Dynamic progression of the pandemic

Here, we study the public health outcomes of COVID-19 mortality, general mortality, and COVID-19 incidence. We follow the population in Scandinavian countries during weeks 1–35, 2020. Please note that week 1, 2020 corresponds to the dates from 30 December 2019 to 5 January 2020.

The initial period of the pandemic took place around weeks 10–18 in the Nordic countries. Weeks 10–35 completed a cycle of rising, plateau, and decline and base for the public health outcome, and they are considered as the first wave of the pandemic [2, 3]. Because it is impossible to know when measures became effective, we divide the entire follow-up into four periods of approximately equal length: weeks 1–9, 10–18, 19–26, and 27–35. Let period \(t\) \((t=1, 2, 3)\) indicate the three periods during weeks 10–35: period \(1\) for weeks 10–18, period \(2\) for weeks 19–26, and period \(3\) for weeks 27–35. Please note that period 2 is one week shorter than periods 1 and 3. In Supplementary Information, we conduct a sensitivity analysis to show that when alternatively dividing the entire follow-up into weeks 1–9, 10–17, 18–26, and 27–35, the result only differs slightly, and the conclusion is the same. To examine the sensitivity of our methodology to periodization, we divide the follow-up into periods of different lengths and obtain essentially the same result and conclusion (results not shown).

During weeks 1–9, the pandemic had not yet broken out, so no measure was taken, and there was only outcome \(_\) for general mortality in population \(_\). During period \(1\) (weeks 10–18), the exposure was \(_=1\) for Swedish measure or \(_=0\) for common measure and yielded outcome \(_\) for population \(_\). From here and on, the common measures refer to those adopted by the other Nordic countries. During period \(2\) (weeks 19–26), the exposure was \(_=1\) for Swedish measure or \(_=0\) for common measure and yielded outcome \(_\) for population \(_\). During period \(3\) (weeks 27–35), the exposure was \(_=1\) for Swedish measure or \(_=0\) for common measure and yielded outcome \(_\) for population\(_\).

Outcome \(_\) represents the initial health status and has an influence on outcomes \(_\), \(_\) and \(_\). Thus, it is a stationary covariate and may confound the causal effects of exposures \(_\), \(_\) and \(_\). Outcome \(_\) represents the updating health status and pandemic situation during exposure \(_\) and has an influence on outcomes \(_\) and \(_\). Thus, it is also a time-dependent covariate between exposures \(_\) and \(_\) and may confound the causal effects of exposures \(_\) and \(_\). Outcome \(_\) represents the updating health status and pandemic situation during exposure \(_\) and has an influence on outcome \(_\). Thus, it is also a time-dependent covariate between exposures \(_\) and \(_\) and may confound the causal effect of exposure \(_\).

Confounding adjustment and the assumption of no hidden confounding covariates

Scandinavian countries are similar to one another in terms of economy, culture, and society. So, most of the stationary covariates, such as gender, education, and socioeconomic status, have similar distributions among these countries and thus do not confound the effects of exposures \(_\), \(_\) and \(_\). As a result, there is no need to adjust for these covariates as is common practice in causal inference. Table 1 lists some characteristics of the populations in the Nordic countries. As seen in this table, the initial general mortality \(_\) and population density \(x\) differ considerably in different regions of these countries and may confound the causal effects. Therefore, we divide Sweden into six regions: Stockholm, Skåne, Gothenburg, Halland, Västmanland, and the rest of Sweden. Because COVID-19 mortality is low in Denmark, Finland, and Norway, we do not divide these countries into small regions. For the COVID-19 incidence, we divide Sweden into only two regions (Stockholm and the rest of Sweden) due to the data quality for the number of tested people for weeks 10–22.

Table 1 Characteristics of study populations in regions of the Nordic countries before the breakout of COVID-19: (1) Stockholm, (2) Skåne, (3) Göteborg, (4) Halland, (5) Västmanland, (6) the rest of Sweden, (1–6) Sweden as a whole, (7) Denmark, (8) Norway, (9) Finland

There may exist other potential confounding covariates, such as immigration status. Because different definitions of immigration status are used in these countries, it is difficult to adjust for immigration status without individual-level data. However, such covariates are often highly associated with population density, and as an approximation, we consider only population density as the confounding covariate in addition to the time-dependent outcomes \(_, _,\) and \(_\). A summary of population densities, exposures, outcomes (covariates) and populations is given in Table 2 together with the probability models for the outcomes.

Table 2 A summary of population densities, exposures, outcomes, and the populations during different periods of the first wave

To summarize the confounding situation in the pandemic progression, we have the assumption of no hidden confounding covariates: (a) conditional on population density \(x\) and outcome \(_\), no other covariates confound the causal effect of an exposure sequence \(_, _,_)\); (b) conditional on population density \(x\) and outcome \(_\), no other covariates confound the causal effect of an exposure sequence \(_,_)\); (c) conditional on population density \(x\) and outcome \(_\), no other covariates confound the causal effect of exposure \(_\). The assumption implies that to study the causal effects of exposures, we need to compare the outcomes of the exposures on the same level of population density and the most recent outcome prior to these exposures. In the Discussion section, we will discuss the limitation of our analysis linked to this assumption. In the Data sources section, we will describe the table data used for our analysis in detail.

Analytic strategy

We will estimate two types of causal effects of the Swedish measures relative to the common measures: sequential causal effects and long-term causal effects. The sequential causal effect compares Swedish sequence versus common sequence for a summary outcome, for instance, Swedish sequence \(_, _,_)=(1, 1, 1)\) versus common sequence \((0, 0, 0)\) for summary outcome \(_+_+_.\) Both the exposure sequences and the summary outcomes are observed for these causal effects, so we can apply regression to estimate them.

