Introduction

COVID-19 was the third leading cause of death in the U.S. in 2020 and 20211. COVID-19 vaccination is an important public health intervention to prevent infection and attenuate illness severity2,3. The primary mechanism of messenger RNA (mRNA) vaccines, BNT162b2 (Pfizer-BioNTech) and mRNA-1273 (Moderna), is the production of antibodies against the spike protein of SARS-CoV-24. Some studies have shown differential antibody responses to vaccination and waning antibody levels over time5,6,7. Variation in vaccine-induced antibody response may be clinically significant since lower humoral responses to SARS-CoV-2 vaccines are predictive of higher risk for breakthrough infections and severe COVID-19 clinical outcomes6,8,9,10. Hence, identification of individuals at risk of lower vaccine-induced antibody response and faster antibody waning could inform personalized vaccination strategies.

Most prior studies on vaccine immunogenicity leveraged clinical trials or highly selected cohorts (e.g., health-care workers and residents of long-term care facilities)6,11,12,13. A general-population study conducted in the United Kingdom (UK), where the majority of individuals received the AstraZeneca vaccine, observed lower rates of post-vaccination seropositivity in older adults, males, and those with chronic health conditions5,14,15. However, the determinants of post-vaccination antibody response, including magnitude and durability of antibody levels, have not been comprehensively investigated in multi-ethnic, diverse, population-based U.S. samples where mRNA vaccines predominate.

This study aimed to identify correlates of anti-S1 IgG antibody levels after COVID-19 vaccination with mRNA vaccines in the Collaborative Cohort of Cohorts for COVID-19 Research (C4R)16. C4R is a national prospective study of U.S. adults participating in 14 longitudinal cohort studies that collectively constitute a large, well-characterized, population-based sample. Anti-S1 IgG antibody levels were measured by serosurvey and examined with respect to pre-pandemic and pandemic-era socio-demographic and clinical factors. Correlates of antibody levels over the period of time since vaccination were elucidated.

Results

Participant characteristics

There were 6245 participants who received two doses of a mRNA COVID-19 vaccine with measured anti-S1 IgG antibody levels (Table 1, Supplementary Fig. 1). The mean time between the first vaccine dose and serosurvey was 4.0 months (SD 1.7; range 0.1–7.1). Mean age was 73 years (range, 21–100), 76.9% of participants were aged ≥65 years, 58.3% were female, 76.4% self-identified as non-Hispanic White, 17.6% as African American/Black, 3.1% as Asian, 2.0% as American Indian, and 0.9% as Hispanic/Latino. 51.8% of participants received the BNT162b2 vaccine and 48.2% received the mRNA-1273 vaccine. Infection prior to serosurvey was self-reported in 18% of C4R participants and 4.8% self-reported infection after vaccination but before serosurvey participation. Of note, compared to the participants eligible for this report, C4R participants who self-reported vaccination but did not complete the serosurvey were younger, more racially and ethnically diverse, and less likely to have received the mRNA-1273 vaccine (Supplementary Table 1).

Table 1 Baseline characteristics of 6245 C4R participants with serology results from February 2021 through August 2022
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Antibody responses

Among the samples, 97% showed antibody reactivity above the laboratory threshold used to confirm prior SARS-CoV-2 exposure (Supplementary Table 2). Nonetheless, there was a large range of continuous antibody levels across the sample (Table 1). Participants in the highest quartile of anti-S1 levels were more likely to be female, younger, recipients of the mRNA-1273 vaccine, and report prior infection (Table 1). Antibody levels were highest at 60 days following the first vaccine dose, after which antibody levels waned, on average, at a rate of 21% per month (Fig. 1). Of note, based on current vaccine recommendations, 60 days following the first vaccine dose corresponds to 32 (BNT162b2) to 39 (mRNA-1273) days following the second dose.

Fig. 1: Anti-S1 IgG levels by COVID-19 infection history over time between first dose of vaccine and antibody measurement.
figure 1

The plot of predicted anti-S1 antibody levels generated from generalized additive model with smoothing splines adjusted for age, sex, race/ethnicity, smoking history, education attainment, body mass index, diabetes, cardiovascular disease, asthma, chronic obstructive pulmonary disease, anti-N, COVID-19 infection history, dried blood spot batch, and vaccine type. The vertical line indicates the 60-day mark. The X-axis was truncated at 30 days to ensure the inclusion of participants who had dried blood spot collection after receiving the second vaccine dose. Lighter color bands indicate 95% confidence intervals.

