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Estimating maternal mortality II
November 2, 2010
Christopher J.L. Murray
Institute Director
Outline
• Outlier detection
• Modeling approaches II: space-time regression
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Outliers: a reality in this dataset
• Maternal mortality is extremely rare, even where MMRs are very high
• This can result in substantial sampling error and stochastic variation
• Measurement error is also always possible
• Together, these factors can result in the presence of outliers
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What’s the problem with outliers?
• What IS an outlier?
o An outlier can be understood as an atypical observation that appears to be derived from some distribution other than the one of interest
o An outlier is an observation that is numerically distant from the rest of the data, or appears to deviate markedly from other members of the sample in which it occurs
• Naive interpretation of statistics derived from data sets that include outliers may be misleading
• Outliers can:
• Distort estimates
• Increase standard errors
• Reduce the accuracy of fits
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What is an outlier in this dataset?
• Outliers relative to other measurements in the same country
• Outliers relative to what would be expected on the basis of the linear model predictions
• Outliers relative to MMRs observed in countries with similar levels of development and health-system access
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Outlier detection
• Numerous methods have been proposed to identify outliers
• However, most agree that they should not be used as a blanket approach to delete outliers from a dataset
• Some degree of judgment and expert review is needed to decide how to treat those outliers
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Approach to outlier detection
• Identify and remove extreme outliers, in three ways:
o Examine relationship of residuals from first stage regression with covariates
o Examine the above relationship with particular attention towards non-VR sources
o Examine the summary MMR measure
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Approach to outlier detection
• Identify and remove extreme outliers, in three ways:
o Examine relationship of residuals from first stage regression with covariates
o Examine the relationship between the outcome and various covariates, with special attention towards non-VR data
─ Blurosphere plots
o Examine the summary MMR measure
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Approach to outlier detection
• Identify and remove extreme outliers, in three ways:
o Examine relationship of residuals from first stage regression with covariates
o Examine the above relationship with particular attention towards non-VR sources
o Examine the summary MMR measure
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Outline
• Outlier detection
• Modeling approaches II: space-time regression
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Recall the steps in the first stage:
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First stage linear regression model
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Robust Regression Coefficient Std. Error
Intercept 4.715 0.100ln(TFR) 1.903 0.022
ln(GDP per capita) -0.511 0.010Neonatal mortality 13.662 0.721
Education -0.086 0.003HIV 0.108 0.005HIV² -0.001 0.000
Age 15-19 -1.176 0.021Age 20-24 -0.374 0.020Age 25-29 -0.077 0.020Age 35-39 -0.165 0.020Age 40-44 -0.633 0.021Age 45-49 -1.390 0.025
But, the linear predictions don’t track the data very well
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The linear regression isn’t enough
• The covariates available (TFR, GDP, neonatal mortality, HIV prevalence, education) can not explain all of the variation in the dependent variable
• There may be other determinants of maternal mortality, not included in the model, that vary systematically across space and time
• So, some of the residual variation in the error term may vary systematically across space and time
• How can we take advantage of that systematic variation to improve the predictions?
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General Modeling Strategy (Two stages)
Linear modelestimation
Spatial-temporallocal regression
Spatial-temporal regression
• Spatial-temporal regression methods are used in geospatial analysis, meteorology, soil chemistry, and other fields to capture this systematic variation
• Use the residuals from the first stage regression
o Take advantage of spatial and temporal patterns in the residuals from the first stage regression
o Run a local fixed effects regression with weights on the data for each country-year regression
• Smooth the residual differences over countries and across time
• Add in these smoothed differences to the predicted trend from step 1
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Weights for spatial-temporal regression
• Space weight
o Countries within the same GBD region will be more related
o 21 GBD regions defined based on epidemiology
• Time weight
o Think that time points closer together will be more related
o Use the tricubic weighting function
• Age weight
o Think that ages closer together will be more related
o Use an exponential decay weighting function
• Final weights the product of the space, time and age weights
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HIV counterfactual estimates
• What would have happened in the absence of HIV?
• In most countries of the region, HIV has had a negligible impact on maternal mortality
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