Characteristics influencing Nicotine Usage

nicotine
substance abuse
modeling
Published

17 January 2024

Introduction

  • Nicotine usage associated with cancer and heart disease
  • Only about 3% of smokers quit nicotine usage successfully each year Methods Diagnostics
  • Personality tendencies often linked to drug usage
  • Survey data of demographics, personality scores, and drug history from 1885 participants

Project Goal: Investigate the relationship between individual personality and demographic characteristics and nicotine usage status

Multinomial logistic regression

If we have more than two categories or groups that we want to model relative to covariates (e.g., we have observations \(i = 1,\cdots,n\) and groups covariates \(j = 1,\cdots,J\)), multinomial is our candidate model

Let

  • \(p_{ij}\) be the probability that the i-th observation belongs to the j-th group
  • \(Y_{ij}\) be the number of observations for individual i in group j; An individual will have observations \(Y_{i1},Y_{i2},…Y_{iJ}\)
  • assume the probability of observing this response is given by a multinomial distribution in terms of probabilities \(p_{ij}\), where \(\sum_{j = 1}^J p_{ij} = 1\) . For interpretation, we have a baseline category \(p_{i1} = 1 - \sum_{j = 2}^J p_{ij}\)

The link between the mean response (probability) \(p_{ij}\) and a linear function of the covariates

\[ \eta_{ij} = \mathbf{x'_i \beta_j} \]

which equals

\[\log \frac{p_{ij}}{p_{i1}}, j = 2,..,J \]

We compare \(p_{ij}\) to the baseline \(p_{i1}\), suggesting

\[ p_{ij} = \frac{\exp(\eta_{ij})}{1 + \sum_{i=2}^J \exp(\eta_{ij})} \]

which is known as multinomial logistic model.

Note:

  • Softmax coding for multinomial logistic regression: rather than selecting a baseline class, we treat all K class symmetrically - equally important (no baseline).

\[ P(Y = k | X = x) = \frac{exp(\beta_{k1} + \dots + \beta_{k_p x_p})}{\sum_{l = 1}^K exp(\beta_{l0} + \dots + \beta_{l_p x_p})} \] then the log odds ratio between \(k-th\) and \(k^{t}th\) classes is

\[ \log (\frac{P(Y=k|X=x)}{P(Y = k' | X=x)}) = (\beta_{k0} - \beta_{k'0}) + \dots + (\beta_{kp} - \beta_{k'p}) x_p \]

Explanatory data analysis

Distribution of Nicotine usage by Gender

Comments

  • the largest proportion of recent users were man

Distribution of nicotine usage by education

Comments

  • University students constitute the greatest percentage of both past and current users
  • Vocational colleges/ some colleges also constitute the greatest percentage of recent users

Distribution of Openess to Experience by Nicotine usage

Distribution of conscientiousness by Nicotine usage

Associations and Analysis of variance

Characteristic N Overall, N = 18851 Never Used, N = 4281 Past User, N = 5821 Recent User, N = 8751 Test Statistic p-value2
Gender 1885



67.88890 <0.001
    Female
50%(942/1885) 64%(275/428) 53%(311/582) 41%(356/875)

    Male
50%(943/1885) 36%(153/428) 47%(271/582) 59%(519/875)

Education 1885



129.50631 <0.001
    Certificate/Trade Degree
14%(270/1885) 16%(70/428) 13%(74/582) 14%(126/875)

    HS Grad
5.3%(100/1885) 2.6%(11/428) 5.3%(31/582) 6.6%(58/875)

    Some College
27%(506/1885) 15%(63/428) 22%(128/582) 36%(315/875)

    Some HS
8.3%(157/1885) 7.0%(30/428) 6.7%(39/582) 10%(88/875)

    University
45%(852/1885) 59%(254/428) 53%(310/582) 33%(288/875)

Oscore 1885 46(7) 44(6) 45(6) 47(7) 37.54855 <0.001
Cscore 1885 41(7) 43(7) 42(7) 40(7) 49.00904 <0.001
Impulsive 1885 255(77) 271(69) 266(72) 240(80) 33.37276 <0.001
1 %(n/N); Mean(SD)
2 Pearson’s Chi-squared test; One-way ANOVA

Comments

  • pleminary results from the chi-square test at 5% level of significance suggest that there is significant association between gender and nicotine usage (p<0.001)
  • results also suggest a significant association between education and Nicotine usage
  • Analysis of variance also suggest and significant different in mean conscientiousness between the different nicotine users (p<0.001)
  • Average Openess to Experience is also significantly different between the types of Nicotine users and so is mean impulsiveness

Fit the model

#> # weights:  30 (18 variable)
#> initial  value 2070.884164 
#> iter  10 value 1900.712626
#> iter  20 value 1846.620744
#> final  value 1846.529384 
#> converged
Characteristic Past User Recent User
OR1 95% CI1 p-value OR1 95% CI1 p-value
Gender





    Female — —
— —
    Male 1.35 1.04, 1.77 0.025 1.75 1.35, 2.26 <0.001
Education





    Certificate/Trade Degree — —
— —
    HS Grad 2.52 1.17, 5.45 0.018 2.36 1.13, 4.95 0.022
    Some College 1.52 0.96, 2.40 0.073 1.67 1.09, 2.55 0.018
    Some HS 1.26 0.70, 2.25 0.4 1.72 1.01, 2.92 0.045
    University 1.09 0.75, 1.58 0.7 0.61 0.42, 0.87 0.006
Oscore 1.04 1.02, 1.06 <0.001 1.07 1.05, 1.09 <0.001
Cscore 0.98 0.96, 1.00 0.13 0.95 0.93, 0.97 <0.001
Impulsive 1.00 1.00, 1.00 >0.9 1.00 1.00, 1.00 0.001
1 OR = Odds Ratio, CI = Confidence Interval

Conclusion

Comment

  • All else being equal, Men have a 35% increased chance of belonging to Past User group relative to the group that has never used, and a 75% increased chance of belonging to the Recent User relative to the group that never used.

  • Higher Openness Scores and lower Conscientious scores associated with Past and Recent User status

  • Education predictor less significant in Past User model, overall, those without university education had higher probability of being Recent of Past Users

The end