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Understanding Adolescent Smoking Behavior: Insights from GEE Models and Random-Effects Analysis

November 15, 2023
Katherine Wilson
Katherine Wilson
🇺🇸 United States
Data Analysis
Katherine Wilson, a proficient data analysis expert with 10+ years' experience, holds a master's from University of Lynchburg. She assists students in completing assignments with expertise and dedication in statistics.
Key Topics
  • Problem Description:
  • GEE population-averaged model:
  • Logistic-normal random-intercept model:
  • Random Effects:
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Problem Description:

The GEE Models assignment involves analyzing a Generalized Estimating Equations (GEE) population-averaged model to understand the association between parental smoking and adolescent smoking. The model is fitted with different correlation structures, and the results are presented with a focus on Odds Ratios (ORs) and confidence intervals.

Solution:

Question 1

GEE population-averaged model Number of obs = 7706

Group and time vars: id wave Number of groups = 1502

Link: logit Obs per group: min = 2

Family: binomial avg = 5.1

Correlation: AR(1) max = 6

Wald chi2(3) = 88.22

Scale parameter: 1 Prob > chi2 = 0.0000

regsmokeCoef.Robust Std. Err.zP>|z|95% Conf.Interval
_Isex_1.2831992.13689812.070.039.014884.5515145
c_wave.3098144.05981815.180.000.1925732.4270557
_IsexXc_wav_1.0288783.0753970.380.702-.1188971.1766537
_cons-2.212193.1026366-21.550.000-2.413357

-2.011029

GEE (auto-regressive order 1 working correlation)
CoefficientStandard error
Constant-2.210.103
Sex(female)0.280.137
Wave(per year): males0.310.060
females0.340.046

Table 1: Analyzing GEE correlation between parental smoking and adolescent

GEE population-averaged model:

Number of observations: 7706

Number of groups: 1502

Correlation structure: AR(1)

Results: The model reveals associations between smoking and various factors. Notably, when using the autoregressive (AR) working correlation structure, some groups were omitted due to unequal spacing or insufficient data. This omission can affect the accuracy of estimated coefficients and standard errors.

Question 2

GEE population-averaged model Number of obs = 8498

Group and time vars: id wave Number of groups = 1702

Link: logit Obs per group: min = 1

Family: binomial avg = 5.0

Correlation: unstructured max = 6

Wald chi2(4) = 177.20

Scale parameter: 1 Prob > chi2 = 0.0000

(Std. Err. adjusted for clustering on id)

regsmoke |Odds RatioRobust Std. Err.zP>|z|95% Conf.Interval
c_wave1.395727.044321110.500.0001.3115071.485355
_Isex_1.9387056.1553567-0.380.702.67866381.298387
parsmk1.728383.31180863.030.0021.213612.461506
_IsexXparsm_11.852877.4499222.540.011&1.151212.98221
_cons.0995425.0114585-20.040.000.0794375.124736

Association within males

regsmokeCoef.Std. Err.zP>|z|95% Conf.Interval
(1).5471863.18040483.030.002.1935993.9007733

Association between females

regsmokeCoef.Std. Err.zP>|z|95% Conf.Interval
(1)1.163926.16234367.170.000.8457381.482113

GEE population-averaged model:

  • Number of observations: 8498
  • Number of groups: 1702
  • Correlation structure: Unstructured

Results:The associations between parental smoking and adolescent smoking are presented as Odds Ratios with 95% confidence intervals. Differences in associations are observed between males and females, emphasizing the importance of considering gender-specific effects.

Question 3a

regsmokeCoef.Std. Err.zP>|z|95% Conf.Interval
_Isex_1.2032646.33096360.610.539-.4454121.8519414
c_wave.6957047.10907326.380.000.4819252.9094843
_IsexXc_wav_1.3547225.14863962.390.017.0633943.6460507
_cons-6.140336.3543214-17.330.000-6.834793-5.445878

Logistic-normal random-intercept model:

Results: Fixed effects coefficients differ from the marginal model, emphasizing the impact of individual participant-level random effects on estimates. This variation is crucial in understanding participant-specific effects.

>Question 3b

sigma_u5.160847.28615464.6293945.753309
rho.89006.0108514.866921.9095953

Likelihood-ratio test of rho=0: chibar2(01) = 2326.41 Prob >= chibar2 = 0.000

Random Effects:

  • Random intercept standard deviation: 5.160847
  • Intra-participant correlation (rho): 0.89006

The high intra-participant correlation indicates that participants with similar characteristics tend to have similar outcomes, underscoring the significance of individual-level factors.

Question 3c

Weighted Average Probability:

  • Weighted Average Probability of Smoking: 0.4427
  • The coefficient associated with the probability: 0.3098

The weighted average probability provides insights into the predicted probability of smoking for men in year zero, considering assigned weights.

In summary, the analysis employs GEE models and a logistic-normal random-intercept model, highlighting the nuances in associations and emphasizing the importance of considering individual-level factors in understanding smoking behaviour among adolescents.

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