Factors associated to the duration of COVID-19 lockdowns in Chile | Scientific Reports – Nature.com

Study location

Localized in South America, Chile occupies a long and narrow coastal strip between the Andes Mountains range and the Pacific Ocean. It borders Peru to the north, Bolivia to the northeast, and Argentina to the east. The country is divided into 16 regions, which are the first-level administrative division of the country. Each region is divided into provinces, which are the second-level administrative division, resulting in 56 provinces. The third level of the administrative division is the communes (or municipalities), totaling 346 communes, of which 147 were under lockdown during the study period; thus, they were considered in this study.

According to the Chilean National Institute of Statistics, the estimated country population was 19,458,173 inhabitants in 2020, much of it concentrated in the Metropolitan Region, whose capital city is Santiago. Regarding the communes, only 55 of 346 have more than 100,000 inhabitants, with the median population being 18,546 inhabitants (minimum 138, maximum 646,000). Chile is among the largest economy in Latin America; however, despite its economic progress and poverty reduction over the last few decades, the country has a Gini coefficient of 0.44, which represents a high social inequality. As elsewhere, the COVID-19 pandemic has severely impacted the Chilean economy. According to the World Bank4, the Chilean per capita gross domestic product decreased 5.8% between 2019 and 2020.

Factors associated with the duration of localized lockdowns during the COVID-19 pandemic in Chile were assessed using a retrospective cohort study design5. In this design, researchers select a group of study units (i.e., commune under lockdown) in such a way that they have been exposed to different levels of certain predictors, and then follow them retrospectively over time to record the occurrence or not of a predefined event. In this particular investigation, the main outcome corresponds to the time elapsed until the end of the lockdown (i.e., the lockdown duration). No formal sampling of communes under lockdown was performed since all lockdowns implemented between March 25th and December 25th, 2020 were included in this study. All methods were performed in accordance with relevant guidelines and regulations.

In follow-up studies, two types of data can be observed: information collected over time (longitudinal data) and time until an event of interest occurs (survival data). In this study, both were included as outcomes. For the time-to-event analysis, we considered the number of days a commune was under lockdown; to do so, we recorded the number and duration of lockdowns implemented in Chile between March 25th and December 25th, 2020. If a commune was still under lockdown on December 25th, it was considered a right-censored observation. In general, lockdowns were implemented at the commune-level; however, at the beginning of the pandemic, some lockdowns were established at the greater administrative division level (i.e., province), which implies that a set of communes followed the same schedule. In this study, lockdowns were considered as commune-level.

For the longitudinal analysis, we studied several epidemiological factors collected at the first or third levels of the administrative division. The number of new asymptomatic and symptomatic cases, the number of patients in ICU, and the number of PCR exams performed were collected at the regional division level. At the commune level, we observed the number of active cases and the deaths per COVID-19 according to their residence. An active case was defined as a living person who met the definition criteria of a suspected case with a positive sample of SARS-CoV-2, whose date of onset of symptoms in the notification was less than or equal to 11days, i.e., people capable of transmitting the infection. On the other hand, new symptomatic/asymptomatic cases correspond to new cases reported in a daily basis. All this information was considered as the number per 100,000 inhabitants. The original information used in this study was published by the Chilean Ministry of Science, Technology, Knowledge and Innovation and can be found on the GitHub repository available at https://github.com/MinCiencia/Datos-COVID19.

Based on the number of new asymptomatic and symptomatic cases and the number of PCR exams performed per region, we calculated a positivity index at the region level, which was expressed as the percentage of new cases relative to the number of PCR exams taken:

$$text{positivity index}=frac{text{number of asymptomatic cases }+text{ number of symptomatic cases }}{text{number of PCR exams}}.$$

As the epidemiological information varies over time, we used two strategies to include them in the model. The number of deaths was included as a weekly sum during the period the commune was under lockdown, while the others were considered as daily average within each week.

Demographic and socioeconomic factors were considered as predictors for the time-to-event model. These consisted of population size (in scale of 100,000 inhabitants), number of immigrants (per 100,000 inhabitants), population density (number of people per km2), overcrowding (number of people over the number of households), a socioeconomic development index (SDI, ranging from 0 to 1), and a rural index of the communes (ranging from 0 to 1). For calculating SDI, which is performed by the Universidad Autnoma de Chile, different indicators are aggregated, including economy (monthly per capita income and poverty), education (average years of schooling), and housing and sanitation (good and acceptable housing material and sewerage or septic tank)6. For the calculation of the rural index, computed by the Ministry of Social and Family Development, it is considered the percentage of the rural population, the proportion of local employment occupied in primary sectors, and the population density. Then, an average of these three values was calculated, resulting in the rural index. Polanco7 has provided details about how to calculate such measure. Besides, we considered whether the commune held the regional or province city capital and whether a commercial airport or harbor exist in it. Apart from demographic and socioeconomic factors, we also included a binary covariate indicating if it was the first or second time that the commune was under lockdown.

