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

Explore the intricate dynamics of adolescent smoking behaviour through a comprehensive analysis employing Generalized Estimating Equations (GEE) models and logistic-normal random-intercept models. This in-depth investigation sheds light on associations between parental smoking and adolescent habits, uncovering gender-specific nuances and emphasizing the pivotal role of individual-level factors. Delve into the complexities of correlation structures, the impact of omitted groups, and the significance of random effects in predicting and interpreting smoking outcomes among adolescents. This exploration not only reveals statistical associations but also provides a deeper understanding of the unique characteristics that influence smoking patterns among the youth.

## 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

 regsmoke Coef. Robust Std. Err. z P>|z| 95% Conf. Interval _Isex_1 .2831992 .1368981 2.07 0.039 .014884 .5515145 c_wave .3098144 .0598181 5.18 0.000 .1925732 .4270557 _IsexXc_wav_1 .0288783 .075397 0.38 0.702 -.1188971 .1766537 _cons -2.212193 .1026366 -21.55 0.000 -2.413357 -2.011029
GEE (auto-regressive order 1 working correlation)
Coefficient Standard error
Constant -2.21 0.103
Sex(female) 0.28 0.137
Wave(per year): males 0.31 0.060
females 0.34 0.046

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 Ratio Robust Std. Err. z P>|z| 95% Conf. Interval c_wave 1.395727 .0443211 10.50 0.000 1.311507 1.485355 _Isex_1 .9387056 .1553567 -0.38 0.702 .6786638 1.298387 parsmk 1.728383 .3118086 3.03 0.002 1.21361 2.461506 _IsexXparsm_1 1.852877 .449922 2.54 0.011& 1.15121 2.98221 _cons .0995425 .0114585 -20.04 0.000 .0794375 .124736

Association within males

 regsmoke Coef. Std. Err. z P>|z| 95% Conf. Interval (1) .5471863 .1804048 3.03 0.002 .1935993 .9007733

Association between females

 regsmoke Coef. Std. Err. z P>|z| 95% Conf. Interval (1) 1.163926 .1623436 7.17 0.000 .845738 1.482113

## 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

 regsmoke Coef. Std. Err. z P>|z| 95% Conf. Interval _Isex_1 .2032646 .3309636 0.61 0.539 -.4454121 .8519414 c_wave .6957047 .1090732 6.38 0.000 .4819252 .9094843 _IsexXc_wav_1 .3547225 .1486396 2.39 0.017 .0633943 .6460507 _cons -6.140336 .3543214 -17.33 0.000 -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_u 5.16085 0.286155 4.62939 5.75331 rho 0.89006 0.0108514 0.866921 0.909595

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.