6  Cleaved Caspase Activity

❖ Data

❖ Description

Variable Description
Stage

Developmental stage

Condition

Hypoxia condition: Normoxia (N) vs Intermittent Hypoxia (IH)

Mouse

Mouse unique identifier

Fluo_Norm

Enzymatic Activity of Caspase 3/7 (Normalized Fluorescence)

Variable Description
Stage

Developmental stage

Condition

Hypoxia condition: Normoxia (N) vs Intermittent Hypoxia (IH)

Mouse

Mouse unique identifier

Fluo_Norm

Enzymatic Activity of Caspase 3/7 (Normalized Fluorescence)

❖ Correlations

6.1 Normalized Fluorescence of Caspase 3 Activity

6.1.1 Data Exploration

❖ Distribution:

Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 0 1.268 1.607 NA 2.131 −2.123 2.096 −0.233 −0.971 20
IH −0.941 1.896 3.595 −2.016 2.071 −6.5 4.105 0.17 1.891 52
Condition Mean SD Variance CoV IQR Min Max Skewness Kurtosis n
N 0 1.268 1.607 NA 2.131 −2.123 2.096 −0.233 −0.971 20
IH −0.941 1.896 3.595 −2.016 2.071 −6.5 4.105 0.17 1.891 52

6.1.2 Models & Diagnostics

Exploring some Generalized Linear (Mixed) model candidates:

❖ Model call:

```{r}
glmmTMB(formula = Fluo_Norm ~ Condition + (1 | Mouse), data = data, 
    family = gaussian("identity"), REML = TRUE, ziformula = ~0, 
    dispformula = ~1)
```

❖ Performance:

performance::performance(mod)
AIC AICc BIC R2_conditional R2_marginal ICC RMSE Sigma
243.28 243.87 252.38 0.76 0.05 0.74 0.80 0.92
AIC AICc BIC R2_conditional R2_marginal ICC RMSE Sigma
243.28 243.87 252.38 0.76 0.05 0.74 0.80 0.92

❖ Residuals:

performance::check_model(
  mod, panel = FALSE,
  check = c("pp_check", "qq", "reqq", "linearity", "homogeneity")
)

❖ Predictions:

Simulating data from the model for pseudo “Posterior Predictive” plots.

♦ Simulated data vs observed data:

♦ Simulated statistics vs observed ones:

❖ Potential outliers:

6.1.3 Effects Analysis

```{r}
glmmTMB(formula = Fluo_Norm ~ Condition + (1 | Mouse), data = data, 
    family = gaussian("identity"), REML = TRUE, ziformula = ~0, 
    dispformula = ~1)
```

6.1.3.1 Coefficients

❖ All effects (Wald):

parameters::parameters(
  mod, component = "conditional", effects = "fixed",
  exponentiate = should_exp(mod), p_adjust = "none", summary = TRUE, digits = 3
)
Parameter Coefficient SE 95% CI z p
(Intercept) -0.470 0.427 (-1.31, 0.37) -1.102 0.271
Condition1 0.470 0.427 (-0.37, 1.31) 1.102 0.271
Model: Fluo_Norm ~ Condition (72 Observations)
Parameter Coefficient SE 95% CI z p
(Intercept) -0.470 0.427 (-1.31, 0.37) -1.102 0.271
Condition1 0.470 0.427 (-0.37, 1.31) 1.102 0.271
Model: Fluo_Norm ~ Condition (72 Observations)

❖ Main effects (Wald Chi-Square):

car::Anova(mod, type = 3)
term statistic df p.value
Condition 1.21 1 0.270
term statistic df p.value
Condition 1.21 1 0.270

❖ Main effects (Likelihood Ratio Test):

LRT(mod, pred = "Condition")
model df aic bic log_lik deviance chisq chi_df pr_chisq
mod_reduced 3 242.53 249.36 -118.26 236.53
mod_full 4 243.21 252.32 -117.60 235.21 1.32 1 0.250
model df aic bic log_lik deviance chisq chi_df pr_chisq
mod_reduced 3 242.53 249.36 -118.26 236.53
mod_full 4 243.21 252.32 -117.60 235.21 1.32 1 0.250
Important

Our LRT() method removes the predictor plus all its interactions

6.1.3.2 Marginal Effects

Marginal means & Contrasts for each predictor:

❖ Marginal Means:

emmeans(mod, specs = pred, type = "response")
Condition emmean SE df lower.CL upper.CL
N 0 0.726 70 −1.447 1.447
IH −0.941 0.45 70 −1.838 −0.043
Condition emmean SE df lower.CL upper.CL
N 0 0.726 70 −1.447 1.447
IH −0.941 0.45 70 −1.838 −0.043 
- Confidence level used: 0.95

❖ Contrasts:

emmeans(mod, specs = pred, type = "response") |> 
  contrast(method = "pairwise", adjust = "none", infer = TRUE)
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 0.941 0.854 70 −0.762 2.644 1.102 0.274
contrast estimate SE df lower.CL upper.CL t.ratio p.value
N - IH 0.941 0.854 70 −0.762 2.644 1.102 0.274 
- Confidence level used: 0.95

❖ Boxplot: