The objective of this analysis was to explore temporal and spatial variation in teen birth rates TBRs across counties in the USA, from 2003 to 2012, by using hierarchical Bayesian models. Prior examination of spatiotemporal variation in TBRs has been limited by the reliance on large-scale geographies such as states, because of the potential instability in TBRs at smaller geographical scales such as counties. We implemented hierarchical Bayesian models with space–time interaction terms and spatially structured and unstructured random effects to produce smoothed county level TBR estimates, allowing for examination of spatiotemporal patterns and trends in TBRs at a smaller geographic scale across the USA. The results may help to highlight US counties where TBRs are higher or lower and to inform efforts to reduce birth rates to adolescents in the USA further.

Teen birth rates (TBRs) have declined over the past several years across
nearly every state in the USA (

TBRs vary by state, with higher values seen across the south and
south-western regions of the country and lower TBRs observed in the north-east
(

Past studies have looked at the risk factors affecting teen pregnancies
(

The objective of this analysis was to explore temporal and spatial variation
in TBRs across 3138 counties in the USA, from 2003 to 2012. Bayesian hierarchical
space–time interaction models (

The plan of this paper is as follows. Section 2 contains information on data and methods. In Section 3, we discuss methods for evaluating model fit, comparisons of the models proposed and residual analysis. Sections 4 and 5 discuss results and findings. Finally, in Section 6, we discuss conclusions and future research directions.

The programs that were used to analyse the data can be obtained from

Data on the number of live births for women aged 15–19 years were
extracted from the national vital statistics birth data files for the years
2003–2012 (e.g.

During the decade of interest, county borders in Alaska changed such that new counties were formed and others were merged. These changes were reflected in the population files but not in the natality files. For this reason, two counties in Alaska had to be collapsed so that the birth and population counts were comparable. Additionally, Kalawao County, which is a remote island county in Hawaii, recorded no births and the census estimates indicated a denominator of 0 (i.e. zero females between the ages of 15 and 19 years residing in the county from 2003 to 2012). Hence, Kalawao County was removed from the analysis and the final analysis was conducted on 3138 counties in the USA.

County level covariates including various socio-economic indicators
(e.g.

The broad scale trends in TBRs were examined by census regions (Midwest,
Northeast, South, and West), census divisions (East North Central, East South,
Mid-Atlantic, Mountain, New England, Pacific, South Atlantic, West North Central
and West South Central) and urban–rural designations as classified by
the National Center for Health Statistics (

For a list of the variables that were used in the final analysis refer
to

We fit a hierarchical Bayesian model by using methods similar to those
established by _{it}_{it}_{it}_{it}_{it}_{it}

The general space–time model structure for modelling
_{it}

_{i}_{t}_{it}

Several models were implemented following this general
space–time modelling framework. The two best competing models are
presented here, representing two special cases of the general space–time
model. One case follows the approach of

The raw county level TBRs exhibited strong spatial auto-correlation
as indicated by a Moran’s

The convolution model includes

a logit link function
log{_{it}_{it}

_{0}, an intercept,

a time trend term
_{1}_{i}_{t}

_{i}_{i}

spatial random effects _{i}

non-spatial random effects _{i}_{i}

a space–time interaction term
_{it}_{it}_{i}_{,}_{t}_{−1},
plus an error term.

Parameters under (e) are modelled via normal conditional
auto-regressive priors (

To discern whether spatially structured random effects offer major improvements in model fit, a basic model without spatially structured random effects was also examined. The basic model is

The basic model includes (

a logit link function
log{_{it}_{it}

_{1}_{i}

the time trend term
_{2}_{i}_{t}

_{i}_{i}

_{it}_{it}_{i}_{,}_{t}_{−1},
plus an error term.

Parameters under (d) and (e) are modelled as in the convolution
model that was described above. Specifically,
_{it}_{0} +
_{i}

Several other models were implemented in WinBUGS, including simpler versions of the two models that were described above. Because of poor convergence or fit of these other models, we present results for only the two best performing models (see Section 4.2).

Since the conditional auto-regressive normal prior is assigned for
the spatial random effects _{i}_{0}. For the
basic model, the county-specific intercepts
_{1}_{i}_{2}_{i}

_{i}_{1}_{i}_{2}_{i}

_{i}^{IID}

The hyperprior of

Sensitivity analyses were conducted with different prior values on
the precisions with a choice of parameters leading to priors with most of
the probability mass around the expected values of the variance parameters
(_{1}_{i}_{i}_{i}_{i}_{it}

Analyses were implemented via Markov chain Monte Carlo (MCMC)
simulations using the WinBUGS freeware (

The posterior probabilities _{it}_{it}

The raw county level TBRs ranged from 0 to 133 per 1000 in 2012, with a
mean of 36 per 1000 (median, 34 per 1000; interquartile range, 21–48 per
1000). By contrast, in 2003, the raw county level TBRs ranged from 0 to 147 per
1000 with a mean of 44 per 1000 (median, 42 per 1000; interquartile range,
28–58 per 1000). The threshold for the exceedance probability

The structural assumptions of the fitted model can be ascertained by the
use of posterior predictive model checks (^{obs} with the posterior predictive distribution
or replicates ^{rep}. We generated replicate data sets
^{rep} for each posterior draw of the model
parameters and then calculated a test quantity
_{it}

(

The posterior probabilities that are produced by each model for each county and year were summed by state and weighted by county population size as a proportion of state population size to create state model-based estimates of the TBR for each year. These model-based estimates were compared with the direct estimates of the TBR for each state and year to ascertain whether one of the models performed better or worse than another in terms of matching the state direct estimates.

