For the proliferation assays, 4 replicate wells were analyzed per experimental treatment in all 4 cell lines; for the migration assays, 4–6 replicate wells were analyzed per experimental treatment in all 4 cell lines; for the colony formation assays, 3 replicate wells were analyzed per experimental treatment in all 4 cell lines. For the subcutaneous tumor experiments, vehicle: n = 5 (16 days) and 4 (18 days); Omipalisib: n = 6; Trametinib: n = 6; SHP099: n = 5; OmiTram: n = 5; OmiSHP: n = 5. Tumor growth among the six experimental groups of mice was measured at baseline and every two days for 18 days (0, 2, 4, 6, 8, 10, 12, 14, 16, and 18). Differences in tumor growth over time among the groups were analyzed using linear mixed models for repeated measure data using SAS (version 9.4) procedure GLIMMIX (SAS Institute Inc.) using an AR(1) covariance structure. For tumor growth between groups over time, interactions were assessed by specifying appropriate contrast statements within the modeling framework. For the in vivo experiments using PKT mice, Vehicle: n = 6; Omipalisib: n = 6; Trametinib: n = 6; OmiTram: n = 7. Survival analysis included all listed mice, but all other post-mortem analyses excluded mice that unexpectedly succumbed to disease before final weights and tissues could be collected (post-mortem analysis: vehicle: n = 5; Omipalisib: n = 6; Trametinib: n = 5; OmiTram n = 6). In all analyses except that of tumor growth rate in the in vivo subcutaneous tumor experiments, statistical significance was assessed by one-way ANOVA with Tukey’s multiple comparison analysis using GraphPad Prism 5 software (* p < 0.05, ** p < 0.01, *** p < 0.001, and **** p < 0.0001). Mice in all in vivo experiments were randomly assigned to each experimental group. Since the study was exploratory, no formal sample size calculation and power analysis were carried out to determine the sample size. The number of mice in the study, as well as sex distribution across treatment groups, was based on the availability of mice for the study.
Glimmix
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GLIMMIX is a software package for fitting generalized linear mixed models. It provides a flexible framework for modeling a wide range of data types, including normal, binary, count, and time-to-event data. GLIMMIX can handle both fixed and random effects, and allows for the specification of complex correlation structures.
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178 protocols using «glimmix»
1
In Vivo Evaluation of Combination Therapies
2
Tumor Growth Kinetics Analysis
Statistical analysis methods are noted in each figure legend. For tumor growth experiments, differences in tumor growth over time among the groups were analyzed using linear mixed models for repeated measure data using the SAS procedure GLIMMIX (SAS Institute) using AR(1) covariance structure. For all analysis, p≤0.05 is considered significant.
3
Dietary Effects on Canine Hair and Activity
Data were analyzed using a PROC GLIMMIX mixed model (SAS Inst., Int., Cary, NC, USA) with dog as the experimental unit; diet, breed, sex, and month as fixed effects; as well as the interactions for the animal characteristics, haircoat parameters, and activity. The July timepoint (start date) was used as a covariate for hair length, hair growth rate, shed hair, and active hours. Outliers were identified as observations beyond ±3 standard deviations of the mean. Statistical significance was determined at p ≤ 0.05 and trends considered when 0.05 ≤ p ≤ 0.10. Means are reported as LS means ± SEM (least square mean ± standard error of the mean). If a significant diet-by-month interaction was detected, a Tukey’s test was run to compare the dietary treatments within month.
4
Dietary Fiber and Feline Digestibility
Least square means of data were estimated by a general linear mixed model in a software (GLIMMIX, SAS version 9.4, SAS Institute Inc., Cary, NC, USA). Pairwise comparisons were conducted using Tukey’s post hoc test. Contrasts comparing control (SBM) versus treatments (5FPP, 10FPP, and 15FPP), and linear, quadratic, and cubic relationships among all diets were considered significant at p < 0.05. For each diet production, sampling was conducted at evenly spaced intervals which were considered replicates. For digestibility trial analysis, the diet was considered a fixed effect while the cat and period were considered random effects in the analysis model. In the palatability experiment, the consumption ratio was analyzed using a t-test in a two-way ANOVA, and the first-choice preference was analyzed using a Chi2 test.
