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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