Models were also evaluated by using the Gelfand and Ghosh statistic,
which compares observed data ^{obs} with the
replicates ^{rep}. This approach minimizes the
posterior predictive loss over all possible predictions of future observations
^{rep} (

(where

With the increasing complexity in models,

Models can be compared by using a criterion utilizing a trade-off
between the fit of the data and the corresponding complexity of the model. The
DIC was proposed by

_{it}_{it}

_{θ}_{|}_{y}_{θ}_{|}_{y}

Models with smaller DIC are preferred.

We employed further model checks by analysing the residuals from each model. Residuals were defined as the difference between the model-based and direct estimates of the TBR for each county and year. The distribution of the residuals was inspected for deviations from normality. Residuals were also examined in relation to county size and year to determine whether there were potential non-linear patterns in TBRs that were not accounted for by the model.

Including covariates can enhance small area predictions. On the basis of
the past research on risk factors affecting teen pregnancies at the state and
national level (

The principal component analysis, using a varimax rotation, indicated
that three components were sufficient as they accounted for 88% of the
total variation. The variables loading on each of the three components are
described in

Several models were implemented in WinBUGS. The best competing
convolution and basic models are described in this analysis. These models were
selected on the basis of the DIC, Gelfand and Ghosh statistic and the Bayesian

The basic and the BYM models performed similarly in terms of the
comparison of model-based and direct estimates of state TBRs. Both models
produced state level TBR estimates that were within 1% of the direct
estimates for all states except for North Dakota, for which the difference
between the model-based and direct estimates was less than 2% (

The BYM and basic models performed similarly in terms of convergence and
residual analysis. In comparisons of model fit, the BYM model provided a better
fit with lower DIC and Gelfand and Ghosh statistics (see

The maps (

TBRs were highest across the entire study period in the South, and
lowest in the Northeast. In 2003, there were bands of particularly higher TBRs
(greater than 80 births per 1000 teens) across west Texas and other states in
the South along the Mississippi River (e.g. Mississippi, Tennessee and
Arkansas), as well as pockets in Alaska, Florida, Georgia, South Carolina, New
Mexico and Oklahoma (see

In 2012, most of the counties across the southern states had very high
probabilities (

Looking at the declines in TBRs by census region, the South had the
highest TBRs over the study period and the Northeast had the lowest. In 2003,
the West had slightly higher TBRs than the Midwest (both in the middle between
the South and Northeast) but TBRs converged for these two regions over the study
period such that they were the same in 2012 (

Consistent with prior research, we found higher TBRs across counties in the
southern USA and lower TBRs in New England counties during the study period,
2003–2012. Whereas TBRs declined across all regions of the country from 2003
to 2012, TBRs remained in excess of 80 births per 1000 adolescent females in several
counties across west Texas and along the Mississippi River, as well as parts of
Georgia and Alaska. In 2012, 50.1% of counties had TBRs in excess of 36
births per 1000 adolescent females (

The posterior MCMC output from WinBUGS for the parameter estimates from the
basic model is shown in

The limitations of this analysis are as follows. Although several models were implemented and evaluated, ranging in complexity, it is possible that alternative models incorporating different covariates or using different specifications would have improved model fit or prediction. The MCMC simulations were extremely computationally intensive, requiring an average of 6 weeks to run on a 150-Gbyte machine, which is a major limiting factor in exploring alternative models. Additionally, the exceedance probabilities are sensitive to the threshold that is selected, and alternative thresholds might be of interest. The threshold that we selected is somewhat arbitrary, but our objective was to demonstrate how this method could be used to examine county level variation in meeting specified public health objectives. Finally, there may be variation in TBRs at the subcounty level, but this variation cannot currently be explored by using data from the national vital statistics system.

The strengths of this analysis include the combination of a detailed
geographic focus (at the county level), over a substantive period of time,
accounting for selected factors that affect teen births, including level of
education, income, poverty and race distribution. To date, most of the work on
estimating TBRs and assessing geographic variation has been done at the state level
(

The Bayesian space–time interaction models that were employed here
allow the estimation of county level TBRs and an examination of how geographic
patterns have changed over time. Results of this analysis suggest that 37%
of counties evidenced TBRs in excess of 36 births per 1000 adolescent females in
2012 (

Results may inform future research seeking to understand spatiotemporal
patterns in teen births better and to target efforts to reduce TBRs in areas where
they remain high. Given differences in TBRs across racial or ethnic subpopulations
and specific age ranges such as 15–17 and 18–19 years, further
examination of spatiotemporal patterns for these specific subgroups may be of
interest. Work is under way to examine hot and cold spots in TBRs as well as spatial
outliers (

The authors thank Alan H. Dorfman, Division of Research and Methodology Staff Chief, for many helpful comments and help in the process of research. We thank, in addition, Peter Meyer, Negasi Beyene and Pavlo Rudyy of the National Center for Health Statistics Research Data Center for providing a high performance computing environment for conducting Bayesian MCMC simulations.