5
Predator-Prey Dynamics in Glacier Foreland
A generalized linear mixed model (GLMM) was employed to explore population abundances along a downhill transect in the glacier foreland, examining both bottom‐up and top‐down control mechanisms within the arthropod predator–prey relationships. The analysis included comparisons of arthropod taxa across different years and habitats, specifically pioneer, crowberry, and gray willow habitats, utilizing a GLMM with a Poisson distribution. The Tukey–Kramer test facilitated multiple means comparisons as part of the SAS procedure GLIMMIX (SAS Institute Inc. 2018 ). Additionally, a Poisson regression was applied to analyze the influence of NDVI and proximity to the glacier snout on selected arthropod taxa, incorporating both linear and second‐degree polynomial models.
The taxonomic richness and Shannon diversity index for all species, predators, and prey alike, were assessed using a linear model that included variables such as position on the transect at three levels (upper, central, and lower), habitat type, and year, along with their interactions, processed through the SAS PROC MIXED procedure (SAS Institute Inc. 2018 ).
In terms of specific predatory behavior, the paired samples t‐test was conducted to compare I. anglicana activity‐density between the two summer periods. To analyze predation frequencies, the econullnetr package in R was utilized, comparing the observed presence of prey DNA in predator guts against the activity‐density data of prey taxa from pitfall traps, using 95% CIs derived from a null model (Vaughan et al. 2018 ).
IGP‐ratios for key predators likeCollinsia holmgreni Thorell 1871, the harvestman, Mitopus morio (Fabricius, 1779), and both adult and larval stages of the ground beetle were quantified by determining the percentage of other predator species found in their guts relative to the total number of species present.
Two separate SEM models were developed to further explore these trophic relationships. These models were constructed using SPSS Amos software (Arbuckle 2022 ), which incorporated hypothesized pathways reflecting trophic interactions from the literature and findings from the DNA gut content analysis. The SEM models highlighted significant relationships and potential influences among the variables, indicating whether positive or negative correlations suggest bottom‐up or top‐down food web dynamics.
Molecular techniques were vital in delineating these food web interactions as traditional visual inspection fails due to many predators being liquid feeders or employing extra oral digestion. These techniques ensure accurate identification of prey in predator guts (Cohen 1995 ; Eitzinger and Traugott 2011 ; Whitney et al. 2018 (link)). Pairing DNA gut content analysis with activity‐density sampling provided a comprehensive approach to describing the food webs, as predator consumption often does not directly correlate with prey population densities (Athey et al. 2016 ). A trophic link between a predator and a potential prey was chosen in the two SEM models if the prey was identified in the predator's gut and there was scientific literature support for choosing such a link. Erythraeoidea was not identified in any predator guts and therefore this group of prey was excluded from the SEM model. If there was no gut content analysis done on a predator—for example, Bdelloidea—or a group of predators—for example, “other Araneae”—a trophic link was chosen solely based on the literature or on expert communication. If we found no significant correlation between a predator and a prey—for example, the dipteran family Simuliidae—this group of prey was excluded from the SEM model.
Data were prepared for SEM analysis with transformations appropriate to the statistical models used, selecting the best models based on Chi‐square goodness‐of‐fit statistics, p‐values, CMIN/df close to one, Comparative Fit Index (CFI), Root Mean Square Error of Approximation (RMSEA), and Root Mean Square Residual (RMR) (Arbuckle 2022 ). The overall arthropod food web for the glacier foreland was modeled using wet pitfall activity‐density data pooled from the summers of 2015 and 2016 (SEM1), while the detailed model in relation to the IGP ofC. holmgreni was based on data sampled during the summer of 2016 (SEM2). These two SEM models are based on DNA gut content analysis performed on arthropod predators sampled with dry pitfall traps during the summer of 2016.
In each SEM analyses, the variances of the error terms associated with the observed variables were fixed to unity. This approach was taken to ensure model identification, as these error terms include unspecified latent variables. While these fixed variances are essential for the proper specification of the models, they are not displayed in the SEM diagrams to maintain clarity. This method allows for meaningful estimation of other model parameters (Arbuckle 2022 ).
