Testing Interaction Effects with Weighted Interval-Censoring Cox Proportional Hazard Models

Testing Interaction Effects with Weighted IntervalCensoring Cox Proportional Hazard Models Adriana Pérez1,2, Sarah Valencia2, Lucas Smith2, Arnold Kuk3 1The University of Texas Health Science Center at Houston, School of Public Health, 1836 San Jacinto Blvd Suite 583, Austin, TX 78701 2Michael and Susan Dell Center for Healthy Living, School of Public Health, 1836 San Jacinto Blvd Suite 510, Austin, TX 78701 3Dell Medical School, The University of Texas, 110 Inner Campus Drive, Austin, TX 78712, Austin, TX 78712 Abstract This study explored the association of the interaction of past 30-day (P30D) electronic nicotine delivery systems (ENDS) with (i) sex and (ii) race/ethnicity on the age of asthma onset among adults who were asthma and COPD free and were never cigarette users. Secondary data analyses were conducted on adults (18+ years of age) of waves 1-6 (2013-2021) of the Population Assessment of Tobacco and Health (PATH) Study, a US nationally representative study. The interaction of P30D ENDS use with (i) sex and (ii) race/ethnicity were evaluated on the age of asthma onset using interval-censoring Cox regression and balanced repeated replicate weights for statistical analysis. Male adults (18+ years of age) who reported P30D ENDS use at the first wave of participation had a 569% increase risk in the onset of asthma at earlier ages in comparison to male adults who did not report P30D ENDS use (HR: 6.69, 95% CI: 1.96-22.79). Hispanic adults (18+ years of age) who reported P30D ENDS use at the first wave of participation had a 589% increase risk in the onset of asthma at earlier ages in comparison to non-Hispanic white adults who reported no P30D ENDS use at the first wave of participation (HR: 6.89, 95% CI: 1.62-29.32). Knowing the potential risk of earlier asthma onset may prevent people from initiating use or motivate particular users to quit using ENDS. Key Words: Sampling weights, Fay's variance estimation, Balanced Repeated Replicate Weights, Interval Censoring Hazard Function, hazard risk, age of onset. 1. Introduction Electronic nicotine delivery systems (ENDS), also known as vapes, vaporizers, vape pens, hookah pen, electronic cigarettes, e-cigarettes or electronic pipes, has been associated with age of asthma onset (Pérez, Valencia, Jani, & Harrell, 2024) and pulmonary function (Esteban-Lopez et al., 2022). In 2021, 11.1 million of adults reported every day” or “some days” ENDS use (Esteban-Lopez et al., 2022). The Population Assessment of Tobacco and Health (PATH) study is a nationally representative longitudinal study of tobacco use, its determinants, and its impacts in adults (18+ years of age) and children (12-17 years of age) in the U.S. (United States Department of Health Human Services, National Institutes of Health, National Institute on Drug Abuse, & Food Drug Administration Center for Tobacco Products, 2020). A U.S. nationally representative study among adults aged 18 years or older in 2021, reported that the prevalence of everyday or some days ENDS use was higher among males (5.1%, 95% CI: 4.7-5.6) in comparison to females (4%, 95% CI: 3.64.4) (Cornelius et al., 2023). Additionally, the prevalence of everyday or some day ENDS use was higher among other non-Hispanic (other single and multiple races) with a prevalence of 8.9% (95%CI: 6.2-12.4) in comparison to Asian non-Hispanic (2.9%, 95%CI: 2.0-4.0), Black non- Hispanic (2.4%, 95%CI: 1.8-3.2), white non-Hispanic (5.2%, 95%CI: 4.8-5.7), and Hispanic (3.3%, 95%CI: 2.8-4.0) (Cornelius et al., 2023). Asthma is one of the costliest diseases with uncontrolled asthma estimated to be $300.6 billion and the burden of uncontrolled asthma expected to continue to grow (Yaghoubi, Adibi, Safari, FitzGerald, & Sadatsafavi, 2019). Asthma in adults is often misdiagnosed as Chronic Obstructive Pulmonary Disease (COPD) or under diagnosed due to adults not being routinely screened for asthma (Hirano & Matsunaga, 2018). The prevalence of asthma in the U.S. among adults 18 years or older in 2021 was reported to be 8.0% representing more than 20 million adults afflicted in 2021 (Centers for Disease Control and Prevention, 2023). Pérez et al. (2025) reported the prevalence of ever being diagnosed with asthma by a doctor or health professional as 11.1% (representing 23.13 million adults) in 2013, and the prevalence of being diagnosed with asthma in the past 12 months varied between 7.09% (representing 16.86 million adults) in 