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Correlates of antibody response

Both unadjusted and multivariable-adjusted models consistently demonstrated associations between antibody levels and several participant characteristics (Table 2). For correlates that were significantly associated with antibody levels in multivariable-adjusted models, associations with antibody levels were plotted over time since the first vaccine dose using linear splines (Figs. 2–4).

Table 2 Correlates of anti-S1 IgG levels after COVID-19 vaccination in unadjusted and multivariable adjusted analyses
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Fig. 2: Anti-S1 IgG levels over time between first vaccine dose and serosurvey by socio-demographic and clinical correlates.
figure 2

Plot of predictited anti-S1 antibody levels by A age, B sex, c body mass index, D smoking history, E diabetes, and F chronic obstructive pulmonary disease. Predicted anti-S1 antibody levels generated from generalized additive model with smoothing spline since vaccination adjusted for age, sex, race/ethnicity, smoking history, education attainment, body mass index, diabetes, cardiovascular disease, asthma, chronic obstructive pulmonary disease, anti-N, COVID-19 infection history, dried blood spot batch, and vaccine type, except for those risk factors of primary interest that are stratified (A–F). Lighter color bands indicate 95% confidence intervals.

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Fig. 3: Anti-S1 IgG levels over time between first vaccine dose and dried blood spot collection by receipt of BNT162b2 mRNA (Pfizer-BioNTech) or mRNA-1273 (Moderna) vaccine.
figure 3

Predicted anti-S1 antibody levels generated from generalized additive model with smoothing spline since vaccination adjusted for age, sex, race/ethnicity, smoking history, education attainment, body mass index, diabetes, cardiovascular disease, asthma, chronic obstructive pulmonary disease, anti-N, COVID-19 infection history, and dried blood spot batch. Lighter color bands indicate 95% confidence intervals.

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Fig. 4: Anti-S1 IgG levels over time between first vaccine dose and serosurvey by severity of acute infection.
figure 4

A Unadjusted anti-S1 IgG levels by acute infection severity and time between first vaccine dose and dried blood spot collection categorized by quartiles in complete case cohort of participants with infection history and anti-S1 levels (n = 3995). Quartile 1 (no infection [n = 1298], non-hospitalized post-vaccine infection [n = 59], non-hospitalized pre-vaccine infection [n = 68], hospitalized pre-vaccine infection [n = 18]), Quartile 2 (no infection [n = 1,069], non-hospitalized post-vaccine infection [n = 47], non-hospitalized pre-vaccine infection [n = 97], hospitalized pre-vaccine infection [n = 20]), Quartile 3 (no infection [n = 620], non-hospitalized post-vaccine infection [n = 52], non-hospitalized pre-vaccine infection [n = 119], hospitalized pre-vaccine infection [n = 32]), Quartile 4 (no infection [n = 294], non-hospitalized post-vaccine infection [n = 57], non-hospitalized pre-vaccine infection [n = 119], hospitalized pre-vaccine infection [n = 26]). B Predicted anti-S1 antibody levels by severity of acute infection generated from generalized additive model with smoothing spline since vaccination adjusted for age, sex, race/ethnicity, smoking history, education attainment, body mass index, diabetes, cardiovascular disease, asthma, chronic obstructive pulmonary disease, anti-N, dried blood spot batch, and vaccine type (n = 6,245 from multiple imputed cohort). No infection (n = 4823), non-hospitalized post-vaccine infection (n = 298), non-hospitalized pre-vaccine infection (n = 910), hospitalized pre-vaccine infection n = 214). For Fig. 4A, the bounds of the box shows the 25th and 75th percentiles, thick black line indicates the median, the vertical upper and lower whiskers extended to the largest observed data point that falls within the 1.5 × interquartile range. Black dots indicate outlier values. For Fig. 4B, lighter color bands indicate 95% confidence intervals.