The taxonomic richness and Shannon diversity index for all species, predators, and prey alike, were assessed using a linear model that included variables such as position on the transect at three levels (upper, central, and lower), habitat type, and year, along with their interactions, processed through the SAS PROC MIXED procedure (SAS Institute Inc. 2018 ).
In terms of specific predatory behavior, the paired samples t‐test was conducted to compare I. anglicana activity‐density between the two summer periods. To analyze predation frequencies, the econullnetr package in R was utilized, comparing the observed presence of prey DNA in predator guts against the activity‐density data of prey taxa from pitfall traps, using 95% CIs derived from a null model (Vaughan et al. 2018 ).
IGP‐ratios for key predators like
Two separate SEM models were developed to further explore these trophic relationships. These models were constructed using SPSS Amos software (Arbuckle 2022 ), which incorporated hypothesized pathways reflecting trophic interactions from the literature and findings from the DNA gut content analysis. The SEM models highlighted significant relationships and potential influences among the variables, indicating whether positive or negative correlations suggest bottom‐up or top‐down food web dynamics.
Molecular techniques were vital in delineating these food web interactions as traditional visual inspection fails due to many predators being liquid feeders or employing extra oral digestion. These techniques ensure accurate identification of prey in predator guts (Cohen 1995 ; Eitzinger and Traugott 2011 ; Whitney et al. 2018 (link)). Pairing DNA gut content analysis with activity‐density sampling provided a comprehensive approach to describing the food webs, as predator consumption often does not directly correlate with prey population densities (Athey et al. 2016 ). A trophic link between a predator and a potential prey was chosen in the two SEM models if the prey was identified in the predator's gut and there was scientific literature support for choosing such a link. Erythraeoidea was not identified in any predator guts and therefore this group of prey was excluded from the SEM model. If there was no gut content analysis done on a predator—for example, Bdelloidea—or a group of predators—for example, “other Araneae”—a trophic link was chosen solely based on the literature or on expert communication. If we found no significant correlation between a predator and a prey—for example, the dipteran family Simuliidae—this group of prey was excluded from the SEM model.
Data were prepared for SEM analysis with transformations appropriate to the statistical models used, selecting the best models based on Chi‐square goodness‐of‐fit statistics, p‐values, CMIN/df close to one, Comparative Fit Index (CFI), Root Mean Square Error of Approximation (RMSEA), and Root Mean Square Residual (RMR) (Arbuckle 2022 ). The overall arthropod food web for the glacier foreland was modeled using wet pitfall activity‐density data pooled from the summers of 2015 and 2016 (SEM1), while the detailed model in relation to the IGP of
In each SEM analyses, the variances of the error terms associated with the observed variables were fixed to unity. This approach was taken to ensure model identification, as these error terms include unspecified latent variables. While these fixed variances are essential for the proper specification of the models, they are not displayed in the SEM diagrams to maintain clarity. This method allows for meaningful estimation of other model parameters (Arbuckle 2022 ).
Top 5 protocols citing «glimmix»
1
Longitudinal Study of PM2.5 and Mental Health
Given the longitudinal study design and multiple participants per household, we used the generalized linear mixed models PROC GLIMMIX procedure (version 9.3; SAS Institute Inc.) to study the association of PM2.5 and each mental health condition, modeled as binary outcome based on a CESD-11 score ≥ 9 and HADS-A ≥ 8 for moderate-to-severe depressive and anxiety symptoms, respectively, and to account for random effects of repeated measurements for participants and households. We fit penalized spline models to evaluate deviations from linearity, with the linear model preferable for each outcome based on Akaike information criterion. We examined associations for PM2.5 exposure windows averaged from previous 7 days, to up to 4 years prior to the interview date of NSHAP participants to study the impact of semi-acute and chronic PM2.5 exposure for mental disorders, respectively.
