HPV vaccine coverage in Texas counties: An application of multilevel, small area estimation

Health departments, research institutions, policy-makers, and healthcare providers are often interested in knowing the health status of their clients/constituents. Without the resources, financially or administratively, to go out into the community and conduct health assessments directly, these entities frequently rely on data from population-based surveys to supply the information they need. Unfortunately, these surveys are ill-equipped for the job due to sample size and privacy concerns. Small area estimation (SAE) techniques have excellent potential in such circumstances, but have been underutilized in public health due to lack of awareness and confidence in applying its methods. The goal of this research is to make model-based SAE accessible to a broad readership using clear, example-based learning. Specifically, we applied the principles of multilevel, unit-level SAE to describe the geographic distribution of HPV vaccine coverage among females aged 11-26 in Texas.^ Multilevel (3 level: individual, county, public health region) random-intercept logit models of HPV vaccination (receipt of ≥ 1 dose Gardasil® ) were fit to data from the 2008 Behavioral Risk Factor Surveillance System (outcome and level 1 covariates) and a number of secondary sources (group-level covariates). Sampling weights were scaled (level 1) or constructed (levels 2 & 3), and incorporated at every level. Using the regression coefficients (and standard errors) from the final models, I simulated 10,000 datasets for each regression coefficient from the normal distribution and applied them to the logit model to estimate HPV vaccine coverage in each county and respective demographic subgroup. For simplicity, I only provide coverage estimates (and 95% confidence intervals) for counties.^ County-level coverage among females aged 11-17 varied from 6.8-29.0%. For females aged 18-26, coverage varied from 1.9%-23.8%. Aggregated to the state level, these values translate to indirect state estimates of 15.5% and 11.4%, respectively; both of which fall within the confidence intervals for the direct estimates of HPV vaccine coverage in Texas (Females 11-17: 17.7%, 95% CI: 13.6, 21.9; Females 18-26: 12.0%, 95% CI: 6.2, 17.7).^ Small area estimation has great potential for informing policy, program development and evaluation, and the provision of health services. Harnessing the flexibility of multilevel, unit-level SAE to estimate HPV vaccine coverage among females aged 11-26 in Texas counties, I have provided (1) practical guidance on how to conceptualize and conduct modelbased SAE, (2) a robust framework that can be applied to other health outcomes or geographic levels of aggregation, and (3) HPV vaccine coverage data that may inform the development of health education programs, the provision of health services, the planning of additional research studies, and the creation of local health policies.^

The number and timing of time -dependent covariate measurements for the Cox regression model

The problem of analyzing data with updated measurements in the time-dependent proportional hazards model arises frequently in practice. One available option is to reduce the number of intervals (or updated measurements) to be included in the Cox regression model. We empirically investigated the bias of the estimator of the time-dependent covariate while varying the effect of failure rate, sample size, true values of the parameters and the number of intervals. We also evaluated how often a time-dependent covariate needs to be collected and assessed the effect of sample size and failure rate on the power of testing a time-dependent effect.^ A time-dependent proportional hazards model with two binary covariates was considered. The time axis was partitioned into k intervals. The baseline hazard was assumed to be 1 so that the failure times were exponentially distributed in the ith interval. A type II censoring model was adopted to characterize the failure rate. The factors of interest were sample size (500, 1000), type II censoring with failure rates of 0.05, 0.10, and 0.20, and three values for each of the non-time-dependent and time-dependent covariates (1/4,1/2,3/4).^ The mean of the bias of the estimator of the coefficient of the time-dependent covariate decreased as sample size and number of intervals increased whereas the mean of the bias increased as failure rate and true values of the covariates increased. The mean of the bias of the estimator of the coefficient was smallest when all of the updated measurements were used in the model compared with two models that used selected measurements of the time-dependent covariate. For the model that included all the measurements, the coverage rates of the estimator of the coefficient of the time-dependent covariate was in most cases 90% or more except when the failure rate was high (0.20). The power associated with testing a time-dependent effect was highest when all of the measurements of the time-dependent covariate were used. An example from the Systolic Hypertension in the Elderly Program Cooperative Research Group is presented. ^

(Table 1) Attenuation coefficient of lateral propagating light in sea ice, southern Beaufort Sea

The attenuation property of a lateral propagating light (LPL) in sea ice was measured using an artificial lamp in the Canadian Arctic during the 2007/2008 winter. A measurement method is proposed and applied whereby a recording instrument is buried in the sea ice and an artificial lamp is moved across the instrument. The apparent attenuation coefficient µ(lamda) for the lateral propagating light is obtained from the measured logarithmic relative variation rate. With the exception of blue and red lights, the attenuation coefficient changed little with wavelength, but changed considerably with depth. The vertical decrease of the attenuation coefficient was found to be correlated with salinity: the greater the salinity, the greater the attenuation coefficient. A clear linear relation of salinity and the lateral attenuation coefficient with R2 = 0.939 exists to address the close correlation of the attenuation of LPL with the scattering from the brine. The observed attenuation coefficient of LPL is much larger than that of the vertical propagation light, which we speculate to be caused by scattering. Part of this scattered component is transmitted out of the sea ice from the upper and lower surfaces.