2014-2015 and 8.70% (representing 17.07 million adults) in 2016-2018 (Pérez, Valencia, Jani, & Harrell, 2025). National 2021 data reported that US women 18 years or older had a higher prevalence of asthma (9.7% representing 12.71 million adults) in comparison to men (6.2% representing 7.58 million adults) (Centers for Disease Control and Prevention, 2023). Additionally, the prevalence of lifetime asthma among U.S. adults in 2021 was the highest among black non-Hispanic (15.7%, SE = 0.79) in comparison to white non-Hispanic (14.0%, SE=0.31), other non-Hispanic (12.5%, SE= 0.97), and Hispanic adults (11.4%, SE = 0.59) (Centers for Disease Control and Prevention, 2023). Pérez et al. (2025) reported the interaction effect of (1) sex with years since first hookah use, and (2) race/ethnicity and years since first hookah use on the age of asthma onset. After controlling for covariates, women, Hispanics and non-Hispanic black adults who reported one or more years since first hookah use had increased risks of asthma onset at earlier ages in comparison to men and non-Hispanic white adults who reported never hookah use, HR= 4.93; 95% CI 2.10-11.58; HR= 5.18; 95% CI 2.21-12.16 and HR=1.63; 95% CI 1.09-2.43, respectively (Pérez et al., 2025). Estimating the interaction effects of: (i) sex and P30D ENDS use and (ii) race/ethnicity and P30D ENDS use on the age of asthma onset has not been reported before and is paramount to protect public health, educate the public, provide evidence to the Food Drug Administration (FDA) and tobacco regulatory science on any potential differences as well as encourage users to stop. 2. Methods 2.1 PATH Study Design and Included Adults The PATH Study was comprised of two cohorts, Wave 1 cohort with a sample size of 32,320 adults (18+ years of age) and Wave 4 cohort with a sample size of 6,065 adults (which was added due to attrition). Secondary longitudinal analysis of restricted datasets Waves 1-6 (2013-2021) and special waves Wave 5.5 (2019-2020) and an adult telephone survey, Wave ATS (2020) of the PATH study were included in this analysis. Adults who reported being never users of cigarettes and were asthma and COPD free upon entry of the PATH study were included in this study. All adults provided informed written consent. Institutional review board approval was obtained from the Committee for the Protection of Human Subjects at the University of Texas Health Science Center at Houston with approval number HSC-SPH-22-0751. 2.2 Asthma and COPD Assessment Adults were asked at the first wave of participation (Waves 1-6), “Has a doctor or other health professional ever told you that you had [asthma]/[COPD]?”. Adults that responded “no” at their first wave of participation were then asked in Waves 2-6 about asthma diagnosis in the past 12months. Age of asthma onset was estimated using adults’ response in Waves 2-6, including Wave 5.5 and ATS. 2.3 Exposure to ENDS/Interaction To asses the effect of P30D ENDS use with (i) sex and with (ii) race/ethnicity, two new variables were created, representing (i) the interaction of P30D ENDS use and sex with males that were not P30D ENDS users as the reference category, and (ii) the interaction of P30D ENDS use with race/ethnicity with non-Hispanic white adults being the reference category. 2.4 Covariates at First Wave of Participation Race and ethnicity variables were included to account for disparities. The response to race and ethnicity questions in the PATH Study were combined to create the following categories: Hispanic, non-Hispanic Black, non-Hispanic White, and other, which included non-Hispanic Asian, multiracial, and any other race or ethnicity not otherwise specified (Pérez et al., 2024, 2025). Other covariates included (i) adults’ education (collapsed as less than high school, high school or general education development test, some college or associate’s degree, and bachelor’s degree or higher), (ii) total number of years that an adult reported ENDS use (1 or 2+ years), (iii) P30D use of other tobacco products (filtered cigars, traditional cigars, cigarillos, hookah, and smokeless tobacco), (iv) binge drinking (male adults, 5+ drinks; female adults, 4+ drinks), (v) ever marijuana use, (vi) total number of waves of emergent cigarette use prior to asthma onset, (vii) any person who uses TPs present at home, (viii) rules at home about any TP use (never allowed vs allowed anywhere, sometimes, or anytime), (ix) and weight status categorized as underweight, healthy weight, obese class 1, obese class 2 (Pérez et al., 2024, 2025). 