In this article, we evaluate the lasting impact of the first-wave COVID-19 pandemic policies on unemployment during the post-first-wave period. Specifically, we analyze the causal effects of the Swedish first-wave policies relative to the Norwegian ones on unemployment during the first-wave period (Q2 and Q3 2020, where Q stands for quarter), the post-first-wave period (Q4 2020 and 2021-2024), and the complete period (Q2 2020 - Q4 2024). The Swedish first-wave policies led to an increase of unemployment with an estimate of 506 (95% CI: 406, 607) more unemployment per 100, 000 labor force members during the first-wave period in Sweden. However, the Swedish first-wave policies led to a reduction of unemployment with an estimate of 585 (95% CI: 485, 684) less unemployment during the post-first-wave period in Sweden. Furthermore, the Swedish first-wave policies led to a reduction of unemployment with an estimate of 471 (95% CI: 375, 567) less unemployment during the complete period in Sweden. This provides causal evidence supporting the view that mild first-wave public-health policies helped preserve supply chains and strengthen long-term economic resilience.

The effect of different sequences of invitations to Faecal Occult Blood Test (FOBT) screening regarding colorectal cancer (CRC) incidence has never been evaluated. In 2008-2012, all residents in Stockholm-Gotland, Sweden, born 1938-1954, were randomly assigned by birth year to different calendar years of invitation to guaiac-based FOBT (g) or Faecal Immunochemical Test (f) screening at 60-69 years (1-5 rounds), or not (0). Linkage was made to the national Cancer- and Cause of Death Registers on CRC diagnosis and mortality 1958-2020, and the Swedish Colorectal Cancer Register regarding stage. Follow-up started age 60 and CRC incidence, calculated per 100,000 person-years, was assessed during screening (age 60-69) and post screening (age 70-73). Stage I-II and III-IV was assessed post screening. 364,668 individuals were included. During screening, incidence rate ratio was significantly higher in sequences (0, g, g, g, g) (RR 1.25, 95% CI 1.09-1.43), (g, g, g, g, f) (RR 1.17, 95% CI 1.01-1.35), and (g, g, f, f, f) (RR 1.14, 95% CI 1.01-1.29). Post screening, the largest decrease was seen in sequences (g, g, g, g, f) and (g, g, g, f, f), RR 0.65, 95%, CI 0.47-0.90, and RR 0.53, 95% CI 0.30-0.94, respectively. There was an overall decreasing trend along sequences from (0, 0, 0, 0, g) to (g, g, f, f, f) post screening and both stages I-II and III-IV (p < 0.001). We could demonstrate a decreased CRC incidence post screening proportional to the number of invitations with implications for future modeling studies and risk-based screening strategies.

In longitudinal studies, treatments are often assigned in the form of a sequence to achieve a certain outcome of interest. The blip effect of treatment in sequence is the net effect of treatment on the outcome. In this article, we introduce a method of estimating and testing the blip effects via the standardized point effects of treatments in sequence. First, we apply available methods to estimate the point effects referring to single-point treatments. Then we standardize the point effects to a small number of strata of relevance to the blip effects of interest. Finally, we use the standardized point effects to estimate and test the blip effects. Our method addresses two issues in complex longitudinal studies: a dimension reduction without strict treatment assignment conditions and a targeted analysis of the blip effects of interest across different times. The simulation study shows that our method achieves unbiased estimates of the blip effect, maintains nominal coverage probability, and demonstrates high power for hypothesis testing. A medical example illustrates the application of our method in observational studies.

Cancer diagnosis is part of a complex stochastic process, in which patients' personal and social characteristics influence the choice of diagnosing methods, diagnosing methods in turn influence the initial assessment of cancer stage, cancer stage in turn influences the choice of treating methods, and treating methods in turn influence cancer outcomes such as cancer survival. To evaluate the performance of diagnoses, one needs to estimate and test the sequential causal effect (SCE) under a specified regime of diagnoses and treatments in such a complex observational study, where the data-generating mechanism is unknown and modeling is needed for statistical inference. In this article, we introduce a method of statistical modeling to estimate and test SCEs under regimes of treatments (diagnoses and treatments in cancer diagnosis) in complex observational studies. By applying the alternative G-formula, we express the SCE in terms of the point effects of treatments in the sequence, so that the modeling can be conducted via the point effects in the framework of single-point causal inference. We illustrate our method by a medical example of cancer diagnosis with data from a Swedish prognosis study of cardia cancer.

