How competing risks affect the epidemiological relationship between vitamin D and prostate cancer incidence? A population‐based study

Abstract We hypothesized that controversial results regarding the epidemiological relationship between circulating 25‐hydroxyvitamin D, 25(OH)D, and risk of prostate cancer (PCA) incidence are partly due to competing risks. To test the hypothesis, we studied associations across 25(OH)D, PCA and death in 2578 middle‐aged men belonging to the Kuopio Ischaemic Heart Disease Risk Factor Study. The men were free of cancer at baseline, and the mean (SD) follow‐up time was 23.3 (9.1) years. During this period, 296 men had a PCA diagnosis, and 1448 men died without the PCA diagnosis. The absolute risk of developing PCA was highest in the highest 25(OH)D tertile (15%), whereas that of death was highest in the lowest 25(OH)D tertile (67%). A competing risk analysis showed that belonging to the highest 25(OH)D tertile increased the risk of PCA incidence and improved survival with the respective hazard ratios (HR) of 1.35 (95% CI = 1.07−1.70) and 0.79 (95% CI = 0.71−0.89). Adjusting for 10 covariates together with 25(OH)D did not significantly change the results, but the respective adjusted HRs for PCA and death were 1.20 and 0.87. To conclude, the competing risk analysis did not eliminate the direct relationship between 25(OH)D and PCA but rather strengthened it.

. Anyway, there is a strong direct relationship between age and the risk of prostate cancer; the probability of developing prostate cancer is 40 times higher among men older than 70 compared with men younger than 50 (Siegel et al., 2019), and this relationship means that many men die for other reasons before they are old enough to develop prostate cancer. This for its part may explain conflicting results regarding the association between circulating 25-hydroxyvitamin D, 25(OH) D, concentrations and the risk of prostate cancer incidence. As high 25(OH)D concentrations are associated with reduced mortality rates in prospective cohorts (Bouillon et al., 2019), prostate cancer incidence rates should be higher among men with higher 25(OH)D concentrations because they tend to live longer.
One explanation for these contradictory results may relate to the vitamin D-binding protein that modulates the impact of vitamin D status on prostate cancer risk (Weinstein et al., 2013).
Many cross-sectional and retrospective studies associate vitamin D deficiency and insufficiency with prostate cancer mortality and, specifically, with aggressive prostate cancer (Choubey et al., 2017;Kumawat et al., 2021;Murphy et al., 2014;Özman et al., 2021;Xie et al., 2017). This association appears to be valid in middle-income countries but not necessarily as evident in high-income countries (Stanaland et al., 2017;Trump et al., 2009;Yaturu et al., 2012).
Vitamin D deficiency and insufficiency also seem to predict prostate cancer mortality (Fang et al., 2011;Shui et al., 2012;Stroomberg et al., 2021), although it is difficult to distinguish the association of vitamin D status with prostate cancer mortality from that with allcause mortality (Fang et al., 2011;Stroomberg et al., 2021). Studies showing no interaction between circulating vitamin D levels and the prognosis of prostate cancer as recurrence-free survival (Thederan et al., 2021) suggest that the association between vitamin D status and prostate cancer mortality mainly reflects the association between vitamin D and all-cause mortality.
To sum, although the same men appear to be prone to both vitamin D deficiency and prostate cancer, there is not necessarily a causative relationship between the vitamin D status and prostate cancer.
Circulating vitamin D concentrations and the vitamin D receptor, of which both are partly genetically determined, may be associated with the risk of lethal prostate cancer but most probably not with the risk of prostate cancer incidence (Guo et al., 2013;Shui et al., 2012;Torkko et al., 2020).
In this study, we hypothesized that the controversial results regarding the epidemiologic relationship between the vitamin D concentration in the blood and the risk of prostate cancer incidence can be partly due to competing risks, specifically, with respect to studies with long follow-up periods. To test our hypothesis, we studied the association between circulating 25(OH)D concentrations and prostate cancer incidence in a large epidemiological data set and interpreted the results with respect to all-cause mortality as a competing event.

| Study participants
The Kuopio Ischaemic Heart Disease Risk Factor Study (KIHD) is an ongoing population-based follow-up study (Salonen, 1988 In this study, we used the main cohort of KIHD, which comprises

| Dependent and independent variables
In KIHD, cancer refers to malign neoplasms and carcinoma in situ Other independent baseline variables were smoking in packyears, alcohol consumption in drinks per week (in Finland, one drink refers to 12 g of pure alcohol), body mass index (BMI), inflammation status measured as high-sensitive C-reactive protein (hsCRP) in milligrams per litre, total physical activity (TPA) measured as metabolic equivalent hours (METh) per day and diet described as fibre and meat intakes in grams per day together with the total energy intake in kilocalories per day. According to the Cancer Society of Finland, these covariates comprise the biggest lifestyle risk factors for cancer (Pukkala et al., 2016). Moreover, we included age in years and height in centimetres as independent variables because these factors in general explain a great proportion of the prostate cancer risk (Rebbeck, 2020). To avoid overadjustment, we did not include fish intake, which is a major source of vitamin D, and sunlight exposure as independent variables. As a variable, the vitamin D concentration in the blood is in the potential causal pathway between the exposure (fish intake and sunlight exposure) and the outcome (prostate cancer). In KIHD, smoking status, alcohol consumption, TPA and diet are based on study participants' own reporting (Lakka et al., 1994;Salonen et al., 1992;Virtanen et al., 2011;Voutilainen et al., 2001).