2.5 Age of Asthma Onset Estimation The PATH study does not disclose the date of birth of adults and uses a complex design that requires balance repeated replicate weights to obtain variance estimates (Pérez et al., 2024, 2025). The age of asthma onset was estimated prospectively by using the age at the adults first wave of participation and the number of weeks between surveys (Pérez et al., 2024, 2025). The lower age bound estimated the age at the last wave where adults did not report asthma. The upper age bound estimated the age at the wave that adults reported asthma incidence (Pérez et al., 2024, 2025). Adults that reported no asthma throughout waves 1-6 were censored. 2.6 Statistical Analysis PATH uses a complex design and requires 100 balanced repeated replicate weights at the first wave of participation with Fay’s adjustment set to 0.3 were used to estimate the variance needed for statistical analysis (Pérez et al., 2024, 2025). Weighted summary statistics were calculated to describe the interaction of P30D ENDS with sex and P30D ENDS with race/ethnicity. Two crude and two multivariable weighted interval-censoring Cox proportional hazard models with cubic splines (3 knots) as the baseline hazard function were used to explore the association of the interaction of (i) P30D ENDS use with sex and (ii) P30D ENDS use with race/ethnicity on the age of asthma onset, respectively. Sampling weights of the first wave of PATH participation were used and Macros were developed in SAS to obtain estimates. Each multivariable model included covariates where a p-value < 0.2 in the crude analysis were observed. The final multivariable model included only significant covariates (p-value < 0.05). Crude and adjusted hazard ratios (HR) and 95% confidence intervals were reported. 3. Results After applying the inclusion/exclusion criteria (i.e., adults who reported being never users of cigarettes and were asthma and COPD free upon entry of the PATH study) the sample size was 7,766 adults representing approximately 80 million (see Table 1). Table 2 represented the demographic and measure characteristics of PATH adults that reported not having asthma or COPD and never used cigarettes at the first wave of participation in the PATH Study. There were 3,211 males (weighted percentage, 40.50%) that reported no P30D ENDS use at the first wave of participation and 94 males (weighted percentage, 0.39%) that did report P30D ENDS use at the first wave of participation. There were 4,395 females (weighted percentage, 58.85%) that reported no P30D ENDS use at the first wave of participation and 66 females (weighted percentage, 0.26) that did report P30D ENDS use at first wave of participation. There were 3,634 non-Hispanic white (weighted percentage, 53.84%), 1,720 Hispanic (weighted percentage, 19.46%), 1,515 non-Hispanic black (weighted percentage, 14.36%) and 737 other race/ethnicity (weighted percentage, 11.70%) adults that reported no P30D ENDS use at the first wave of participation. Table 1: Adults excluded or included in analysis among adults that were asthma/COPD free and never cigarette users in the PATH Study (2013-2021) at the first wave of participation. Adult Variable reported at the first wave of participation in the PATHa Study Sample No. Estimated national population No. Weighted % (SEb) Excluded adults A doctor or other health professional said adult had asthma 1,108 9,621,006 3.55 (0.13) Age was missing 3 45,487 0.02 (0.01) Answer to “doctor or other health professional said you had asthma?” was missing 39 472,621 0.17 (0.04) Cigarette use status was missing 24 306,990 0.11 (0.03) P30D use of ENDSc was missing 17 280,672 0.10 (0.03) Reported cigarette use 29,376 179,672,781 66.29 (0.58) Reported COPDd 23 445,480 0.16 (0.04) Reported COPDd and asthma 29 194,195 0.07 (0.02) Included adults Asthma/COPDd free and who reported never use of cigarettes 7,766 80,006,590 29.52 (0.52) Total 38,385 271,045,821 100 a. The restricted file received disclosure to publish: 10/25/23-10/31/23. United States Department of Health and Human Services. National Institutes of Health. National Institute on Drug Abuse, and United States Department of Health and Human Services. Food and Drug Administration. Center for Tobacco Products. Population Assessment of Tobacco and Health (PATH) Study [United States] Restricted-Use Files. Inter-university Consortium for Political and Social Research [distributor], 2023-05-19. https://doi.org/10.3886/ICPSR36231.v36. b. Any difference