State-level variations and factors associated with adult vaccination coverage: a multilevel modeling approach

State-level variations and factors associated with adult vaccination coverage: a multilevel modeling approach

Journal: PharmacoEconomics - Open

Authors: Diana Garbinsky, Shannon Hunter, Elizabeth M. La, Sara Poston, Cosmina Hogea Correspondence: Sara Poston; GSK, sara.a.poston@gsk.com

Conflicts of interest: EL, SP and CH are employed by the GSK group of

companies and hold shares in the GSK group of companies. DG and SH are employees of RTI Health Solutions, which was contracted by the GSK group of companies to design and implement the present study. The authors declare no other financial and non-financial relationships and activities.

Online Resource 4

Additional Details on Statistical Methods VPC Equation

VPC= σ² σ²+π²

3 MOR Equation

MOR=exp

(

√

)

where Φ⁻¹(⋅) is the cumulative distribution function of the standard normal distribution with mean 0 and variance 1.

Impact of Individual-Level Variables

To assess the simultaneous contribution of individual-level characteristics associated with adult vaccination and because all outcomes were dichotomous measures, the following formula was used:¹⁷

logit(p)=β₀+β_iState_i+β_jYear_j+β_ijState_iYear_j+β_kX_k, (Equation 1) where:

 logit(p) is the log of the OR that the dichotomous outcome measure of interest is 1

 State_i is the state of residence

 ^Yearj is the survey year (for models with >1-year data)

 State_iYear_j is the interaction term of state of residence and survey year (for models with >1-year data)

 ^Xk is a vector of underlying individual-level covariates:

o For the influenza and pneumococcal vaccination coverage models, all individual-level covariates were included

o For Tdap and HZ coverage, all socio-demographic, health status, and health care utilization covariates were included

o The model for compliance with age-appropriate recommended influenza and Tdap vaccinations among individuals aged 18–59 years included all socio- demographic, health status, and health care utilization behavior covariates o The model for compliance with age-appropriate recommended influenza, Tdap, and HZ vaccinations among individuals aged 60–64 years included control variables for race/ethnicity, educational attainment, annual household income, health status, and inability to pay for care

o The model for compliance with age-appropriate recommended influenza, pneumococcal, Tdap, and HZ vaccinations among individuals aged >65 years included all socio-demographic, health status, and health care utilization behavior covariates except for the control variable for whether respondents had a designated care provider

o For consistency and interpretability across studies, the same set of individual- level variables were used when updating the analyses with current BRFSS data

 β are the regression coefficients

All covariates were categorical, including age which was reported in the BRFSS data in the predefined years range categories. Post-estimation commands were used to produce linear combinations of the fixed-effect parameter estimates. The average marginal prediction M for the study’s basic measurements was as follows (shown for the example model in which only one year of data is used for simplicity; in models that included more than one year of data, the

year variable and interaction term of state × year was included in the equation as needed) [17]:

M=

∑

w_i

{

⁽

⁾

[

⁽

⁾ ] }

∑

w_i

, (Equation 2)

Where:

 ^β are the weighted maximum likelihood estimators of the regression coefficients and

 wi is the sample weight of the i^th observation

The vector M contains the average marginal predictions for each level of a categorical group variable (in this case, state and year). The actual covariates x were used in these predictions rather than generating predictions at an arbitrary average or median value across observations. These calculations were performed using the PREDMARG statement following the RLOGIST procedure in SAS-callable SUDAAN 11 (RTI International; Research Triangle Park, North Carolina; 2012)

References to the Online Resource

17. Bieler GS, Brown GG, Williams RL, Brogan DJ. Estimating model-adjusted risks, risk differences, and risk ratios from complex survey data. Am J Epidemiol.

2010;171(5):618-623.