Estimating maternal mortality II November 2, 2010 Christopher J.L. Murray Institute Director
Outline <ul><li>Outlier detection </li></ul><ul><li>Modeling approaches II: space-time regression </li></ul>
Outliers: a reality in this dataset <ul><li>Maternal mortality is extremely rare, even where MMRs are very high </li></ul>...
What’s the problem with outliers? <ul><li>What IS an outlier?  </li></ul><ul><ul><li>An outlier can be understood as an  a...
What is an outlier in this dataset? <ul><li>Outliers relative to other measurements in the same country  </li></ul><ul><li...
Outlier detection <ul><li>Numerous methods have been proposed to identify outliers </li></ul><ul><li>However, most agree t...
Approach to outlier detection <ul><li>Identify and remove extreme outliers, in three ways: </li></ul><ul><ul><li>Examine r...
Approach to outlier detection <ul><li>Identify and remove extreme outliers, in three ways: </li></ul><ul><ul><li>Examine r...
Approach to outlier detection <ul><li>Identify and remove extreme outliers, in three ways: </li></ul><ul><ul><li>Examine r...
Outline <ul><li>Outlier detection </li></ul><ul><li>Modeling approaches II: space-time regression </li></ul>
Recall the steps in the first stage:
First stage linear regression model   Robust Regression   Coefficient Std. Error Intercept 4.715 0.100 ln(TFR) 1.903 0.022...
But, the linear predictions don’t track the data very well
The linear regression isn’t enough <ul><li>The covariates available (TFR, GDP, neonatal mortality, HIV prevalence, educati...
  General Modeling Strategy (Two stages) Linear model estimation Spatial-temporal local regression
Spatial-temporal regression <ul><li>Spatial-temporal regression methods are used in geospatial analysis, meteorology, soil...
Weights for spatial-temporal regression <ul><li>Space weight  </li></ul><ul><ul><li>Countries within the same GBD region w...
HIV counterfactual estimates <ul><li>What would have happened in the absence of HIV? </li></ul><ul><li>In most countries o...
maternal mortality sri lanka estimating maternal mortality ii_lozano_110210_ihme
maternal mortality sri lanka estimating maternal mortality ii_lozano_110210_ihme
maternal mortality sri lanka estimating maternal mortality ii_lozano_110210_ihme
maternal mortality sri lanka estimating maternal mortality ii_lozano_110210_ihme
maternal mortality sri lanka estimating maternal mortality ii_lozano_110210_ihme
maternal mortality sri lanka estimating maternal mortality ii_lozano_110210_ihme
maternal mortality sri lanka estimating maternal mortality ii_lozano_110210_ihme
maternal mortality sri lanka estimating maternal mortality ii_lozano_110210_ihme
maternal mortality sri lanka estimating maternal mortality ii_lozano_110210_ihme
maternal mortality sri lanka estimating maternal mortality ii_lozano_110210_ihme
maternal mortality sri lanka estimating maternal mortality ii_lozano_110210_ihme
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maternal mortality sri lanka estimating maternal mortality ii_lozano_110210_ihme

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

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