The detailed study design and methods of the UK Biobank have been described elsewhere (22). Briefly, UK Biobank is a large-scale prospective population-based cohort study with over 500,000 volunteers aged 40-69 years recruited in 2006-2010. The information on social demographics, lifestyle and other health-related information was collected through touch-screen questionnaires and physical measurements. Blood samples were collected for genotyping. The UK Biobank has approval from the North West Multi-center Research Ethics Committee. All participants provided written informed consent for the study.

Among the 502,507 participants with available data, we excluded participants with prevalent cancer at recruitment (n=46,533), self-reported gender differed from genetic sex (n=318), missing data on smoking status (n=2,666) and psychological distress (n =47,098), leaving a total of 405,892 participants in the primary analysis. In addition, 394,061 individuals with available genetic information were included in the further genetic analysis. The details of the process for the construction of the analytical cohort are shown in Supplementary Figure 1 .

Psychological distress was measured using the 4-item Patient Health Questionnaire (PHQ-4) (23), which is a brief self-report questionnaire consisting of a 2-item depression scale (PHQ-2) and a 2-item anxiety scale (GAD-2) (24). Responses to each item were either “not at all” (scored 0), “several days” (scored 1), “more than half of the days” (scored 2), or “nearly every day” (scored 3). Therefore, the total score ranges from 0 to 12, with a higher score indicating greater distress. To determine a possible dose-response relationship, participants were divided into four groups based on quartiles of the PHQ-4 score: 0, 1, 2-3, and 4-12.

Covariates were selected based on scientific plausibility and prior evidence (10, 25). According to the smoking status from the respondents’ self-report, participants were classified into never, former, or current smokers. Pack-years smoking (PY) was calculated based on self-reported information on age at smoking initiation, the number of cigarettes smoked daily, age of smoking cessation (for former smokers) and age at recruitment (for current smokers). Subsequently, we categorized smoking levels as non-smoking (never smokers), light smoking (PY<30), and heavy smoking (PY≥30).

Other covariate data were collected at baseline using standard protocols, including socioeconomic characteristics (age at recruitment, sex, ethnic background, education, Townsend deprivation index and family history of lung cancer), and lifestyle factors (healthy diet score, BMI and physical activity). The healthy diet score was calculated based on the following diet factors: fruits: ≥3 pieces/day; vegetables: ≥ 4 tablespoons/day; fish: ≥ 2 times/week; unprocessed red meat intake ≤ 2 times/week; and processed meat intake ≤ 2 times/week (26). Missing data on covariates were coded as a missing indicator for categorical variables and with sex-specific median values for continuous variables.

Detailed information on the procedure for genotyping, imputation and quality control in the UK Biobank cohort has been previously reported (27). In the present study, we created a polygenic risk score (PRS) for lung cancer using 18 independent single nucleotide polymorphisms (SNPs) based on the largest available lung cancer genome-wide association studies (GWAS) of European descent ( Supplementary Table 1 ) (28). The PRS was calculated using the equation: PRS =β1 × SNP1 + β2 × SNP2 +…+βn × SNPn. Individual SNP was recoded as 0, 1, or 2 according to the number of risk alleles, and the effect size (β-coefficient) for each SNP was obtained from the GWAS data. According to PRS, we classified participants into three groups of low (lowest tertile), intermediate (second tertile) and high (highest tertile) genetic risk of lung cancer.

In UK Biobank study, cancer cases were identified through linkage to national cancer registries in England, Wales, and Scotland. The complete follow-up date was March 31, 2016 for England and Wales, and October 31, 2015 for Scotland. We defined lung cancer outcome according to the 10th Revision of the International Classification of Diseases (ICD-10): C33 and C34. Participants were followed-up until the date of the diagnosis of lung cancer, death, loss to follow-up, or censoring date (March 31, 2017, for England; October 31, 2016, for Scotland; and February 29, 2016, for Wales), whichever came first.

Cox proportional hazards model was used to estimate the hazard ratio (HR) and corresponding 95% confidence intervals (CIs). Follow-up time was treated as the time scale. The proportional hazards assumption was tested using Schoenfeld residuals. Psychological distress was tested as a categorical variable split into quartiles and as a continuous variable (per 1-standard deviation (19) increment), respectively. The first model was adjusted for age at recruitment (continuous), sex, ethnic background (white, non-white), education (college or university degree, no degree), Townsend deprivation index (quintiles) and family history of lung cancer (no, yes). A second model further adjusted for smoking, including smoking status (never, former, current) and pack-years of smoking (continuous). In the third model, other factors include healthy diet score (continuous), BMI (kg/m2, <25, 25-29.9, ≥30), and physical activity (MET-h/week, <10, 10-50, ≥50) were added to the first model. Lastly, the fourth model contained all the covariates mentioned above. For the genetic analyses, we further adjusted for the first ten genetic principal components and the genotyping array.

Psychological distress was also significantly associated with smoking, the most important risk factor of lung cancer. Thus, psychological distress could probably influence lung cancer risk by increasing smoking amount. To further clarify the causal path of psychological distress on lung cancer risk, the causal mediation analysis was implemented within a Cox proportional hazard framework to assess mediation by pack-years of smoking on the distress-lung cancer association. With these models, we estimated the direct effect of continuous psychological distress and the indirect effect mediated through continuous pack-years. The mediation analysis was performed using the R packages of “regmedint”, based on the product method proposed by Valeri and Vanderweele (29, 30). In addition, we also evaluated whether the association between psychological distress and lung cancer risk differed by smoking level or PRS by using multiplicative and additive interaction analyses. To quantify multiplicative interactions, we added an interaction term in the Cox proportional hazards regression models. In order to evaluate the interaction effect of smoking and psychological distress, we put the multiplication term of smoking and psychological distress in the model as the interaction term. In the model evaluating the interaction effect of PRS and psychological distress, we put the multiplication term of PRS and psychological distress as the interaction term. Relative excess risk due to interaction (RERI) and the attributable proportion because of the interaction (AP) was used to measure the interaction on the additive scale (31). The 95% CIs of the RERI and AP would not include 0 if there was additive interaction (32).