The pandemic progression is a dynamic process, in which measures yield outcomes, and outcomes in turn influence subsequent measures and outcomes. Due to the dynamics of pandemic progression, it is challenging to analyse the long-term influence of an individual measure in the sequence on pandemic outcomes. To demonstrate the problem and find solutions, in this article, we study the first wave of the pandemic—probably the most dynamic period—in the Nordic countries and analyse the influences of the Swedish measures relative to the measures adopted by its neighbouring countries on COVID-19 mortality, general mortality, COVID-19 incidence, and unemployment. The design is a longitudinal observational study. The linear regressions based on the Poisson distribution or the binomial distribution are employed for the analysis. To show that analysis can be timely conducted, we use table data available during the first wave. We found that the early Swedish measure had a long-term and significant causal effect on public health outcomes and a certain degree of long-term mitigating causal effect on unemployment during the first wave, where the effect was measured by an increase of these outcomes under the Swedish measures relative to the measures adopted by the other Nordic countries. This information from the first wave has not been provided by available analyses but could have played an important role in combating the second wave. In conclusion, analysis based on table data may provide timely information about the dynamic progression of a pandemic and the long-term influence of an individual measure in the sequence on pandemic outcomes.

A cancer diagnosis is part of a complex stochastic process, which involves patient's characteristics, diagnosing methods, an initial assessment of cancer progression, treatments and a certain outcome of interest. To evaluate the performance of diagnoses, one needs not only a consistent estimation of the causal effect under a specified regime of diagnoses and treatments but also reliable confidence interval, P-value and hypothesis testing of the causal effect. In this article, we identify causal effects under various regimes of diagnoses and treatments by the point effects of diagnoses and treatments and thus are able to estimate and test these causal effects by estimating and testing point effects in the familiar framework of single-point causal inference. Specifically, using data from a Swedish prognosis study of stomach cancer, we estimate and test the causal effects on cancer survival under various regimes of diagnosing and treating hospitals including the optimal regime. We also estimate and test the modification of the causal effect by age. With its simple setting, one can readily extend the example to a large variety of settings in the area of cancer diagnosis: different personal characteristics such as family history, different diagnosing procedures such as multistage screening, and different cancer outcomes such as cancer progression.

A controversy about the Swedish strategy of dealing with COVID-19 during the early period is how decision-making was based on evidence, which refers to data and data analysis. During the earliest period of the pandemic, the Swedish decision-making was based on subjective perspective. However, when more data became available, the decision-making stood on mathematical and descriptive analyses. The mathematical analysis aimed to model the condition for herd immunity while the descriptive analysis compared different measures without adjustment of population differences and updating pandemic situations. Due to the dubious interpretations of these analyses, a mild measure was adopted in Sweden upon the arrival of the second wave, leading to a surge of poor public health outcomes compared to the other Nordic countries (Denmark, Norway, and Finland). In this article, using data available during the first wave, we conduct longitudinal analysis to investigate the consequence of the shred of evidence in the Swedish decision-making for the first wave, where the study period is between January 2020 and August 2020. The design is longitudinal observational study. The linear regressions based on the Poisson distribution and the binomial distribution are employed for the analysis. We found that the early Swedish measure had a long-term and significant effect on general mortality and COVID-19 mortality and a certain mitigating effect on unemployment in Sweden during the first wave; here, the effect was measured by an increase of general deaths, COVID-19 deaths or unemployed persons under Swedish measure relative to the measures adopted by the other Nordic countries. These pieces of statistical evidence were not studied in the mathematical and descriptive analyses but could play an important role in the decision-making at the second wave. In conclusion, a timely longitudinal analysis should be part of the decision-making process for containing the current pandemic or a future one.

In sequential causal inference, two types of causal effects are of practical interest, namely, the causal effect of the treatment regime (called the sequential causal effect) and the blip effect of treatmenton on the potential outcome after the last treatment. The well-known G-formula expresses these causal effects in terms of the standard paramaters. In this article, we obtain a new G-formula that expresses these causal effects in terms of the point observable effects of treatments similar to treatment in the framework of single-point causal inference. Based on the new G-formula, we estimate these causal effects by maximum likelihood via point observable effects with methods extended from single-point causal inference. We are able to increase precision of the estimation without introducing biases by an unsaturated model imposing constraints on the point observable effects. We are also able to reduce the number of point observable effects in the estimation by treatment assignment conditions.

In this article we estimate confidence regions of the common measures of (baseline, treatment effect) in observational studies, where the measure of a baseline is baseline risk or baseline odds while the measure of a treatment effect is odds ratio, risk difference, risk ratio or attributable fraction, and where confounding is controlled in estimation of both the baseline and treatment effect. We use only one logistic model to generate approximate distributions of the maximum-likelihood estimates of these measures and thus obtain the maximum-likelihood-based confidence regions for these measures. The method is presented via a real medical example.

In observational studies for the interaction between treatments, one needs to estimate and present both the treatment effects and the interaction to learn the significance of the interaction to the treatment effects. In this article, we estimate the treatment effects and the interaction jointly by using only one logistic model and based on maximum-likelihood. We present the interaction by (1) point estimate and confidence interval of the interaction, (2) point estimate and confidence region of (treatment effect, interaction) and (3) point estimate and confidence interval of the interaction when the maximum-likelihood estimate of one treatment effect falls into specified range.