The two sources of information presented in this study are often analyzed separately through a survival analysis and a longitudinal analysis. However, in some situations, one may also be interested in the association between longitudinal measurements and the event of interest. In these cases, a joint approach is indicated, where information is shared between two or more models and each part provide relevant knowledge to the other. This procedure depends on the type of time-dependent covariates8. When this information is exogenous, i.e., variables whose cause is external to the model, an extended Cox model can be used9. On the other hand, when the longitudinal covariates are endogenous, i.e., variables that are changed or determined by their relationship with others, it is necessary to use a new class of models known as joint models10.

The idea behind joint modeling of longitudinal and time-to-event data is to couple a model for repeated measurements with a survival model to explain the event of interest. The most common joint model specification is to connect a mixed-effects sub-model fitted to describe the evolution of the longitudinal information with a proportional hazard sub-model fitted to the survival information. This approach had been limited to a single longitudinal and a single time-to-event outcome for a long time. However, a model with multiple longitudinal and/or multiple time-to-event outcomes can also be considered11,12. Thus, a joint model for (k) longitudinal outcomes can be formulated as follows:

$$left{ begin{array}{l} y_{{ik}} left( t right) = m_{{ik}} left( t right)~ + ~varepsilon _{{ik}} left( t right) = ~x_{{ik}} ^{T} left( t right)~beta _{k} + z_{{ik}} ^{T} left( t right)~b_{{ik}} + ~varepsilon _{{ik}} left( t right), hfill \ h_{i} left( t right) = h_{0} left( t right)exp left{ {{{gamma }}^{T} {text{w}}_{{text{i}}} + {{~alpha ~}}m_{{ik}} left( t right)} right}, hfill \ end{array} right. $$

where ({y}_{ik}left(tright)=({{y}_{i1}}^{T}(t), dots , {{y}_{il}}^{T}(t))) represents the k-variate vector of continuous longitudinal measurement for the (i)th commune at time (t) with (k=1, dots , l). This vector is modeled by a mixed-effects sub-model, where ({beta }_{k}) denotes the regression coefficients associated with the design vector for the fixed effects ({x}_{ik}(t)). Besides, ({z}_{ik}(t)) denotes the design vector for the random ({b}_{ik}) for the commune (i). Finally, ({varepsilon }_{ik}left(tright)) represents the model error term. The longitudinal sub-model included fixed intercepts and random slopes. The joint model is completed with the time-to-event sub-model. In this case, the outcome is modeled by a proportional hazard. This kind of strategy focuses directly on the hazard function ({h}_{i}left(tright)), considering the baseline hazard function, ({h}_{0}left(tright)), and a second term that includes baseline covariates, ({text{w}}_{text{i}}), and the true and unobserved value of longitudinal outcome for the commune (i) at time (t), which is denoted by ({m}_{ik}left(tright)) and modeled by the longitudinal sub-model. Finally, represents the association between the longitudinal and time-to-event outcome.

In this study, we were interested in investigating the time until a Chilean commune comes out of lockdown, which motivated the use of time-to-event sub-model. In addition, we wanted to add epidemiological information to the study; such information was obtained at the commune-level and over time during the follow-up period. Consequently, the most indicated strategy was to build a mixed longitudinal sub-model. Finally, the joint approach connected both parts, including the information obtained by the longitudinal model in the time-to-event model. Active cases, ICU patients, and deaths were logarithmically transformed for joint analysis, while the positivity index was handled as proportion.

The model was built in two stages. First, we fitted univariate joint models for each longitudinal factor (active cases, ICU patients, deaths, and positivity index). At this point, we identified that the association between the number of deaths and the duration of lockdown was not statistically significant, i.e., the p-value was higher than 0.05. Then, a bivariate joint model was fitted, considering pairs of the significant variables. Finally, a multivariate joint model was fitted; however, the association between ICU patients and the duration of lockdown was not statistically significant. Consequently, the bivariate model, including the number of active cases and the positivity index, was considered the final version.

The second stage was aimed to select the social and demographic covariates included in the bivariate joint model. To do so, we used the stepwise backward elimination approach, starting from a full model, which included all the predictors described in the previous section. Covariates with the highest p-values were removed from the model one at a time until all predictors were below the significance threshold (p-value0.05). Finally, the joint model included two longitudinal information, number of active cases and positivity index, and one demographic and socioeconomic factor, overcrowding. All the statistical analyses were performed with R statistical software (version 4.1.0), with the level of significance set at 5%. Package joineRML was used to fit the joint model extended to multiple continuous longitudinal measures11.

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Factors associated to the duration of COVID-19 lockdowns in Chile | Scientific Reports - Nature.com