 0.62 (0.42, 0.93). No evidence of statistical interaction by race or household poverty was observed. Conclusions. Our findings suggest alcohol consumption has a different association with YOBC than postmenopausal breast cancer—lifetime consumption was not linked to increased risk and younger age at alcohol use initiation was associated with a decreased risk of triple-negative YOBC. Future studies on alcohol consumption in YOBC subtypes are warranted.Item Performance of a Genetic Algorithm for Estimating DeGroot Opinion Diffusion Model Parameters for Health Behavior Interventions(MDPI AG, 2021-12) Johnson, Kara Layne; Walsh, Jennifer L.; Amirkhanian, Yuri A.; Carnegie, Nicole BohmeLeveraging social influence is an increasingly common strategy to change population behavior or acceptance of public health policies and interventions; however, assessing the effectiveness of these social network interventions and projecting their performance at scale requires modeling of the opinion diffusion process. We previously developed a genetic algorithm to fit the DeGroot opinion diffusion model in settings with small social networks and limited follow-up of opinion change. Here, we present an assessment of the algorithm performance under the less-than-ideal conditions likely to arise in practical applications. We perform a simulation study to assess the performance of the algorithm in the presence of ordinal (rather than continuous) opinion measurements, network sampling, and model misspecification. We found that the method handles alternate models well, performance depends on the precision of the ordinal scale, and sampling the full network is not necessary to use this method. We also apply insights from the simulation study to investigate notable features of opinion diffusion models for a social network intervention to increase uptake of pre-exposure prophylaxis (PrEP) among Black men who have sex with men (BMSM).Item Using social contact data to improve the overall effect estimate of a cluster‐randomized influenza vaccination program in Senegal(Wiley, 2021-09) Potter, Gail E.; Carnegie, Nicole Bohme; Sugimoto, Jonathan D.; Diallo, Aldiouma; Victor, John C.; Neuzil, Kathleen M.; Halloran, M. Elizabethhis study estimates the overall effect of two influenza vaccination programs consecutively administered in a cluster-randomized trial in western Senegal over the course of two influenza seasons from 2009-2011. We apply cutting-edge methodology combining social contact data with infection data to reduce bias in estimation arising from contamination between clusters. Our time-varying estimates reveal a reduction in seasonal influenza from the intervention and a nonsignificant increase in H1N1 pandemic influenza. We estimate an additive change in overall cumulative incidence (which was 6.13% in the control arm) of -0.68 percentage points during Year 1 of the study (95% CI: -2.53, 1.18). When H1N1 pandemic infections were excluded from analysis, the estimated change was -1.45 percentage points and was significant (95% CI, -2.81, -0.08). Because cross cluster contamination was low (0-3% of contacts for most villages), an estimator assuming no contamination was only slightly attenuated (-0.65 percentage points). These findings are encouraging for studies carefully designed to minimize spillover. Further work is needed to estimate contamination – and its effect on estimation – in a variety of settings.Item Using a novel genetic algorithm to assess peer influence on willingness to use pre-exposure prophylaxis in networks of Black men who have sex with men(Springer Science and Business Media LLC, 2021-03) Johnson, Kara Layne; Walsh, Jennifer L.; Amirkhanian, Yuri A.; Borkowski, John J.; Carnegie, Nicole BohmeThe DeGroot model for opinion diffusion over social networks dates back to the 1970s and models the mechanism by which information or disinformation spreads through a network, changing the opinions of the agents. Extensive research exists about the behavior of the DeGroot model and its variations over theoretical social networks; however, research on how to estimate parameters of this model using data collected from an observed network diffusion process is much more limited. Existing algorithms require large data sets that are often infeasible to obtain in public health or social science applications. In order to expand the use of opinion diffusion models to these and other applications, we developed a novel genetic algorithm capable of recovering the parameters of a DeGroot opinion diffusion process using small data sets, including those with missing data and more model parameters than observed time steps. We demonstrate the efficacy of the algorithm on simulated data and data from a social network intervention leveraging peer influence to increase willingness to take pre-exposure prophylaxis in an effort to decrease transmission of human immunodeficiency virus among Black men who have sex with men.Item Calibration of an Adaptive Genetic Algorithm for Modeling Opinion Diffusion(MDPI AG, 2022-01) Johnson, Kara Layne; Carnegie, Nicole BohmeGenetic algorithms mimic the process of natural selection in order to solve optimization problems with minimal assumptions and perform well when the objective function has local optima on the search space. These algorithms treat potential solutions to the optimization problem as chromosomes, consisting of genes which undergo biologically-inspired operators to identify a better solution. Hyperparameters or control parameters determine the way these operators are implemented. We created a genetic algorithm in order to fit a DeGroot opinion diffusion model using limited data, making use of selection, blending, crossover, mutation, and survival operators. We adapted the algorithm from a genetic algorithm for design of mixture experiments, but the new algorithm required substantial changes due to model assumptions and the large parameter space relative to the design space. In addition to introducing new hyperparameters, these changes mean the hyperparameter values suggested for the original algorithm cannot be expected to result in optimal performance. To make the algorithm for modeling opinion diffusion more accessible to researchers, we conduct a simulation study investigating hyperparameter values. We find the algorithm is robust to the values selected for most hyperparameters and provide suggestions for initial, if not default, values and recommendations for adjustments based on algorithm output.