(Table 2) Similarity Indexes (Pearson's correlation coefficient) of the silicoflagellate assemblages of IODP Exp302

The silicoflagellate and ebridian assemblages in early middle Eocene Arctic cores obtained by IODP Expedition 302 (ACEX) were studied in order to decipher the paleoceanography of the upper water column. The assemblages in Lithologic Unit 2 (49.7-45.1 Ma), one of the biosiliceous intervals, were usually endemic as compared to the assemblages that occurred outside of the Arctic Ocean. The presence of these endemic assemblages is probably due to a unique environmental setting, controlled by the degree of mixing between the low-salinity Arctic waters and relatively high salinity waters supplied from outside the Arctic Ocean, such as the Atlantic and possibly the Western Siberian Sea. Using the basin-to-basin fractionation model, the early middle Eocene Arctic Ocean corresponds to an estuarine circulation type, which includes the modern-day Black Sea. The abundant down-core occurrence of ebridians strongly suggests the past presence of low-salinity waters, and may indicate that low oxygen concentrations prevailed in the euphotic layer, on the basis of the ecology of the modern ebridian Hermesinum adriaticum.

(Table 1) Age model for ODP Site 175-1077 based on oxygen isotopes of Globigerinoides ruber pink

Palynological records from the Congo fan reveal environmental change in equatorial Africa occurring 1.05 Ma ago, 100 k.y. before the mid-Pleistocene climatic shift at 0.9 Ma. Prior to 1.05 Ma, a glacial-interglacial rhythm is not obvious in the African vegetation variation. Afterwards, Podocarpus spread in the mountains of central Africa mainly during glacials and Congo River discharge decreased. The sequence of vegetation variation associated with the mid-Pleistocene glacials and interglacials differed from that observed during the late Pleistocene. Between 0.9 and 0.6 Ma, interglacials were characterized by warm dry conditions and glacials were characterized by cool humid conditions, while during the past 0.2 Ma glacials were cold and dry and interglacials warm and humid. Our data indicate that before the Northern Hemisphere ice caps dramatically increased in size (0.9-0.6 Ma), low-latitude climate forcing and response in the tropics played an important role in the initiation of 100 k.y. ice-age cycles. During the mid to late Pleistocene, however, the climate conditions in the tropics were increasingly influenced by the glacial-interglacial variations of continental ice sheets.

(Table 1) Krill (Euphausia superba) biomass estimates at South Georgia Island from 2001-2005

The South Georgia region supports a large biomass of krill that is subject to high interannual variability. The apparent lack of a locally self-maintaining krill population at South Georgia means that understanding the mechanism underlying these observed population characteristics is essential to successful ecosystem-based management of krill fishery in the region. Krill acoustic-density data from surveys conducted in the early, middle and late period of the summers of 2001 to 2005, together with krill population size structure over the same period from predator diet data, were used with a krill population dynamics model to evaluate potential mechanisms behind the observed changes in krill biomass. Krill abundance was highest during the middle of the summer in 3 years and in the late period in 2 years; in the latter there was evidence that krill recruitment was delayed by several months. A model scenario that included empirically derived estimates of both the magnitude and timing of recruitment in each year showed the greatest correlation with the acoustic series. The results are consistent with a krill population with allochthonous recruitment entering a retained adult population; i.e. oceanic transport of adult krill does not appear to be the major factor determining the dynamics of the adult population. The results highlight the importance of the timing of recruitment, especially where this could introduce a mismatch between the peak of krill abundance and the peak demand from predators, which may exacerbate the effects of changes in krill populations arising from commercial harvesting and/or climate change.

Larcform 1 - single column model intercomparison of Arctic air formation, link to model results in NetCDF format

Weather and climate models struggle to represent lower tropospheric temperature and moisture profiles and surface fluxes in Arctic winter, not least because they lack or misrepresent physical processes that are specific to high latitudes. The Arctic boundary layer in winter has been observed to be in either a radiatively clear or cloudy state: The radiatively clear state is characterized by strong surface radiative cooling leading to the build-up of surface-based temperature inversions, whereas the cloudy state occurs when cloud liquid water is present in the atmospheric column, allowing little or no surface radiative cooling and leading to weaker and typically elevated temperature inversions. Many large-scale models have been shown to lack the cloudy state, and some do substantially underestimate stability in the clear state. We here present results from the first Lagrangian ARCtic air FORMation experiment (Larcform 1), a GASS (Global atmospheric system studies) single-column model intercomparison which reproduces these biases of large-scale models in an idealised setup.