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The impact of missing data in the estimation of concentration index: a potential source of bias

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Abstract

The purpose of this paper is to raise awareness of missing data when concentration indices are used to evaluate health-related inequality. Concentration indices are most commonly calculated using individual-level survey data. Incomplete data is a pervasive problem faced by most applied researchers who use survey data. The default analysis method in most statistical software packages is complete-case analysis. This excludes any cases where any variables are missing. If the missing variables in question are not completely random, the calculated concentration indices are likely to be biased, which may lead to inappropriate policy recommendations. In this paper, I use both a case study and a simulation study to show how complete-case analysis may lead to biases in the estimation of concentration indices. A possible solution to correct such biases is proposed.

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Notes

  1. The unweighted percentage is 2.62%. It becomes 2.59% after we apply population sampling weights. All the percentage numbers referred below in this section are population-weighted.

  2. The total household income in the top category is assumed at $100,000.

  3. We must acknowledge here that the statistical inference does not account for the fact that both concentration indices are calculated from the same sample. For a detailed discussion on potential problems and possible solutions, please refer to [15, 16].

  4. Population sampling weights capture differences between the original sample design and resulting response rates. They may also capture some of the patterns in the item-non-response that we are looking at. If we calculate the concentration indices without sampling weights, we can find that the differences between the concentration indices calculated from different methods are all slightly larger than those presented in the fourth column of Table 2. This finding may imply that the bias from using data with missing values would be less severe if we use population sampling weights.

  5. For more detailed discussions on this reranking effect in the context of the Gini coefficient, please refer to [22, 23]; for a discussion in the context of the concentration index, please refer to [21, 24].

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Acknowledgments

I would like to thank Jerry Hurley and an anonymous referee for their helpful comments. I am solely responsible for any remaining errors and omissions.

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Authors and Affiliations

  1. School of Public Finance and Public Policy, Central University of Finance and Economics, 39 South College Road, 100081, Beijing, China

    Hai Zhong

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  1. Hai Zhong
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Correspondence to Hai Zhong.

Appendix

Appendix

See Tables 5 and 6.

Table 5 Variables included in imputation of individual level covariates
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Table 6 Variables included in imputation of household income
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Zhong, H. The impact of missing data in the estimation of concentration index: a potential source of bias. Eur J Health Econ 11, 255–266 (2010). https://doi.org/10.1007/s10198-009-0170-5

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