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Lower antibody levels were observed in older participants, men, and participants with a history of obesity, smoking, diabetes, or COPD (Fig. 2, Table 2). AIAN and Asian race were associated with a lower and greater antibody response, respectively, compared to Non-Hispanic White race. However, the confidence intervals were wide in the setting of relatively small sample sizes for these groups. In models testing for differences in the slope of anti-S1 IgG waning, the rate of antibody decline increased monotonically in smokers. Current smokers realized an anti-S1 IgG decline that was 6.8% per month (95% CI, 1.0–12.1) greater than never smokers, adjusting for other covariates. Other socio-demographic and pre-pandemic clinical factors were not consistently associated with rate of antibody waning (Supplementary Table 3).

With respect to vaccine history, receipt of the mRNA-1273 vaccine was associated with a higher antibody response compared to receipt of the BNT162b2 vaccine (Fig. 3). The BNT162b2 vaccine was also associated with faster antibody waning versus the mRNA-1273 vaccine (Supplementary Table 3).

Compared to uninfected participants, those with a self-reported history of infection prior to vaccination showed higher antibody levels, particularly those with a history of hospitalization with COVID-19 (Fig. 4). Anti-nucleocapsid antibody level, an objective marker of natural infection, was also associated with higher anti-S1 IgG. Infections occurring after vaccination (sometimes called “breakthrough” infections), but prior to the serosurvey, were not associated with antibody levels after multivariable adjustment (Fig. 4, Table 2). Infections after vaccination were associated with a lesser rate of antibody waning, as was higher anti-nucleocapsid antibody titer (Supplementary Table 3), which could be due to the fact that time since vaccination does not correspond to time since most recent SARS-CoV-2 antigen exposure in this group.

Sensitivity analyses

Results were similar in complete case analyses (Supplementary Table 4) and in models excluding cases of self-reported infection that lacked confirmatory testing (Supplementary Table 5). Findings were also consistent in models using different approaches to assess potential cohort heterogeneity, including models adjusting for cohort (Supplementary Table 6) and stratified models that were restricted to, or excluded, the three cohorts (ARIC, FHS, REGARDS) contributing the largest number of participants to the main analysis (Supplementary Fig. 2a–d).

Discussion

Antibody responses to COVID-19 vaccination varied according to socio-demographic and clinical characteristics in a large, multi-ethnic, US population-based cohort, in which all participants received mRNA-based vaccines. Male sex, obesity, smoking history, diabetes, and COPD were associated with significantly lower antibody responses. Moreover, even after accounting for clinical conditions, smoking was associated with both lower peak antibody responses to vaccination and faster antibody waning. A history of SARS-CoV-2 infection and receipt of the mRNA-1273 vaccine were associated with higher antibody responses. Our findings suggest clinical characteristics that could be used to inform recommendations regarding re-vaccination.

Compared to prior studies, many of which included individuals with limited information on pre-pandemic health conditions9,14,15,17, our work is distinguished by its use of prospectively-collected pre-pandemic and pandemic-era risk factor data in racially and ethnically diverse U.S. cohorts. Our study design reduces the potential role of confounding by unmeasured pre-pandemic phenotypes and enhances generalizability to the U.S. population. C4R findings also extend knowledge regarding real-world population responses to mRNA vaccines. UK population-based studies were comprised mostly of individuals who received the BNT162b2 or ChAdOx1 vaccines; in contrast, our study sample included participants who received mRNA vaccines, and approximately half received the mRNA-1273 vaccine15,17. Compared to BNT162b2, the mRNA-1273 vaccine was associated with substantially higher antibody responses and slower antibody waning. Whether this may be due to differences in dosing between the two mRNA vaccines for the primary series (mRNA-1273: 100 mcg/dose; BNT162b2: 30 mg/dose), differences in the recommended dosing schedule, or other differences in vaccine formulations merits further investigation. Our findings may also have implications for dosing considerations relating to additional “booster” vaccines, since Moderna decreased the “booster” dose to 50 mcg. Unfortunately, we did not have sufficient data to assess the antibody response to three or more doses of vaccine in this study; we intend to investigate this in the future using additional follow-up in C4R, which will yield repeated measures on vaccinations and antibody responses.

