iii) Methods

To obtain valid estimates to examine policy adoption, we employ survival analysis. This method allows explaining events occurring to countries over a specified period [26]. Survival analysis has been used for various types of events ranging from decolonization [27] to policy adoption [28]. We particularly use the Weibull hazard function since its ρ value can be used to interpret whether policy adoption significantly increases during the observed period. The Weibull function (h₀(t)) is specified as h₀(t) = ρ * t ^{ρ −1}. If ρ is less than 1, the speed of policy adoption (i.e. hazard of failure) decreases with time, while if it is greater than 1, the speed of the policy adoption increases with time. We hypothesize that, if the thesis of convergence is supported, the ρ value will be greater than 1, because it would run counter to the heterogeneity bias. In reporting the results we call this shape parameter “speed,” [28] as its sign and magnitude provide information on whether baseline adoption increases or slows during the observed period. For the thesis of convergence to be supported by the results, the parameter ρ should increase significantly, because it would run counter to the heterogeneity bias. However, a lower parameter ρ can be the product of high-hazard countries, which leave behind the group of low-hazard cases leading to the suggestion that the overall parameter has declined with time. If the convergence process was a response to a national stimulus, with those countries most predisposed to reporting or adopting first, then the parameter would not increase as the first adopters were censored. If instead an ongoing global diffusion process is boosting the adoption of the two events, a significant increase in the parameter of the models should be observed.

It is important to notice that since outcomes could be a result of modeling countries as if they had been equally or not exposed to the same time risk, we defined three different onsets of risk: i) December 31^st, 2019, when China alerted WHO’s authorities to a cluster of pneumonia in Wuhan; ii) January 31^st, 2020, when WHO declared COVID-19 to be a global health emergency; and iii) the first case detected in each country. The first two were used to assess when the first case of COVID-19 was reported per country, and each onset of risk were used to predict school closure. Information to determine the two first onsets were derived from WHO’s press conferences [11, 24].

Since unobserved heterogeneity could also arise from information that countries share due to their regional closeness, implying that unobserved processes could bias the results of the parameters [26], we adjusted the precision of the estimates for their adoption rates in reference to 22 regional clusters based on the United Nations geoscheme [29] (S2 File has the regional cluster list with the countries). In other words, each regional cluster was assigned a random effect—whose distribution does not depend on the observed variables—to model the potential impact of information exchange among countries within each cluster.

When needed, differences in the association of parameters were tested by comparing the value of d/SEd to the standard normal distribution, where d is the difference between the two estimates, and 〖SE〗_d = √(〖SE〗_1^2+〖SE〗_2^2) is the standard error of the difference [30].

We carried out several sensitivity analyses to (1) indirectly assess whether the results were robust to model specification and (2) using alternative distributions (exponential, and Gompertz models) (Tables S3.1 and S3.2 in S3 File). We also carried out sensitivity analysis with countries in which national decisions were not taken but had begun a process by closing school in states or provinces. In this case we used the date in which the last state or province had close schools (Table S4.1 in S4 File). We also use linear regression and negative binomial models assuming that countries were independent of each other at the time of closing schools (Tables S5.1 and S5.2 in S5 File). We used Stata/SE 14.0 for all the analyses (codes available in S6 File) [31].