Linking Time-Use Data to Explore Health Outcomes: Choosing to Vaccinate Against Influenza

Abstract

To inform public health and medical decision makers concerning vaccination interventions, a methodology for merging and analyzing detailed activity data and health outcomes is presented. The objective is to investigate relationships between individual’s activity choices and their decision to receive an influenza vaccination. Data from the Behavioral Risk Factor Surveillance System (BRFSS) are used to predict vaccination rates in the American Time Use Survey (ATUS) data between 2003 and 2013 by using combined socioeconomic and demographic characteristics. The correlations between the extensive (do or not do) and intensive (how much) decisions to perform activities and influenza vaccination are further explored. Significant positive and negative correlations were found between several activities and vaccination. For some activities, the sign of the correlation flips when considering either the intensive or the extensive decision. This flip occurs with highly studied activities, like smoking. Correlations between activities and vaccination can provide an additional metric for targeting those least likely to vaccinate. The methodology outlined in this paper can be replicated to explore correlation among actions and other health outcomes.

Appendix

Vaccination and Activity Choice

Two regression models are used to examine the relationship between vaccination and activities at the extensive (logistic regression) and intensive (Poisson regression) margins.

Estimating the Do–Don’t Do Decision (Extensive Choices)

The logistic regression of whether or not individuals perform an activity consists of a binary indicator equal to one if respondent $i = 1, \ldots ,n$ does activity $j = 1, \ldots ,J$ as a function of the probability of vaccination, $\hat{v}_{i}$, and the vector of controls, $\varvec{x}$.

$$\Pr \left( {Bin\_a_{{ij}} = 1} \right) = \frac{1}{{1 + e^{{ - \left( {\beta _{0} + \beta _{1} \hat{v}_{i} + \varvec{\beta ^{\prime}x}_{i} } \right)}} }} $$

(2)

When $\Pr \left( {Bin\_a_{ij} = 1} \right)$, the individual chooses to participate in an activity, otherwise it equals zero. The estimated vaccination probabilities, $\hat{v}_{i}$, have associated prediction error. Therefore, Monte Carlo simulation is used to estimate the vaccination coefficient and associated standard errors. The Monte Carlo procedure is as follows:

• 1. Draw a vaccination probability from a normal distribution with mean equal to the coefficient estimated from the preliminary logistic regression in Eq. (1), $\eta_{v}$, and its standard error.

• 2. Estimate the logistic activity regression in Eq. (2) and store coefficient $\beta_{1}$.

• 3. Repeat steps 1 and 2 100 times.

• 4. Calculate the mean and standard error based on the 100⁵ different coefficient estimates from each run.

Odds ratios are calculated for the impact of a 1% increase in vaccination probability on the likelihood of performing an activity. All odds ratios and risk ratios are calculated for a 1% increase in relative risk of vaccination. Odds ratios from Eq. (2) are interpreted as the odds that an individual participates in activity $j$, conditional on $\hat{v}_{i}$ being 1% higher, relative to the odds that an individual participates in $j$ conditional on their vaccination probability being unchanged.

Estimating Time Spent (Duration Decision)

The intensive activity decision, conditional on doing the activity, is modeled as a Poisson regression. The minutes spent doing an activity, $a_{ij}$, is regressed on the continuous probability of being vaccinated $\hat{v}_{i}$ and a vector of controls $\varvec{x}_{i}$,

$$ \Pr \left( {a = a_{ij} |x_{i} } \right) = \frac{{e^{{ - \mu_{ij} }} \mu_{ij}^{{\hat{a}_{ij} }} }}{{\hat{a}_{ij} !}}, \quad a_{ij} = 0,1,2 \ldots $$

$${\text{ln}}\left( {\mu _{{{\text{ij}}}} } \right) = \delta _{0} + \delta _{1} \hat{v}_{i} + \varvec{\delta }^{\prime} \varvec{x}_{i} + \epsilon _{i} $$

(3)

which is estimated with quasi-Poisson errors, which assume that variance is a linear function of the mean to control for possible over dispersion. The coefficient, $\delta_{1}$, and its standard error are estimated by the Monte Carlo simulation methods described in the previous section.

Risk ratios are calculated for the second equation in (3) and are interpreted as the ratio of the probability an individual spends another minute participating in an activity conditional on their vaccination probability being 1% higher, relative to the probability of spending another moment participating in that activity conditional on their vaccination probability being unchanged.

Grocery Shopping

We also estimate a model of activity choice and grocery store attendance. Because it is not necessary to statistically match the datasets, we use the full ATUS dataset and do not perform Monte Carlo simulations. We observe the duration of each activity done by respondents on their interview day as well as time spent at the grocery store location.

Estimating time spent (duration decision) consists of a logit model of the decision of how much time to spend at the grocery store on the extensive decision to participate in an activity. Let $g_{i}$ be the total minutes respondent $i$ spends at a grocery store and the binary variable, $d_{i}^{g}$, be equal to one if respondent $i$ spends at least 1 min at a grocery store.

$$ Pr\left( {{\text{Bin}}_{{a_{{ij}} }} = 1} \right) = \frac{1}{{1 + e^{{ - \left( {\gamma _{0} + \gamma _{1} d_{i}^{g} + \gamma _{2} g_{i} *d_{i}^{g} + \varvec{\alpha ^{\prime}x}_{i} } \right)}} }}\quad \forall ~i,j $$

(4)

Variable $a_{ij}$ remains the time spent on activity $j$ by person $i$ and $d_{i}^{g}$ is time spent at a grocery store. We include the vector $x_{i}$ of controls that consist of age, sex, income, education, the day of the week, month and year as well as the state. We again estimate this equation for each activity $j$ in the ATUS. The model contains both the binary grocery store variable and the interaction between the binary and continuous variables. Including both variables provides flexibility to the model to accommodate the difference between the effect of zero and 1 min versus 10 and 11 min on activity.

We calculate odds ratios for all activities in Eq. (3) for both the first minute spend in a grocery store, and every additional minute. The interpretation of the odds ratio for $\gamma_{1}$ is the ratio of the odds that an individual participates in activity $j$ subject to spending any time at all in a grocery store (binary variable, $d_{i}^{g}$) relative to the odds that an individual participates in activity $j$ subject to not spending time in a grocery store. The odds ratio for $\gamma_{2}$ is the ratio of the odds an individual participates in an activity conditional on spending an additional minute at the grocery store, versus not having spent more time at the grocery store (but still having gone to a grocery store for at least 1 min).

We use a count model to study the association between intensive activity decisions and the extensive decision to spend time in grocery store, $d_{i}^{g} ,$ and the amount of time in grocery store, $g_{i}$,

$$ \Pr \left( {a = a_{ij} |x_{i} } \right) = \frac{{e^{{ - \lambda_{ij} }} \lambda_{ij}^{{\hat{a}_{ij} }} }}{{\hat{a}_{ij} !}} $$

$$\ln \left( {\lambda _{{ij}} } \right) = \gamma _{0} + \gamma _{1} d_{i}^{g} + \gamma _{2} g_{i} *d_{i}^{g} + \varvec{\alpha }^{\prime} \varvec{x}_{i} + \epsilon _{i} $$

(5)

The model uses quasi-Poisson methods as an ad hoc control for over dispersion. The risk ratio of $\gamma_{1}$ and $\gamma_{2}$ is analogous to the odds ratios for $\gamma_{1}$ and $\gamma_{2}$ in the first stage, except they are not ratios of probabilities instead of odds.