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Table 2 Evaluation metrics of imputed data with varying missing proportions of various health indicators in comparison with complete data

From: How much missing data is too much to impute for longitudinal health indicators? A preliminary guideline for the choice of the extent of missing proportion to impute with multiple imputation by chained equations

Imputed datasets with missing criteria

Adolescent mortality rate

Under-five mortality rate

Infant mortality rate

Neonatal mortality rate

Stillbirth rate

Root Mean Square Error—RMSE (RMSE value close to zero is desirable)

 10%

4.205a

1.509a

1.201a

0.406a

0.366a

 20%

4.082a

2.323a

1.500a

0.485a

0.300a

 30%

13.531a

2.453a

1.099a

0.819a

0.346a

 40%

7.930a

4.361a

3.574a

3.817a

0.466a

 50%

20.691a

7.944a

5.204a

4.489b

1.577a

 60%

13.587a

15.328b

13.324c

4.165b

3.728b

 70%

39.886b

17.341b

11.897c

5.007b

5.276c

 80%

46.129b

22.143c

15.310c

8.586c

5.697c

90%

72.885c

29.888c

17.796c

11.712c

7.385c

Mean Absolute Deviation—MAD (MAD value close to zero is desirable)

 10%

2.961a

1.049a

0.785a

0.342a

0.263a

 20%

3.006a

1.538a

1.053a

0.395a

0.228a

 30%

5.768a

1.743a

0.770a

0.507a

0.229a

 40%

4.311a

1.990a

1.326a

1.206a

0.298a

 50%

7.231a

2.653a

2.041a

1.559a

0.499a

 60%

6.755a

6.055a

4.980b

1.638a

1.581a

70%

17.243a

9.157b

5.511b

2.285a

2.526b

80%

29.143b

12.672b

8.752b

5.033b

3.291b

 90%

58.671c

20.224c

13.267c

10.131c

5.217c

BIAS (BIAS value of zero indicates no bias, a positive value indicates the overestimation and a negative value indicates an underestimation of complete data)

 10%

0.248a

0.149a

0.003a

− 0.097a

− 0.016a

 20%

0.279a

0.295a

0.023a

0.002a

− 0.016a

 30%

3.074b

0.059a

− 0.054a

− 0.026a

− 0.048a

40%

− 1.358a

0.254a

0.439a

− 0.719b

− 0.018a

 50%

− 4.113b

− 1.228a

0.216a

− 0.527b

0.262a

 60%

− 1.476a

− 2.048a

− 3.492c

− 0.780b

− 0.357b

 70%

− 1.268a

− 1.408a

− 0.350a

0.546b

− 1.065c

 80%

7.686c

− 2.493a

− 2.081b

− 1.242c

0.100a

90%

− 4.823b

− 8.249c

1.137a

− 0.570b

− 0.203a

Proportionate Variance—PV (The PV value closer to 1 is desirable)

 10%

0.968a

1.002a

0.992a

1.005a

1.010a

 20%

1.005a

1.056a

0.984a

1.014a

0.995a

 30%

0.984a

1.023a

0.994a

1.003a

0.989a

 40%

0.977a

0.953a

0.965a

0.901a

1.004a

 50%

0.886a

0.928a

0.955a

0.864a

0.978a

 60%

0.981a

0.774a

0.690b

0.912a

0.838a

 70%

0.698a

0.743a

0.710b

0.849a

0.664b

 80%

0.613b

0.565b

0.514c

0.495c

0.590b

 90%

0.002c

0.208c

0.338c

0.018c

0.299c

  1. aHigh performance; bmedium performance; clow/cautionary performance
  2. The categorization details of the performance levels of evaluation metrics are presented in an additional file [see Additional file 4]