In the basic models, we adjusted for age, sex, race, year, season and day of week of questionnaire completion, region of residence (West, Midwest, South, Northeast), and whether participants lived within a metropolitan statistical area (MSA). Multivariable models were also constructed to control for confounding by socioeconomic measures (SES) as assessed using individual-specific education attainment and family income, and census-level median household income and percent of population with income below poverty level. To further evaluate potential confounding, additional wave-specific covariates were selected a priori based on their previous associations with mental illness or air pollution: individual-specific obesity status [i.e., body mass index (BMI) ≥ 30)], current smoking status, physical activity, alcohol consumption (drinks per day), UCLA Loneliness scale (range: 0–9), current use of antidepressant medication, and history of diabetes, hypertension, stroke, heart failure, emphysema, chronic obstructive pulmonary disease (COPD) or asthma (see Table S2). Two covariates (i.e., BMI and family income) had 10% and 29% missing data, respectively; their missing values were imputed by simple mean substitution. Missing data of other covariates (< 5%) were not imputed. Both base and SES-adjusted analyses were restricted to a subset of data for which values for all covariates were not missing [i.e., 6,199 nonmissing out of 6,382 total observations (97.1%) for covariates]. Additional covariates were added individually in separate basic models to avoid multicollinearity and reduce potential bias on the estimates if covariates were not shown to be confounders (Xing and Xing 2010 (link)). Since certain covariates (e.g., sex) could be possible effect modifiers, their modification of PM2.5-mental health findings was examined through interaction terms, using the PROC GLIMMIX procedure, which provides added options to compute customized odds ratios and the corresponding confidence intervals (CIs) automatically for each level of the interaction term.
We conducted several sensitivity analyses. First, we considered mental health measures as continuous rather than binary measures. Second, we restricted the longitudinal analysis to individuals who participated in both waves, to those living in MSAs only, those who did not move between waves or did not currently take antidepressant medication, respectively. We also reanalyzed the models using multiple imputation technique. Third, we constructed the model using PM2.5 concentrations measured at the nearest U.S. EPA ambient monitors within 60 km of the residential address. Lastly, we considered our depression and anxiety outcomes to be chronic relapsing disorders, by restricting our analyses to Wave 2 participants who did not have moderate-to-severe depressive (CESD-11 < 9) or anxiety (HADS-A < 8) symptoms in Wave 1. In doing so, we acknowledge that if mental disorders are chronic conditions, PM2.5 exposures for Wave 2 could not be associated with mental disorders that occurred at Wave 1 or earlier. If that is the case, inclusion of individuals reporting mental disorders in Wave 1 in longitudinal analyses would bias the effect estimates towards the null. Since information on the history of mental illness was not available in the study, we conducted logistic regression analysis examining the association between PM2.5 exposure and incident moderate-to-severe depressive and anxiety symptoms in Wave 2. Results are expressed as the odds ratio (OR) per 5 μg/m3 increment in PM2.5 exposure; all effect estimates and their corresponding confidence intervals were obtained through the ODDSRATIO (DIFF = ALL) option in the GLIMMIX procedure.
In the basic models, we adjusted for age, sex, race, year, season and day of week of questionnaire completion, region of residence (West, Midwest, South, Northeast), and whether participants lived within a metropolitan statistical area (MSA). Multivariable models were also constructed to control for confounding by socioeconomic measures (SES) as assessed using individual-specific education attainment and family income, and census-level median household income and percent of population with income below poverty level. To further evaluate potential confounding, additional wave-specific covariates were selected a priori based on their previous associations with mental illness or air pollution: individual-specific obesity status [i.e., body mass index (BMI) ≥ 30)], current smoking status, physical activity, alcohol consumption (drinks per day), UCLA Loneliness scale (range: 0–9), current use of antidepressant medication, and history of diabetes, hypertension, stroke, heart failure, emphysema, chronic obstructive pulmonary disease (COPD) or asthma (see Table S2). Two covariates (i.e., BMI and family income) had 10% and 29% missing data, respectively; their missing values were imputed by simple mean substitution. Missing data of other covariates (< 5%) were not imputed. Both base and SES-adjusted analyses were restricted to a subset of data for which values for all covariates were not missing [i.e., 6,199 nonmissing out of 6,382 total observations (97.1%) for covariates]. Additional covariates were added individually in separate basic models to avoid multicollinearity and reduce potential bias on the estimates if covariates were not shown to be confounders (Xing and Xing 2010 (link)). Since certain covariates (e.g., sex) could be possible effect modifiers, their modification of PM2.5-mental health findings was examined through interaction terms, using the PROC GLIMMIX procedure, which provides added options to compute customized odds ratios and the corresponding confidence intervals (CIs) automatically for each level of the interaction term.
