Impact of ignoring sampling design in the prediction of binary health outcomes through logistic regression: evidence from Malawi demographic and health survey under-five mortality data; 2000-2016

Kaombe, Tsirizani M.; Hamuza, Gracious A.

doi:10.1186/s12889-023-16544-4

Table 4 Bias in under-five mortality estimate using unweighted and weighted logit model, as well as unweighted and weighted predicted mortality estimate

From: Impact of ignoring sampling design in the prediction of binary health outcomes through logistic regression: evidence from Malawi demographic and health survey under-five mortality data; 2000-2016

n	\(\widehat{\boldsymbol\pi}\boldsymbol(\mathbf x\boldsymbol)\boldsymbol(\boldsymbol S\boldsymbol.\boldsymbol E\boldsymbol.\boldsymbol)\)	\(\boldsymbol\pi\)	\(\boldsymbol b\boldsymbol i\boldsymbol a\boldsymbol s\boldsymbol(\widehat{\boldsymbol\pi}\boldsymbol(\textbf{x}\boldsymbol)\boldsymbol)\)	\(\widehat{\boldsymbol\pi}\boldsymbol(\mathbf x\boldsymbol)\boldsymbol(\boldsymbol S\boldsymbol.\boldsymbol E\boldsymbol.\boldsymbol)\)	\(\boldsymbol\pi\)	\(\boldsymbol b\boldsymbol i\boldsymbol a\boldsymbol s\boldsymbol(\widehat{\boldsymbol\pi}\boldsymbol(\textbf{x}\boldsymbol)\boldsymbol)\)
	2004 unweighted model, unweighted \(\hat{\pi }(\textbf{x})\)			2004 weighted model, weighted \(\hat{\pi } (\textbf{x})\)
10,914	0.004 (0.001)	0.133	-0.129	0.086 (0.000)	0.133	-0.047
8,292	0.004 (0.001)	0.133	-0.129	0.091 (0.000)	0.133	-0.042
5,624	0.004 (0.001)	0.133	-0.129	0.087 (0.000)	0.133	-0.046
2,878	0.004 (0.001)	0.133	-0.129	0.089 (0.000)	0.133	-0.044
	2004 unweighted model, weighted \(\hat{\pi }(\textbf{x})\)			2004 weighted model, unweighted \(\hat{\pi } (\textbf{x})\)
10,914	0.090 (0.000)	0.133	-0.043	0.004 (0.001)	0.133	-0.129
8,292	0.091 (0.000)	0.133	-0.042	0.004 (0.001)	0.133	-0.129
5,624	0.089 (0.000)	0.133	-0.044	0.004 (0.001)	0.133	-0.129
2,878	0.090 (0.000)	0.133	-0.043	0.004 (0.001)	0.133	-0.129
	2010 unweighted model, unweighted \(\hat{\pi }(\textbf{x})\)			2010 weighted model, weighted \(\hat{\pi }(\textbf{x})\)
19,967	0.003 (0.000)	0.112	-0.109	0.077 (0.000)	0.112	-0.035
15,064	0.003 (0.001)	0.112	-0.109	0.076 (0.000)	0.112	-0.036
10,153	0.003 (0.001)	0.112	-0.109	0.074 (0.000)	0.112	-0.038
5,030	0.003 (0.001)	0.112	-0.109	0.070 (0.000)	0.112	-0.042
	2010 unweighted model, weighted \(\hat{\pi }(\textbf{x})\)			2010 weighted model, unweighted \(\hat{\pi }(\textbf{x})\)
19,967	0.077 (0.000)	0.112	-0.035	0.003 (0.000)	0.112	-0.109
15,064	0.077 (0.000)	0.112	-0.035	0.003 (0.001)	0.112	-0.109
10,153	0.075 (0.000)	0.112	-0.037	0.003 (0.001)	0.112	-0.109
5,030	0.072 (0.000)	0.112	-0.040	0.003 (0.001)	0.112	-0.109
	2015 unweighted model, unweighted \(\hat{\pi }(\textbf{x})\)			2015 weighted model, weighted \(\hat{\pi }(\textbf{x})\)
17,286	0.002 (0.000)	0.063	-0.061	0.040 (0.000)	0.063	-0.023
13,099	0.002 (0.000)	0.063	-0.061	0.038 (0.000)	0.063	-0.025
8,644	0.002 (0.001)	0.063	-0.061	0.038 (0.000)	0.063	-0.025
4,314	0.002 (0.001)	0.063	-0.061	0.045 (0.000)	0.063	-0.018
	2015 unweighted model, weighted \(\hat{\pi }(\textbf{x})\)			2015 weighted model, unweighted \(\hat{\pi }(\textbf{x})\)
17,286	0.042 (0.000)	0.063	-0.021	0.002 (0.000)	0.063	-0.061
13,099	0.039 (0.000)	0.063	-0.024	0.002 (0.000)	0.063	-0.061
8,644	0.040 (0.000)	0.063	-0.023	0.002 (0.001)	0.063	-0.061
4,314	0.046 (0.000)	0.063	-0.017	0.002 (0.001)	0.063	-0.061

\(\hat{\pi }(\textbf{x})\) = overall predicted under-five mortality rate; S.E. = standard error of \(\hat{\pi }(\textbf{x})\);
\(\pi\)= raw under-five mortality rate from MDHS report; \(bias(\hat{\pi }(\textbf{x}))\)=\(\hat{\pi }(\textbf{x})-\pi\)

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ISSN: 1471-2458

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