Relative to UK data, our C4R data show peak antibody levels occurring at approximately 60 days and antibody waning was evident by 90 days. This suggests that the U.S. peak was sooner than in the Virus Watch and REACT-2 cohorts, in which the peak occurred closer to 90 days after the first dose, but later than in the ONS cohort, in which the peak occurred approximately 28 days after the first dose14,15,17. Nonetheless, the timing of the peak antibody response in C4R was similar to that observed in a longitudinal U.S.-based study of BNT162b2 recipients6. In our U.S.-based cohort, waning occurred more rapidly relative to the U.K. population, in which anti-spike IgG levels showed no obvious sign of waning by 90 days. Of note, longer intervals between the first and second dose implemented in the U.K. (8–12 weeks) versus in the U.S. (3–4 weeks) have been hypothesized to provoke a more durable immune response; this issue deserves more careful attention in future research studies. The faster waning observed in our sample may also be attributable to the fact that C4R participants are older and have more comorbidities linked to immunosenescence. Another important distinction between data collected in C4R vs. U.K. cohorts relates to the timing of serological assessments: published U.K. studies occurred primarily in 2021, while C4R results span from mid-2021 to mid-2022.

Our work confirms that antibody responses are higher in persons with a history of both vaccination and natural infection, or “hybrid” immunity. History of hospitalized infection was associated with the highest antibody levels, followed by non-hospitalized infection prior to vaccination. Non-hospitalized infection following vaccination (“breakthrough”) was associated with higher antibody responses versus non-infection in unadjusted analyses. The lack of statistical significance in the multivariable-adjusted analyses may be due to the relatively small number of post-vaccination infections in the sample, and thus limited power. The stronger association of hospitalized versus non-hospitalized infection with antibody response is consistent with prior literature showing augmented antibody production following severe COVID illness18,19,20. Of importance, prior literature has also found that a subset of severely affected patients mount lower antibody responses, which has been hypothesized to contribute to impaired clearance of and recovery from SARS-CoV-2 in some individuals. Associations between post-vaccination and post-infection antibody responses and post-acute sequelae of SARS-CoV-2 infection (PASC) warrant further investigation.

Many of the factors associated with lower anti-S1 IgG MFI in this report are known to increase risk of severe acute COVID-1921,22,23, and are also known to impact innate immune system dysfunction which is implicated as a risk factor for SARS-CoV-2 infection and poor clinical trajectories24. Our findings support the hypothesis that the associations of older age, male sex, obesity, diabetes and COPD with more severe acute COVID-19 could be partially mediated by an impaired immune response to SARS-CoV-2. Clinical trials and observational studies, including ours, have confirmed that additional vaccine doses are associated with higher antibody responses25,26. Higher anti-S1 responses to vaccines have been shown to be correlated with a lower risk of future infection9. Taken together, our results suggest that additional (or higher) vaccine doses should be particularly encouraged for individuals at risk of lower anti-S1 responses to vaccination, including older individuals and those with obesity, diabetes, and/or COPD27,28,29. Future research will be important to determine if more frequent vaccination or higher dosing in these vulnerable groups are effective in preventing severe COVID-19.

Strengths and limitations

Strengths of our study include a prospective, highly characterized, multi-ethnic, US general population-based sample that has comprehensive pre-pandemic phenotyping; semi-quantitative assessment of anti-S1 IgG responses using validated methods; an integrated definition of prior infection using self-report, hospital records, and anti-N antibody response; and extended follow-up after vaccination. Nonetheless, there are several limitations. First, information on neutralizing antibodies was not available, nor were other immunoglobulin isotypes (IgM, IgA) or measures of cellular immunity examined. Second, almost all of our participants had antibody levels above the threshold for “reactivity”30 and it is unknown to what extent variation of antibody levels above that threshold is clinically meaningful. In future work, we intend to test if differences in anti-S1 IgG levels are associated with prospective risk of infection severity and PASC. Third, we did not have repeated antibody measures to examine within-person temporal trends in anti-S1 levels; nonetheless, our findings regarding antibody trends over time since vaccination resemble those from longitudinal vaccine trials with repeated measures. For example, although we only captured the date of the first vaccine dose, the observed antibody peak was 30-40 days following the anticipated date of the second vaccine dose, which is consistent with prior literature5,6,7. Fourth, for interpretability, our analysis was limited to participants who had received two doses of an approved vaccine. The dynamics and clinical significance of antibody levels in unvaccinated individuals and in individuals with three or more doses remain important areas for further investigation. Fifth, certain time-varying risk factors for differential antibody response may be misclassified. Clinical conditions, and smoking status, were measured several years prior to the serosurvey, which may conservatively bias our estimates. Infection history was defined primarily by self-report and could be subject to false-positive or false-negative classification, with uncertain influence on our estimates. We did not have data regarding health-related behaviors (e.g., masking and participation in large gatherings) that could correlate with probability of subclinical, unreported infection. Nonetheless, our models included anti-nucleocapsid antibody levels, which are an objective, sensitive biomarker of potential prior clinical or subclinical infection among vaccinated populations31. Results in a sensitivity analysis limited to participants with a history of a positive COVID-19 test yielded similar results. Of note, the measures used in this study were completed prior to the emergence of the Omicron variants, which may demonstrate different immunogenicity compared to earlier variants; this is another important area for investigation in future work. Sixth, the meta-cohort was not directly representative of the U.S. population and is subject to healthy volunteer bias, which likely biased our results towards the null and limits generalizability to groups that were relatively underrepresented, including younger adults and minoritized groups. Overall, the cohort was older and a significant proportion had co-morbidities. While adverse associations with advanced age were clearly shown, no consistent associations with race or ethnicity were observed, with the exception of higher and lower antibody levels in participants reporting Asian and AIAN, respectively, versus non-Hispanic White race. These subgroups were small, hence the finding should be interpreted with caution, but it is somewhat consistent with a prior study on higher antibody levels in Asian participants32. Finally, cohort heterogeneity could influence our results, yet C4R ascertained COVID-related exposures using standardized measures16, pre-pandemic characteristics were harmonized following established protocols, and cohort-adjusted and cohort-stratified sensitivity analyses yielded highly consistent results.

