Materials & Methods
This study was a cross-sectional investigation conducted through a web-based questionnaire to assess the PA levels of participants and the frequency of colds they experienced in the past year ( Figure 1 ). Participants’ inclusion criteria: (i) aged 40 years and above; (ii) clear consciousness, no communication barriers, ability to use mobile phones to complete web-based questionnaires; (iii) signed web-based informed consent. It was conducted using a multi-stage random sampling method for online dissemination and diffusion by the researchers, spanning from November 30, 2020, to November 1, 2021. Interested participants voluntarily answered all relevant questions on the questionnaire platform by scanning the provided QR code. The questionnaire aimed to gather essential information about the participants, including basic personal and occupational details, as well as the duration, intensity, frequency, and type of PA they engaged in. It also inquired about the number of colds participants had contracted in the past year (see Appendix A for questionnaire details). To prevent duplicate submissions, the IP address of each respondent was recorded. The web-based questionnaire was extensively circulated in various provinces and cities across eastern, central, and western China. Participation was strictly voluntary, with no monetary or material incentives offered by the researchers or associated organizations. All participants electronically signed the informed consent form online. The study’s protocol received approval from the Sports Science Experimental Ethics Committee of Beijing Sport University (2019067H).

The sample size for this study was determined using the formula outlined in Eq. (1) , employing a 95% confidence interval with a z-value magnitude of 1.96. The P value indicates the proportion of the target population, and, drawing from prior research, a coefficient of variation as high as 0.5 was deemed the upper limit. The E value represents an acceptable sampling error, which typically ranges from no less than 2–3% ( Tu, Lu & Tao, 2022 ). (1) N = z 2 ∗ P 1 − P / E 2

Based on this calculation, we assumed a response rate of 95% for the questionnaire used in this study, leading to a minimum required sample size of 1,616 questionnaires. During the actual research process, 1,723 questionnaires were distributed online, and 1,683 were returned with complete responses, resulting in an effective response rate of 97.68%. An effective questionnaire is defined as one that is fully completed and uploaded; specific survey results are detailed in the results section.

This study employed a web-based questionnaire to gather data from the target population, individuals aged 40 years and older. The questionnaire covered essential details such as participants’ age, sex, chronic disease prevalence, residence, physical activity levels, and the frequency of colds experienced in the past year.

The frequency of colds in the last year was assessed with the question, “How many times have you had a cold in the past year?” This question, adapted from prior research, allowed respondents to choose from “0 times”, “1 time”, “2 times”, “3 times”, or “ ≥ 4 times” as their answers ( Bensenor et al., 2001 ; Matthews et al., 2002 ; Ouchi et al., 2012 ). Before responding, participants were briefed by the researchers that clinical symptoms of the common cold include nasal congestion, runny nose, sneezing, sore throat, and coughing, helping in the self-diagnosis ( Heikkinen & Järvinen, 2003 ).

Participants were also prompted to indicate their preferred form of PA from among 16 listed exercises in the questionnaire or to specify any other forms of exercise not listed. The level of PA, a critical indicator for this study, was determined using Eq. (2) . (2) PA level = frequency ∗ intensity ∗ duration time

Exercise frequency refers to how often participants engage in physical activity each week. This was determined by asking, “How many times per week have you exercised in the last year?” with response options of “Never”, “1–2 times”, “3–5 times”, and “almost every day”. The final statistical analysis utilized the average values for each category ( e.g. , 0, 1.5, 4, and 6 times per week).

Exercise intensity was assessed using the Brog CR-10 scale ( Borg, Ljunggren & Ceci, 1985 ), which corresponds to the question, “How do you feel overall during your exercise workout?” Subjective fatigue includes general muscular, cardiac, and respiratory fatigue. Participants answered questions with options ranging from 0 to 10. Higher scores indicate greater exercise intensity. Based on previous research, exercise intensity was considered low if the CR-10 score was <2.5, moderate if the CR-10 score was 2.5–4, and high if the CR-10 score was >4 ( Thompson et al., 2013 ). The metabolic equivalents (METs) corresponding to these intensity levels, based on the relationship between rated perceived exertion (RPE) and METs from earlier studies, are 1.5 METs for low intensity, 4.5 METs for moderate intensity, and 7.5 METs for high intensity ( Heesch, Burton & Brown, 2011 ). Therefore, calculations were made by integrating these criteria to translate the RPE scores provided by participants into corresponding MET value ranges for evaluation. According to these calculations, participants’ weekly PA levels were categorized as low (<500 MET minutes per week (MET-min/wk)), moderate (500–1,000 MET-min/wk), and high (>1,000 MET-min/wk) ( Thompson et al., 2013 ).

The reliability and validity of the questionnaire were assessed using AMOS 22 (IBM Corp. Armonk, NY, USA) and SPSS 21.0 (SPSS, Chicago, IL, USA), respectively, prior to the formal execution of the study. The Cronbach’s alpha coefficient and the KMO-Bartlett’s test coefficient for the questionnaire were 0.62 and 0.802, respectively, surpassing the accepted threshold of 0.6. To further validate the questionnaire before its official distribution, 30 participants were enlisted to fill it out twice for a pilot test. These individuals were then requested to complete the questionnaire again two weeks following their initial submission. Pearson’s correlation coefficients for the responses to identical questions were 0.812 and 0.885, respectively, both greater than 0.6. The cumulative variance contribution was 64.3%, which was greater than 50%. The rotated component matrix revealed that all variables had factor loadings above 0.5. These findings indicate that the questionnaire possesses satisfactory reliability and validity, making it suitable for extensive research applications.

Statistical processing and data analysis were carried out using Excel 2019 (Microsoft Corp., Redmond, WA, USA) and R version 4.2.1 ( R Core Team, 2022 ). Prior to analysis, all data underwent normality testing using the Shapiro–Wilk test. The non-normally distributed data were presented with median and quartiles or numbers (proportions). Differences in PA level between groups were compared by Kruskal–Wallis test. The χ 2 test was used to compare colds in the past year between middle-aged and elderly individuals with different characteristics. The frequency of colds experienced by the subjects in the past year served as the dependent variable, with occurrences categorized and assigned values of 0, 1, and ≥2 for no colds, one cold, and two or more colds, respectively. Variables that showed statistically significant differences across groups were selected as independent variables for further analysis through an ordered multiple logistic regression model. The magnitude of the effect was quantified using the odds ratio (OR). To examine the dose–response relationship between weekly PA level and frequency of colds, a restricted cubic spline model was employed, and the resulting curves were illustrated using the ggplot2 package in R version 4.2.1. A two-tailed p -value of <0.05 was considered indicative of statistical significance.