To assess the robustness of the results, we conducted several sensitivity analyses: (1) excluding participants who with less than two years of follow-up; (2) reclassified smoking levels based on 20 pack-years of smoking (none: never smoker, light: PY<20, and heavy: PY ≥20) (33); (3) genetic analysis only included participants of European descent. All analyses were performed using R Software (version 3.6.0), and a two-sided P-value <0.05 was considered to be statistically significant.

During a median of follow-up time 7.1 years (IQR 6.4-7.7 years), 1754 incident lung cancer cases were recorded. Table 1 reports the baseline characteristics of the participants according to psychological distress categories. Participants with higher levels of psychological distress were more likely to be slightly younger, female, less educated, and more deprived. In addition, they were more likely to have adverse lifestyle factors (smoking, obesity, physical inactivity and unhealthy diet).

The higher score of psychological distress was associated with an increased risk of incident lung cancer in a dose-response fashion ( Table 2 and Supplementary Figure 2 ). In primary models, psychological distress was significantly associated with a higher risk of incident lung cancer (HR_{per 1-SD}= 1.21, 95% CI: 1.16-1.26). However, after further adjustment for smoking status and pack-years of smoking, the relationship was substantially attenuated (HR_{per 1-SD}= 1.07, 95% CI: 1.03-1.12), and this association did not appreciably alter after further adjustment for other lifestyle factors (HR_{per 1-SD}= 1.07, 95% CI: 1.02-1.11) ( Table 2 ). These results suggested that smoking might be an important mediator of the distress-lung cancer association. In the sensitivity analyses, results did not change appreciably after excluding individuals with less than two years of follow-up ( Supplementary Table 2 ).

Similar positive associations were observed in the stratified analyses according to age at recruitment, sex, ethnic background, education, Townsend deprivation index, family history of lung cancer, smoking status, alcohol intake frequency, BMI, physical activity, healthy diet score, and histological subtypes (all P _{heterogeneity}>0.05) ( Supplementary Table 3 ). Of the individual psychological distress items, depressed mood (HR=1.08, 95% CI: 1.00-1.15), and tiredness/lethargy (HR=1.10, 95% CI: 1.04-1.16) were positively associated with incident lung cancer ( Supplementary Table 4 ).

The result of the mediation analysis was shown in Figure 1 and Supplementary Table 5 . Mediation analysis further confirmed that the association between psychological distress and risk of lung cancer was partly mediated by smoking. Specifically, participants with higher psychological distress were associated with increased smoking (beta=0.55, 95% CI: 0.53-0.58), and there was a significant direct effect of psychological distress on lung risk (HR=1.08, 95% CI: 1.05-1.10). The indirect effect of smoking was also significant (HR=1.02, 95% CI: 1.01-1.02). These findings indicated that 16.8% (95% CI: 13.0%-20.6%) of the total effect of psychological distress on lung cancer risk was mediated by smoking.

We found that PRS of lung cancer was significantly associated with an increased risk of incident lung cancer (HR_{per 1-SD}= 1.20, 95% CI: 1.15-1.26), which did not change with additional adjustment for psychological distress ( Supplementary Table 6 and Supplementary Figure 3 ). We further observed the joint association of the smoking or PRS with psychological distress on the risk of incident lung cancer in a dose-response manner (P trend=3.00×10^-306 for smoking; P trend=2.16×10^-14 for PRS). Compared with never smokers with no distress, those with heavy smoking and high distress had the highest risk of lung cancer (HR=18.57, 95% CI: 14.51-23.76) ( Figure 2A ). A similar pattern of joint effect was observed for PRS and psychological distress, the greatest relative increase of risk was observed among those with high genetic risk and high distress (HR=1.87, 95%CI: 1.50-2.33) ( Figure 2B ). Additionally, the positive associations between psychological distress and the risk of lung cancer were also observed in the stratified analyses according to smoking levels or PRS categories ( Supplementary Table 7-8 ). We repeated the analyses by the reclassification of smoking levels or the inclusion of only participants with European ancestry in genetic analysis, and the results were not materially changed ( Supplementary Figure 4 A, B ).

Table 3 shows the results of the interaction analysis. We observed both multiplicative (P=2.90×10^-8) and additive interactions between smoking and psychological distress in lung cancer. Specifically, for heavy smokers with high distress, the RERI was 4.05 (95%CI: 0.83- 7.26), which suggested that there would be 4.05 relative excess risk because of the additive interaction, accounting for 22% (95%CI: 7%-36%) of lung cancer risk in participants who had both heavy smoking and high distress. Additionally, there was an additive interaction but not multiplicative (P=0.269) interaction of PRS with psychological distress. For participants with high PRS and high distress, RERI was 0.47 (95%CI: 0.05-0.89), and 25% (95%CI: 4%-46%) of the risk of lung cancer exposed to both risk factors was attributable to the additive interaction. The results remained similar after reclassifying smoking levels and excluding participants of non-European descent in genetic analyses ( Supplementary Table 9 ).