Conclusions

We identified differential anti-S1 antibody responses related to vaccine-related, socio-demographic, and clinical factors in a diverse U.S. population sample. Our findings might help to identify subgroups of adults who benefit from more frequent vaccination or other COVID-19 prevention strategies. Strategies to optimize COVID-19 vaccine responsiveness at the individual level, and deployment at the population level, warrant further research and development.

Methods

Study Participants

To study the impact of the COVID-19 pandemic on US adults, C4R aimed to perform standardized assessment of COVID-19 in participants in 14 longstanding NIH-funded prospective cohort studies (see Supplementary Methods)16. All cohort participants who were alive on March 1, 2020, and had not withdrawn consent for cohort participation, were considered eligible for C4R enrollment. Institutional review board approval was obtained from all study sites. Informed consent was obtained from each study participant.

Inclusion criteria for the present analysis were self-report of two mRNA vaccinations for COVID-19 (BNT162b2 mRNA or mRNA-1273) prior to submission of a valid dried blood spot (DBS) for serology assay. We excluded participants who reported only one vaccination prior to serosurvey completion, or were eligible for a third vaccination prior to their date of serosurvey completion (Supplementary Fig. 1).

C4R serosurvey

The C4R serosurvey was accomplished via DBS, as previously described16,30. Briefly, the DBS requires that several drops of whole blood, from a finger prick or blood collection tube, be absorbed into a specially designed card. Participants who consented to the serosurvey completed the DBS at home or at an in-person exam. DBS samples were shipped to the central laboratory at the University of Vermont. The present study includes DBS samples collected between February 2021 and August 2022.

Serology assays were performed on DBS eluates by the Wadsworth Center, New York State Department of Health (Albany, NY, USA), using validated methods30. The assays were designed to detect IgG for SARS-CoV-2 S1 protein, which may be induced by natural infection or currently approved COVID-19 vaccines, and nucleocapsid (N) protein, which is induced by natural infection only. Briefly, SARS-CoV-2 S1 and N antigens (Sino Biological, Wayne, PA, USA) were covalently coupled to Magplex-C microspheres (Luminex Corp., Austin, TX, USA) with different bead regions coupled to the SARS-CoV-2 S1 and N antigens (Sino Biological, Wayne, PA, USA). Median fluorescence intensity (MFI) was analyzed using a FlexMap 3D instrument (Luminex Corp., Austin, TX, USA). Five separate bead sets were used over the period of analysis.

Antibody response was classified as reactive or non-reactive based on the mean and standard deviation (SD) of anti-S1 MFI values in uninfected (pre-pandemic) DBS samples30. For each bead set, the reactivity threshold was calculated as the mean + 6 SD of the uninfected (pre-pandemic) MFI. Samples above this threshold were classified as reactive.

