Note¶
This analysis includes a quadratic term for time_to_first (i.e., both the variable and its square are included in the model).
Primary Analysis: time_to_first vs time_to_fof¶
Analysis of time_to_first vs time_to_fof.
Unadjusted Model Results¶
Simple quadratic regression examining the direct relationship between time_to_first and time_to_fof.
Model diagnostics warning: High multicollinearity detected (condition number > 30). Residuals may not be normally distributed (p < 0.05).
Outcome: time_to_fof Predictor: time_to_first and its square
OLS Regression Results
==============================================================================
Dep. Variable: time_to_fof R-squared: 0.049
Model: OLS Adj. R-squared: 0.040
Method: Least Squares F-statistic: 5.778
Date: Tue, 05 Aug 2025 Prob (F-statistic): 0.00357
Time: 04:27:57 Log-Likelihood: -904.59
No. Observations: 228 AIC: 1815.
Df Residuals: 225 BIC: 1825.
Df Model: 2
Covariance Type: nonrobust
====================================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------------
const 9.4518 3.485 2.712 0.007 2.584 16.320
time_to_first 0.1742 0.155 1.127 0.261 -0.130 0.479
time_to_first_sq -0.0003 0.002 -0.222 0.825 -0.003 0.003
==============================================================================
Omnibus: 58.671 Durbin-Watson: 1.519
Prob(Omnibus): 0.000 Jarque-Bera (JB): 107.619
Skew: 1.324 Prob(JB): 4.27e-24
Kurtosis: 5.078 Cond. No. 1.21e+04
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.21e+04. This might indicate that there are
strong multicollinearity or other numerical problems.
Unadjusted Plot¶
Plot showing relationship between time_to_first and time_to_fof (LOESS with CI and Quadratic prediction).
Model Variables (Adjusted Analysis)¶
Outcome: time_to_fof Indep: time_to_first Gestational Age Var: gestational_age_weeks Confounders: ['gestational_age_weeks', 'birth_weight_grams', 'mechanical_ventilation', 'o2_device_at_36_weeks'] Covariates: ['medicalcomplexity']
Adjusted Model Results¶
Multiple regression examining the relationship between time_to_first and time_to_fof, controlling for gestational age and other potential confounders.
Model diagnostics warning: High multicollinearity detected (condition number > 30). Residuals may not be normally distributed (p < 0.05).
Outcome: time_to_fof Predictors: time_to_first, gestational_age_weeks, time_to_first_sq, birth_weight_grams, mechanical_ventilation_no history of mechanical ventilation, o2_device_at_36_weeks_did NOT require respiratory support at 36 weeks, medicalcomplexity_Children with noncomplex chronic disease, medicalcomplexity_Children without chronic disease
OLS Regression Results
==============================================================================
Dep. Variable: time_to_fof R-squared: 0.142
Model: OLS Adj. R-squared: 0.110
Method: Least Squares F-statistic: 4.522
Date: Tue, 05 Aug 2025 Prob (F-statistic): 4.18e-05
Time: 04:27:58 Log-Likelihood: -892.87
No. Observations: 228 AIC: 1804.
Df Residuals: 219 BIC: 1835.
Df Model: 8
Covariance Type: nonrobust
=========================================================================================================================================
coef std err t P>|t| [0.025 0.975]
-----------------------------------------------------------------------------------------------------------------------------------------
const 97.4413 27.610 3.529 0.001 43.025 151.857
time_to_first -0.3951 0.205 -1.930 0.055 -0.799 0.008
gestational_age_weeks -1.9702 0.932 -2.113 0.036 -3.808 -0.133
time_to_first_sq 0.0018 0.002 1.133 0.259 -0.001 0.005
birth_weight_grams -0.0050 0.004 -1.109 0.269 -0.014 0.004
mechanical_ventilation_no history of mechanical ventilation -5.3953 2.049 -2.633 0.009 -9.434 -1.357
o2_device_at_36_weeks_did NOT require respiratory support at 36 weeks -2.3489 2.159 -1.088 0.278 -6.604 1.906
medicalcomplexity_Children with noncomplex chronic disease -1.0891 4.970 -0.219 0.827 -10.885 8.707
medicalcomplexity_Children without chronic disease -2.2604 3.912 -0.578 0.564 -9.971 5.450
==============================================================================
Omnibus: 87.555 Durbin-Watson: 1.687
Prob(Omnibus): 0.000 Jarque-Bera (JB): 268.843
Skew: 1.657 Prob(JB): 4.18e-59
Kurtosis: 7.161 Cond. No. 1.02e+05
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.02e+05. This might indicate that there are
strong multicollinearity or other numerical problems.
Adjusted Plot¶
Plot showing adjusted relationship between time_to_first and time_to_fof (LOESS with CI).
Optimal Value¶
Adj. model optimal time_to_first: 108.34, Predicted time_to_fof: 6.68.