in categories of response with the total sum of the estimated population size is due to rounding of decimals, SE=standard error. c. ENDS: Electronic nicotine delivery systems or vapes, vaporizers, vape pens, hookah pens, electronic cigarettes, and/or e-pipes. d. COPD: Chronic obstructive pulmonary disease. Table 2: Demographic characteristics adults who were asthma-free never used cigarettes at the first wave of participation in the PATH Study Variable reported at the first wave of participation in the PATHa Study Sample No. (n=7,766) Estimated national population No. (N=80,006,590) Weighted % (SE) Wave of entry into the PATHa Study Wave 1 (2013-2014) 6,197 68,787,579 85.98 (0.42) Wave 4 (2016-2018) 1,569 11,219,011 14.02 (0.42) Age [Weighted Mean (SE)] 43.64 (0.27) Interaction of sex and P30D ENDSb use Male reported no P30D ENDS use 3,211 32,405,293 40.50 (0.62) Male reported yes P30D ENDS use 94 311,834 0.39 (0.05) Female reported no P30D ENDS use 4,395 47,082,479 58.85 (0.62) Female reported yes P30D ENDS use 66 206,983 0.26 (0.05) Interaction of race/ethnicity P30D ENDSb use Non-Hispanic white reported no P30D ENDS use 3,634 43,074,880 53.84 (0.78) Non-Hispanic white reported yes P30D ENDS use 78 281,472 0.35 (0.06) Hispanic reported no P30D ENDS use 1,720 15,567,189 19.46 (0.45) Hispanic reported yes P30D ENDS use 45 129,784 0.16 (0.03) Non-Hispanic black reported no P30D ENDS use 1,515 11,488,033 14.36 (0.40) Non-Hispanic black reported yes P30D ENDS use 19 46,646 0.06 (0.01) Otherc reported no P30D ENDS use 737 9,357,676 11.70 (0.37) Otherc reported yes P30D ENDS use 18 60,915 0.08 0.02) a. The restricted file received disclosure to publish: 02/09/2024-03/19/2024. United States Department of Health and Human Services. National Institutes of Health. National Institute on Drug Abuse, and United States Department of Health and Human Services. Food and Drug Administration. Center for Tobacco Products. Population Assessment of Tobacco and Health (PATH) Study [United States] Restricted-Use Files. Inter-university Consortium for Political and Social Research [distributor], 2023-05-19. https://doi.org/10.3886/ICPSR36231.v36. b. ENDS include vapes, vaporizers, vape pens, hookah pens, electronic cigarettes, and/or electronic pipes. c. Other included Non-Hispanic Asian, multiracial, and any other race/ethnicity not otherwise specified. Figure 1 shows the prevalence of P30D ENDS use and ever being diagnosed with asthma by a doctor as reported by each wave (not including special collection waves) in the PATH Study. The 20182019 and 2022-2023 prevalence of P30D ENDS use was 9.21% (representing 23.69 million adults in the U.S.) and 9.15% (representing 23.85 million adults) see Figure 1. Table 3 shows the crude and the adjusted Cox proportional hazard models for the interaction of (i) sex with P30D ENDS use and (ii) race/ethnicity with P30D ENDS use on the age of asthma onset. Male adults who reported P30D ENDS use at the first wave of participation had a 569% increase risk in the onset of asthma at earlier ages in comparison to male adults who did not report P30D ENDS use (HR: 6.69, 95% CI: 1.96-22.79). Hispanic adults who reported P30D ENDS use at the first wave of participation had a 589% increase risk in the onset of asthma at earlier ages in comparison to non-Hispanic white adults who reported no P30D ENDS use at the first wave of participation (HR: 6.89, 95% CI: 1.62-29.32). Figure 1: The prevalence of P30D ENDS use and the prevalence of ever being diagnosed with asthma by a doctor or health professional among adults in the PATH study (2013-2023) 4. Discussion This cohort study prospectively estimated the interaction of P30D ENDS use with (i) sex or (ii) race/ethnicity among adults that never used cigarettes and did not have asthma or COPD at the first wave of participation in the PATH Study using interval-censoring survival analyses. When exploring the interaction of P30D ENDS use with sex statistically significant differences were found among females that were P30D ENDS users. Previous research reported that current asthma is more frequently reported by females (Rhodes, Moorman, & Redd, 2005). When exploring the interaction of P30D ENDS use with race/ethnicity, we found that Hispanic adults who reported P30D ENDS use were at higher risk of earlier age of asthma onset which was consistent with previous studies that indicated that the burden of asthma falls disproportionately on Hispanics (Asthma and Allergy Foundation of America, 2020). There were three strengths