C4R questionnaires

C4R collected information on SARS-CoV-2 infection and vaccination status via two waves of questionnaires conducted from April 2020 through February 2023; the current report includes data from questionnaires collected through August 2022. Questionnaires were administered by telephone interview, electronic survey, in-person examination, and/or mailed pamphlet. Participants were asked about history of SARS-CoV-2 infection, SARS-CoV-2 testing, COVID-19 hospitalization, COVID-19 vaccination status, date of first vaccine administration, number of vaccines received, and vaccine manufacturer. Infections were dichotomized according to whether they were, or were not, associated with hospitalization. Definite history of SARS-CoV-2 infection was classified based on self-report of a positive SARS-CoV-2 test, adjudication of medical records for a COVID-19 hospitalization, or evidence of anti-nucleocapsid antibody reactivity on DBS; self-reported infections not meeting any of these criteria were classified as probable (Supplementary Table 7). Both definite and probable cases of infection were included in the main analyses, and a sensitivity analysis was performed that excluded probable cases.

Pre-pandemic measures

C4R cohorts have performed longitudinal data collection on participants for up to 51 years. C4R harmonized these data across cohorts, as previously described16. Age, sex, and educational attainment were self-reported. Race and ethnicity, which were self-reported and categorized according to the 2000 Census methods33,34, were included in this study to address specific knowledge gaps about disparities in COVID-19 outcomes among members of historically marginalized or underserved populations. Time-varying risk factors were defined using the most recently collected data by each cohort. Smoking status was self-reported as never, former or current. Height, weight, blood pressure, fasting lipids and blood glucose were measured using standardized protocols. Hypertension was defined as a systolic blood pressure≥140 mm Hg, diastolic blood pressure≥90 mm Hg, or antihypertensive medication use. Diabetes was defined as fasting blood glucose≥126 mg/dL or use of insulin or hypoglycemic medications. Chronic kidney disease was defined as estimated glomerular filtration rate (eGFR)<45 mL/min/1.73m2. Cardiovascular disease, asthma, and chronic obstructive pulmonary disease (COPD) were identified via self-report or by the ascertainment of relevant clinical events, confirmed by medical record review, over cohort follow-up.

Statistical analysis

Natural log-transformed anti-S1 IgG level was regressed on candidate risk factors, time-since-vaccination (defined as days from first vaccination to serosurvey), and laboratory batch, using linear regression. Associations with candidate risk factors were tested with and without multivariable adjustment for other candidate risk factors under consideration. For interpretability purposes, we exponentiated the beta coefficient and presented the results as mean percent difference in anti-S1 level in the comparison vs. reference group.

Generalized additive models were used to examine differences in log-transformed anti-S1 IgG level over time-since-vaccination. Based on prior literature and empiric data in this study5,7, we fitted linear splines for the periods before and after the peak antibody level at 60 days-since-vaccination. Using the linear spline model, predicted antibody levels were plotted over time by risk factor strata. To test associations of candidate risk factors with rate of antibody waning during the second (post-60 day) period, we assessed the beta coefficient for the interaction term, “risk factor×slope of time from vaccine to serosurvey (per 30 days).” The beta coefficient was exponentiated with positive coefficients indicating slower decline, and negative coefficients more rapid decline, in anti-S1 IgG levels.

Multiple imputation by chained equations was applied to handle covariate missing data (Supplementary Table 8). Ten imputed datasets were created, and Rubin’s rule was applied to combine the estimates from the imputed datasets35. Characteristics of complete cases were similar to the imputed (primary) dataset (Supplementary Table 9). Complete case analysis was performed as a sensitivity analysis.

To explore whether inclusion of a certain cohort or set of cohorts was influential with respect to the overall results, we repeated the main analysis using a “leave-one-out” approach by separately removing participants in the three largest cohorts in this analysis (ARIC, FHS, and REGARDS) from the pooled analysis sample. We also performed a sensitivity analysis in which we only included participants from ARIC, FHS, and REGARDS. Analyses were also repeated with exclusion of participants reporting only one dose of vaccine. Results from all sub-group analyses should be interpreted with caution due to the possibility for type 1 or type 2 error.

All analyses were conducted in R (R Statistical Foundation, Vienna, Austria)16. R packages used for analysis include: “tidyverse”, “ggplot2”, “arsenal”, “mice”, “mgcv”, and “lspline”. Two-sided p-values < 0.05 were considered statistically significant.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.