We conducted several sensitivity analyses. First, we considered mental health measures as continuous rather than binary measures. Second, we restricted the longitudinal analysis to individuals who participated in both waves, to those living in MSAs only, those who did not move between waves or did not currently take antidepressant medication, respectively. We also reanalyzed the models using multiple imputation technique. Third, we constructed the model using PM2.5 concentrations measured at the nearest U.S. EPA ambient monitors within 60 km of the residential address. Lastly, we considered our depression and anxiety outcomes to be chronic relapsing disorders, by restricting our analyses to Wave 2 participants who did not have moderate-to-severe depressive (CESD-11 < 9) or anxiety (HADS-A < 8) symptoms in Wave 1. In doing so, we acknowledge that if mental disorders are chronic conditions, PM2.5 exposures for Wave 2 could not be associated with mental disorders that occurred at Wave 1 or earlier. If that is the case, inclusion of individuals reporting mental disorders in Wave 1 in longitudinal analyses would bias the effect estimates towards the null. Since information on the history of mental illness was not available in the study, we conducted logistic regression analysis examining the association between PM2.5 exposure and incident moderate-to-severe depressive and anxiety symptoms in Wave 2. Results are expressed as the odds ratio (OR) per 5 μg/m3 increment in PM2.5 exposure; all effect estimates and their corresponding confidence intervals were obtained through the ODDSRATIO (DIFF = ALL) option in the GLIMMIX procedure.
2
Estimating Eligible Women for CDP:EWC Services
We used the small-area estimation method (4 (link),8 ,19 ,20 (link)) to generate regression-based estimates of the proportion of women eligible for CDP:EWC services. To demonstrate the usefulness of this method for estimating local and sparse target populations, we calculated estimates of service-eligible women by county and by racial/ethnic group within each county. We performed the regression analysis using SAS Version 8 and a corresponding macro, GLIMMIX, (SAS Institute Inc, Cary, North Carolina) (21 ).
To obtain the parameter estimates, we fitted the model using the restricted/residual pseudolikelihood method (22 ). All county variables were standardized to observe the mean and standard deviations. We included individual and county variables as covariates in a generalized, linear, mixed-effect model with eligibility status as the outcome variable. To account for the variation not explained by the regression variables, a county random effect variable, ai, was included in the model:
In the model, Xij is the jth observation in county i for racial/ethnic group, educational level, marital status, unemployment rate, percentage of women living in poverty, median household income, and the interaction terms between these variables; yij is a Bernoulli random-response variable with probability pij; and ai is assumed to be normally distributed with a mean of zero and a variance equal to σ2.
During preliminary analysis, we compared the Akaike Information Criterion (AIC) values of the model variables to assess their relative contribution to the model. Education level and marital status, which had the lowest AIC values and did not contribute to the model selection, were not included as variables. The racial/ethnic and county variables and the interaction terms were maintained in the preliminary model.
Next we used backwards selection (23 ) to determine which variables and interactions of variables to select for the final model. To increase predictability, we set the selection criteria for the model at a = 0.30, rather than at a lower level (24 ). The variables representing unemployment rate, percentage of women living in poverty, median household income, each racial/ethnic group, and significant interaction terms remained in the final model (Table 1 ).
We used the Monte Carlo method (25 ) to estimate the proportion of eligible women in each racial/ethnic group in each county and the bootstrap method (26 ) to calculate the standard error of the estimated proportions in each racial/ethnic group and in all races combined. We calculated 95% confidence intervals for each standard error. We computed the coefficient of variation (CV) to assess the reliability of the estimated prevalence points (4 (link),27 ) and considered proportions with a CV greater than 0.23 unreliable. All county estimates were found to be reliable.
To obtain the parameter estimates, we fitted the model using the restricted/residual pseudolikelihood method (22 ). All county variables were standardized to observe the mean and standard deviations. We included individual and county variables as covariates in a generalized, linear, mixed-effect model with eligibility status as the outcome variable. To account for the variation not explained by the regression variables, a county random effect variable, ai, was included in the model:
In the model, Xij is the jth observation in county i for racial/ethnic group, educational level, marital status, unemployment rate, percentage of women living in poverty, median household income, and the interaction terms between these variables; yij is a Bernoulli random-response variable with probability pij; and ai is assumed to be normally distributed with a mean of zero and a variance equal to σ2.