The long-term causal effect compares, for instance, mixed sequence \(_, _,_)=(1, 0, 0)\) to common sequence \((0, 0, 0)\) for the summary outcome \(_+_+_\). Because mixed sequence cannot be observed, we cannot apply regression to estimate the long-term causal effect. Due to Robins [21], sequential causal inference is developed to estimate long-term causal effects under unobserved sequences of exposures by using observed data. Notably, the new general formula (G-formula) reveals a rather intuitive observation that the causal effect of an exposure sequence must be the sum of contributions of individual exposures in the sequence [22]. The new G-formula allows us to estimate the long-term causal effect from the estimated sequential causal effect without introducing additional modeling assumptions. In the following subsections, we will describe analyses and the results in detail.

Sequential causal effects of the Swedish sequences relative to common sequences

We estimate the following three sequential causal effects of interest: (i) an increase in summary outcome \(_+_+_\) during periods 1, 2, and 3 (weeks 10–35) under the Swedish sequence \(_, _, _)=(1, 1, 1)\) relative to the common sequence \((0, 0, 0)\), (ii) an increase in summary outcome \(_+_\) during periods 2 and 3 (weeks 19–35) under the Swedish sequence \((_,_)=(1, 1)\) relative to the common sequence \((0, 0)\), and (iii) an increase in outcome \(_\) during period 3 (week 27–35) under the Swedish measure \(_=1\) relative to the common measure \(0\). In the context of the pandemic, the exposure sequence takes either the Swedish sequence or the common sequence. The outcomes are observed under the exposure sequences in causal effects (i), (ii) and (iii), so we can use regression to estimate these causal effects [21, 22]. The results are summarized in Table 3. A detailed description of the probability models and regression models is given in the Method section below.

Table 3 Estimate, 95% CI, and p-value for sequential causal effects of the Swedish sequence relative to the common sequence on summary public health outcomes

As shown from causal effect (i) in Table 3, the Swedish strategy performed far worse than the common strategy throughout the complete follow-up (weeks 10–35) for all public health outcomes: it led, per 100,000 individuals, to 42.6 (95% Confidence Interval: 41.0–44.1) more COVID-19 deaths, 25.0 (18.7–30.7) more general deaths and 19,094.5 (18,916.6–19,212.3) more COVID-19 incidences. As shown from causal effects (ii) and (iii), the Swedish strategy improved its performance during weeks 19–35 and 27–35, particularly for general mortality: it led, per 100,000 individuals, to 20.0 (11.1–28.2) fewer general deaths during week 19–35 and 17.6 (12.6–22.5) fewer general deaths during week 27–35. The reason might be that the Swedish public health system regained its usual level of general medical care after the early pandemic period of weeks 10–18. In the Supplementary Information, we conduct a sensitivity analysis to show that the improvement was not due to population change caused by more general deaths during weeks 10–18.

Long-term causal effects of the Swedish measures relative to common measures

To reveal the critical role of the early measures in combating the pandemic, we then estimate two long-term causal effects (iv) and (v). Causal effect (iv) is an increase in summary outcome \(_+_+_\) during periods 1, 2, and 3 (weeks 10–35) under the mixed sequence \(_, _,_)=(1, 0, 0)\) relative to the common sequence \((, 0, 0)\), and it describes the long-term influence of the Swedish measure during period 1 on the summary outcome during periods 1, 2, and 3. Causal effect (v) is an increase in summary outcome \(_+_\) during periods 2 and 3 (weeks 19–35) under the mixed sequence \((_,_)=(1, 0)\) relative to the common sequence \((0, 0)\), and it describes the long-term influence of the Swedish measure during period 2 on the summary outcome during periods 2 and 3.

Here, the outcomes are not observable because the population is never exposed to mixed sequence \(_, _,_)=(1, 0, 0)\) or \((_,_)=(1, 0)\), so we cannot use regression to estimate long-term causal effects (iv) and (v). However, by the new G-formula [22], sequential causal effect is a sum of contributions from individual exposures in the sequence, and therefore we obtain the equality that causal effect (ii) is equal to the sum of causal effects (v) and (iii). The equality is illustrated by the fact that the sequences in causal effects (ii), (v) and (iii) are \((_,_)=(1, 1)\), \((_,_)=(1, 0)\) and \(_=1\). By using this equality, we obtain the estimate of causal effect (v) from the estimates of causal effects (ii) and (iii). Similarly, causal effect (i) is equal to the sum of causal effects (iv), (v), and (iii). We obtain the estimate of causal effect (iv) from the estimates of causal effects (i), (v) and (iii). A detailed description of this method is given in the Method section below. The estimates of causal effects (iv) and (v) are presented in Table 4.

Table 4 Estimate, 95% CI, and p-value for long-term causal effects of the Swedish measure relative to the common measure on public health outcome during different periods

Table 4 shows that the early Swedish measure had a long-term and significant influence on public health outcomes. As shown from causal effects (iv), the Swedish measure during the early period (weeks 10–18) led, per 100,000 individuals, to 25.1 (23.0–27.0) more COVID-19 deaths, 44.3 (34.5–54.2) more general deaths and 10,422.1 (8553.8–12,290.5) more COVID-19 incidences for the whole first wave (weeks 10–35). From causal effects (iv), (v) in Table 4, and (iii) in Table 3 together, we see a continual improvement in the Swedish measures relative to the common measures along weeks 10–18, 19–26, and 27–35.