of this study, (i) the use of the PATH Study which is a nationally representative sample of U.S. adults, (ii) testing hypotheses with longitudinal data on tobacco related health outcomes, and (iii) the implementation of interval-censoring Cox regression models with balance repeated replicate weights. There were several limitations to this study. First, there was a lack of software required to implement interval-censoring Cox regression models with balance repeated replicate weights but we created macros to complete this task similar to the program described by Liu, 2020 (B. Liu, 2020). Other risk factors that may influence the age of asthma onset such as environmental factors, nutritional intake, maternal smoking status, genes, allergies, dust mites, and family history of asthma were not measured in the PATH Study and results must be cautiously interpreted (Forno & Celedon, 2009; Hosseini, Berthon, Wark, & Wood, 2017; Kuruvilla, Vanijcharoenkarn, Shih, & Lee, 2019; T. Liu et al., 2009; Mirabelli, Hsu, & Gower, 2016; Ndanuko, Tapsell, Charlton, Neale, & Batterham, 2016; Neuman et al., 2012; Pettigrew et al., 2007; PlattsMills, Erwin, Heymann, & Woodfolk, 2009). We provided evidence on how the interaction of (i) sex with P30D ENDS use, and (ii) race/ethnicity with P30D ENDS use played a differential role in the age of asthma onset which have not been reported in the literature before. Knowing the potential risk of earlier asthma onset may prevent people from initiating use or motivate particular users to quit using ENDS. Table 3: Association of the interaction of (i) sex with P30D ENDS use and (ii) race/ethnicity with P30D ENDS use on the age of asthma onset among adults who were asthma-free and never used cigarettes at the first wave of participation in the PATHa Study Variable reported at the first wave of participation in the PATHa Study Crude Association Adjusted Model HR (95% Cl) HR (95% CI) Interaction of sex with P30D ENDSb use Male reported no P30D ENDS usec 1 1 Male reported yes P30D ENDS usec 16.94 (5.15-55.68) 6.69 (1.96-22.79) Female reported no P30D ENDS usec 1.13 (0.79-1.60) 1.35 (0.92-1.98) Female reported yes P30D ENDS usec 5.27 (1.36-20.45) 2.03 (0.30-13.84) Interaction of race/ethnicity with P30D ENDSb use Non-Hispanic white reported no P30D ENDS used 1 1 Non-Hispanic white reported yes P30D ENDS used 9.67 (2.32-40.36) 4.25 (0.92-19.70) Hispanic reported no P30D ENDS used 0.84 (0.53-1.33) 1.02 (0.58-1.81) Hispanic reported yes P30D ENDS used 10.19 (2.00-51.96) 6.89 (1.62-29.32) Non-Hispanic black reported no P30D ENDS used 1.48 (0.99-2.21) 1.44 (0.96-2.16) Non-Hispanic black reported yes P30D ENDS used 5.61 (0.36-86.86) 0.36 (0.01-11.14) Othere reported no P30D ENDS used 0.90 (0.39-2.09) 0.84 (0.44-1.58) Othere reported yes P30D ENDS used 14.30 (0.98-209.13) 4.76 0.25-91.09) a. The restricted file received disclosure to publish: 02/09/2024-03/19/2024. United States Department of Health and Human Services. National Institutes of Health. National Institute on Drug Abuse, and United States Department of Health and Human Services. Food and Drug Administration. Center for Tobacco Products. Population Assessment of Tobacco and Health (PATH) Study [United States] Restricted-Use Files. Inter-university Consortium for Political and Social Research [distributor], 2023-05-19. https://doi.org/10.3886/ICPSR36231.v36. b. ENDS include vapes, vaporizers, vape pens, hookah pens, electronic cigarettes, and/or electronic pipes. c. Adjusted for race/ethnicity, adults’ education, weight status, total number of years that an adult reported ENDS use, P30D use of other tobacco products, binge drinking, ever marijuana use. d. Adjusted for sex, adults’ education, weight status, total number of years that an adult reported ENDS use, P30D use of other tobacco products, binge drinking, ever marijuana use. e. Other included Non-Hispanic Asian, multiracial, and any other race/ethnicity not otherwise specified. Acknowledgements We express our gratitude to all PATH Study participants for their participation across time. We thank Mr. Luis Mijares for formatting Figure 1. The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Research reported in this publication was supported to Dr Pérez by grant number R21HL165401 from the National Heart, Lung, and Blood Institute (NHLBI) and the Food and Drug Administration (FDA) Center for Tobacco Products (CTP). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health (NIH) or FDA. 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