Table 1. Data characteristics and linear regression analysis outcomes of original Miller-Goldman study and the reanalysis by Nysetvold et al.
aWhen the residuals are not normally distributed, the hypothesis is that they are not from a random dataset. The amount of residual error in the model is inconsistent across the full range of observed data.
bThe model is sensitive to these outliers that represent poor quality data from Third World nations with the highest IMRs. This has the effect of changing the magnitude of the correlation coefficient and altering both the slope and y-intercept of the best-fit line.
cThe linear regression analysis of Nysetvold et al. is irredeemably confounded due to varying vaccination rates and socioeconomic disparities between developed and Third World nations that have the effect of attenuating the significant positive correlation between IMR and number of vaccine doses that was found among nations with top-ranked IMRs.
| Parameter | Linear regression analysis performed by | |
| Miller and Goldman [1] | Nysetvold et al. [2] | |
| Number of nations (n) | 30 | 185 |
| Appropriateness of data for linear regression analysis | Valid | Invalid (due to a trumpet or cone appearance of data points) |
| Number of unexplained nations missing from analysis | 0 | 6 (Libya, Laos, Myanmar, South Africa, Venezuela, and Vietnam) |
| Number of nations excluded due to IMR instability | 4 (Andorra, Liechtenstein, Monaco, and San Marino) | 0 (Five nations with IMR instability were not excluded) |
| Range of IMRs | 2.31 to 6.22 | 2.31 to 180.21 |
| Best-fit equation | y = 1.6 + 0.15x | y = 2.7 + 1.6x |
| Correlation direction | Positive | Positive |
| Correlation coefficient (r) | 0.70 (95% CI: 0.51 to 0.89) | 0.16 (95% CI: 0.018 to 0.30) |
| p-value | < .0001 | < .03 |
| Coefficient of determination (r2) | 0.49 | 0.026 |
| Residual normality | Normal | Not normala |
| Outliers | 0 | 4 (Afghanistan, Angola, Liberia, and Sierra Leone)b |
| Vaccination rate of selected nations | Consistently >90% | Widely variable (<40% to >90%), resulting in confounding |
| Uniformity of socioeconomic factors of selected nations | Homogeneous | Heterogeneous |
| Robustness of results | Primarily reflects influence of vaccine doses (minimal influence of socioeconomic confounders) | Confounded by factors other than vaccine doses (i.e., varying vaccination rates and socioeconomic disparities)c |