The findings and conclusions in this paper are those of the authors and do not necessarily represent the official positions of the National Center for Health Statistics, Centers for Disease Control and Prevention.

Additional ‘

_{0} is assigned an improper
flat prior

The prior for _{1} is

where

where

and

The prior for type II random-walk interaction is defined above
and can be regarded as a form of residual (

where

The intrinsic conditionally auto-regressive prior for
_{i}_{−}_{i}

and is termed correlated heterogeneity (variability), where

_{i}_{i}_{ij}_{ij}_{ij}_{u}

The prior for _{i}

and is termed uncorrelated heterogeneity (variability), where
_{v}_{v}

Prior assumptions: for the non-spatial model

The hyperprior for

The inverse of

Principal component analysis: construct 1—high poverty and low income (higher TBRs occur in areas where poverty is high and income is low (darker areas))

Principal component analysis: construct 2—educational level (higher TBRs occur in low education areas (lighter areas))

Principal component analysis: construct 3—race or ethnicity, percentage white (higher TBRs occur in areas where the percentage of the population is predominantly non-white (lighter areas))

Differences between state model-based (from the convolution model) and direct
estimates:

Differences between state model-based (from the convolution model) and direct
estimates by state population size:

Residuals from the convolution model by year: the few outlying points reflect
counties with very small population denominators, typically

Convolution model and basic model residuals for the year 2012 exhibit similar patterns as they fall on the line of equality

Predicted TBRs (per thousand) from the convolution model for year 2003

Predicted TBRs (per thousand) from the convolution model for year 2012

Difference in predicted TBRs (per thousand) from the convolution model for years 2003–2012

Exceedance probabilities from the convolution model for year 2012 illustrate where the TBRs exceed 36 per 1000 with high or low probabilities

Exceedance probabilities from the convolution model for year 2003 illustrate where the TBRs exceed 36 per 1000 with high or low probabilities

Trends in the predicted TBRs (per thousand) from the convolution model over time
by census region:

Trends in predicted TBRs (per thousand) from the convolution model over time by
urban–rural classification:

Trends in predicted TBRs (per thousand) from the convolution model over time by
division:

Scatter plot of TBRs with the three orthogonal component scores and the scatter
plot for the three orthogonal component scores with each other: (a)

Variables included in the principal component analysis

Variable | Principal component analysis component | ||
---|---|---|---|

| |||

1 | 2 | 3 | |

% white population 2010 | −30 | 2 | 89 |

% non-Hispanic white population 2010 | −25 | 11 | 92 |

Median household income 2011 | −78 | 43 | −17 |

% persons in poverty 2011 | 89 | −28 | −26 |

% persons in poverty 2010 | 89 | −29 | −26 |

% persons in poverty 2009 | 91 | −27 | −22 |

% persons in poverty 2008 | 91 | −30 | −22 |

% persons in poverty 2007 | 90 | −29 | −24 |

% persons in poverty 2006 | 89 | −30 | −25 |

% persons in poverty 2005 | 89 | −29 | −26 |

% persons in poverty 2000 | 84 | −35 | −27 |

% persons age 0–17 years in poverty 2011 | 84 | −37 | −20 |

% persons below poverty level 2006–2010 | 87 | −27 | −25 |

% families below poverty level 2006–2010 | 81 | −35 | −29 |

% persons age ≥ 25 years with less than High School Diploma 2006–2010 | 42 | −82 | −30 |

% persons age ≥ 25 years with High School Diploma or more 2006–2010 | −42 | 82 | 30 |

% persons age ≥ 25 years with ≥ 4 years college 2006–2010 | −32 | 81 | −23 |

Unemployment rate, ≥ 16 years, 2005 | 52 | −29 | −21 |

Significant positive (or negative) contribution to the component score.

Model selection and fit based on the Gelfand and Ghosh statistic, Bayesian

Model | G | P | D | p-value | DIC |
---|---|---|---|---|---|

Convolution | 6271059417 | 6076027.018 | 6277135444 | 0.5717 | 210493 |

Basic | 6274389428 | 6135753.038 | 6280525182 | 0.5632 | 210553 |

Parameter estimates for the convolution model: orthogonal scores coefficients

Node | Mean | sd | Monte Carlo error | 2.5 percentile | Median | 97.5 percentile |
---|---|---|---|---|---|---|

_{1} | 0.2008 | 0.006403 | 2.58×10^{−4} | 0.1881 | 0.2009 | 0.2131 |

_{2} | −0.2815 | 0.006194 | 2.84×10^{−4} | −0.2931 | −0.2816 | −0.269 |

_{3} | −0.1809 | 0.006711 | 4.13×10^{−4} | −0.1936 | −0.181 | −0.1677 |

sd( | 0.00706 | 1.98×10^{−4} | 8.27×10^{−6} | 0.006681 | 0.007059 | 0.007457 |