Public health improvements and mortality in interwar Tokyo: a Bayesian disease mapping approach

Abstract

Recent studies have found that modern water supply systems played an important role in mitigating the mortality risks in major US cities in the early twentieth century. Modern water supply systems were installed also in Japanese cities during the interwar period. This study examines how the modern water supply system in Tokyo City reduced mortality risks in the interwar period. By employing a Bayesian disease mapping approach with a block-level lattice dataset of Tokyo for 1930, we found that wider access to purified water through water supply systems played an important role in mitigating mortality risks during the study period. Our estimation results show that clean water accounted for approximately 41.3 and 34.9 % of improvements in crude and child death rates, respectively, between 1921 and 1937 in Tokyo.

Appendix: Marginal effect of WATER and PHR

We can interpret the estimates in terms of the marginal effects of the covariates in the following way. Under the log link function, a 1 % increase in the coverage rate of the water supply and the poverty ratio, with the other factors fixed, changes the relative risk by $\exp (\frac{1}{100}(\beta _1+\beta _3{\text{PHR}}_i)$ and $\exp (\frac{1}{100}(\beta _2+\beta _3{\text{WATER}}_i)$, respectively, because the estimates are obtained based on the rescaled WATER and PHR. Similarly, an additional doctor and person over 60 years old change the relative risk by $\exp (\frac{1}{100}\beta _4)$ and $\exp (\beta _{5})$ times, respectively. A similar calculation applies in the case of the logit link function for the effect of the mortality rate on the odds ratio.

We also calculate the marginal effect of the countermeasures on the mortality rate per mil for each block. This effect under the log link specification is given by

$$\begin{aligned} {\text{ME}}_{\text{log}, {\text{WATER}_i}}=\frac{1000}{n_i}\times \frac{1}{100} \times \frac{\partial E_i\eta _i}{\partial {\text{WATER}_i}} =\frac{10}{n_i}\times {E_i\eta _i} \times (\beta _1 + \beta _3 {\text{PHR}}_i). \end{aligned}$$

Likewise, the marginal effects of PHR on the mortality rate are given by

$$\begin{aligned} {\text{ME}}_{\text {log},\text {PHR}_i}=\frac{10}{n_i}\times E_i\eta _i \times (\beta _2 + \beta _3 {\text{WATER}}_i). \end{aligned}$$

The marginal effects of WATER and PHR on the mortality rate under the logit link specification are given by

$$\begin{aligned} {\text{ME}}_{\text {logit}, {\text{WATER}}_i}&=10\times p_i(1-p_i) \times (\beta _1 + \beta _3 \text {PHR}_i), \\ {\text{ME}}_{\text {logit}, {\text{PHR}}_i}&=10\times p_i(1-p_i) \times (\beta _2 + \beta _3 {\text{WATER}}_i). \end{aligned}$$