During preliminary analysis, we compared the Akaike Information Criterion (AIC) values of the model variables to assess their relative contribution to the model. Education level and marital status, which had the lowest AIC values and did not contribute to the model selection, were not included as variables. The racial/ethnic and county variables and the interaction terms were maintained in the preliminary model.
Next we used backwards selection (23 ) to determine which variables and interactions of variables to select for the final model. To increase predictability, we set the selection criteria for the model at a = 0.30, rather than at a lower level (24 ). The variables representing unemployment rate, percentage of women living in poverty, median household income, each racial/ethnic group, and significant interaction terms remained in the final model (
We used the Monte Carlo method (25 ) to estimate the proportion of eligible women in each racial/ethnic group in each county and the bootstrap method (26 ) to calculate the standard error of the estimated proportions in each racial/ethnic group and in all races combined. We calculated 95% confidence intervals for each standard error. We computed the coefficient of variation (CV) to assess the reliability of the estimated prevalence points (4 (link),27 ) and considered proportions with a CV greater than 0.23 unreliable. All county estimates were found to be reliable.
3
Suicidality Risk Across DVPX Studies
The meta-analysis methodology employed by the FDA in the evaluation of suicidality risk across 11 AEDs was utilized as the primary method to assess the risk of suicidality across multiple DVPX studies [4 ]. Delayed-release and extended-release DVPX formulations were combined and analyzed as DVPX treatment. To be consistent with the conservative approach employed by the FDA, the most severe suicidality event was included in the evaluation in situations where subjects experienced more than one event. The overall ORs of suicidality events across studies and associated 95% CIs were calculated using the exact method controlling for study [18 ]. For studies with no suicidality events, OR could not be calculated due to zeros in both the numerator and denominator. Therefore these studies could not be included in any of the overall OR analyses controlling for study. Zelen's test, an exact test for homogeneity of OR among studies, was conducted [18 ]. As a sensitivity analysis, SAS procedure GLIMMIX [19 ] (SAS, Cary, NC, USA) was used to estimate the OR using a generalized linear mixed model where study was considered as a random factor. The Mantel-Haenszel risk difference controlling for study and associated CI [20 (link)] were generated which included the zero-event studies. Relative risk analysis employing the exact method was also conducted [18 ]. This analysis used subject time as the unit of analysis rather than using the subject as the unit in the estimation of the OR. The overall absolute risks and relative risks from the pooled dataset were calculated for all placebo-controlled studies combined, for all placebo-controlled and low-dose-controlled studies combined, and by indication. These calculations did not use study as a stratification factor.
4
Genome-wide association study of substance use traits
5
Phytohormonal Profiling in Plum Cultivars
The study was performed using four biological replicates from each genotype and two genotypes from each group, thus eight technical replicates from each group. Hormonal data of the European and Japanese plums were analyzed together using general linear mixed models (proc GLIMMIX) in SAS v9.4 (SAS Institute Inc., 111, Hampton Woods Ln, Raleigh, NC 27607, USA). Shapiro–Wilk normality tests and studentized residual plots were used to test error assumptions of variance analysis including random, homogenous, and normal distributions of error. Outliers were removed using Lund’s test. Means were calculated using the LSMEANS statement, and significant differences between the treatments were determined using a post hoc LSD test α ≤ 0.05 and are mentioned in each figure.
The phytohormonal contribution in BK disease development was analyzed using principal component analysis (PCA) at the 1st and 5th stages. Here, PCA was conducted separately on phytohormonal data from resistant and susceptible genotypes of European and Japanese plums, using PROC PRINCOMP in SAS v9.4 (SAS Institute Inc., 111, Hampton Woods Ln, Raleigh, NC 27607, USA).
The phytohormonal contribution in BK disease development was analyzed using principal component analysis (PCA) at the 1st and 5th stages. Here, PCA was conducted separately on phytohormonal data from resistant and susceptible genotypes of European and Japanese plums, using PROC PRINCOMP in SAS v9.4 (SAS Institute Inc., 111, Hampton Woods Ln, Raleigh, NC 27607, USA).
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