| Statistical analyses
Since circulating 25(OH)D levels of people living in Scandinavia vary seasonally (Klingberg et al., 2015), we used season-specific concentrations of 25(OH)D in the analyses. First, we identified two seasons, 'summer' and 'winter' that, respectively, represent 25(OH)D accumulated either during the sunniest or less sunnier months. Second, we distributed study participants into tertiles based on their season-specific levels of 25(OH)D. To substitute missing values, we applied the mean imputation approach and used 25(OH)D tertile-specific averages as substitutes. In many cases, mean imputation can even outperform multiple imputation, when imputing baseline covariates (Sullivan et al., 2018). The number of missing values per covariate ranged from zero (age) to 84 (pack-years). In the analysis of baseline characteristics, we used the analysis of variance (ANOVA) and the Kruskal-Wallis test to detect differences across the 25(OH)D tertiles. IBM ® SPSS ® Statistics Version 27 served as a statistical platform for the baseline analysis.
To estimate the probability of prostate cancer incidence, we calculated the proportion of a to b, where a is the number of prostate cancer cases and b is the total number of study participants at risk.
To generate unadjusted survival estimates, we used the Kaplan-Meier model, and to generate hazards adjusted for additional covariates, we used the Cox proportional hazards model. In the models, numerical values from 1 to 3 represented the 25(OH)D tertiles in ascending order. In KIHD, the follow-up time is based on linkages to national health registers. Regarding cancer, Finnish health care providers are obligated to report all diagnoses and their dates to the Finnish Cancer Registry and because KIHD is linked to it, the present study misses no cancer cases. Correspondingly, all non-events were censored as they did not have the diagnosis in the registers. In this study, we applied the register-based data updated till 31 December 2018.
In the competing risk analysis, we considered death as a competing risk and computed the competing risk regression (CRR) using the R version 3.5.3 (R Core Team, 2019) and the R package 'cmprsk' version 2.2.10 (Gray, 2020). The unadjusted regression included only 25(OH)D tertiles as covariates, whereas the adjusted regression included all baseline characteristics. The purpose of adjusting for several covariates was to estimate the magnitude of the effect of 25(OH)D on PCA incidence and death by comparing it to that of other potential risk and protective factors. Table 1 presents baseline characteristics of the 2578 study participants at different 25(OH)D tertiles. Briefly, distributions of covariates were skewed, and the total energy intake was the only characteristic that differed across the 25(OH)D tertiles based on both means and medians. The intake was highest in the first tertile (Table1). Overall, with respect to adequate 25(OH)D levels (NIH, 2021;Rosen, 2011), 68% of the study participants had the circulating 25(OH)D concentration <50 nmol l −1 , and 7% of them had it ≥75 nmol l −1 .

| Incidence rates of prostate cancer and allcause death
The mean (SD) follow-up time was 23.3 (9.1) years. During this period, 296 men had a prostate cancer diagnosis, 1616 men died, and 54 of them died to prostate cancer. The mean (SD) age of prostate cancer diagnosis was 76.3 (9.2) years, and that of death was 74.2     (Table 2). Age, smoking, alcohol drinking, higher BMI and higher hsCRP concentrations increased the HR for death (Table 2).

| Competing risk analysis
Regarding prostate cancer, the adjusted CRR indicated statistically  (Grant, 2011), the effect does not concern most prospective studies of prostate cancer. In general, the relative risk of prostate cancer incidence is highest in prospective studies with the shortest follow-up times and decreases together with increasing follow-up times (Grant, 2011). From the viewpoint of our study, this may denote underestimated HRs for the risk of prostate cancer incidence.
The few prospective studies of prostate cancer that consider a competing risk approach deal with the metabolic syndrome (Grundmark et al., 2010;Häggström et al., 2014). By and large, associations across prostate cancer, the metabolic syndrome and circulating 25(OH)D levels are complex, as 25(OH)D concentrations appear to modify the relationship between prostate cancer and metabolic syndrome so that the latter increases the likelihood of the former but only when 25(OH)D concentrations are low (Tuohimaa et al., 2007). Among the KIHD study participants, most of whom have insufficient serum 25(OH)D levels, the metabolic syndrome increases the risk of prostate cancer (Laukkanen et al., 2004).
In addition to the relationship between prostate cancer and metabolic syndrome, levels of circulating 25(OH)D appear to complicate the relationship between prostate cancer and smoking.
Overall, smoking increases the risk of prostate cancer (Huncharek et al., 2010). In the present study, however, smoking is associated with a lower risk of prostate cancer, and we suggest this result is due to the inverse relationship between circulating 25(OH)D concentrations and smoking. In other words, as smoking associates with Notes: Numbers indicate hazard ratios and 95% confidence intervals. Asterisks indicate statistical significance as follows: *p < 0.05, **p < 0.01 and ***p < 0.001.
The 1st 25(OH)D tertile served as the reference category, expect for the unadjusted CRR that compared the 3rd tertile to other tertiles.
Abbreviations: CRR, competing risk regression; CSH, cause-specific hazard; EFS, event-free survival; PCA, prostate cancer. reduced circulating 25(OH)D levels (Jiang et al., 2016;Kassi et al., 2015;Virtanen et al., 2011), and if lower 25(OH)D concentrations are associated with the reduced risk of prostate cancer incidence, it is possible to detect a negative correlation between smoking and the risk of prostate incidence without causality.

| Strengths and limitations
The main strength of this study is its good reliability. Owing to the KIHD 25(OH)D measurements at the follow-up visit, we were able to repeat our analyses and compare their results to the results based on baseline measurements.
The main limitations of this study relate to a lack of genetic information. Prostate cancer is a heritable disease, and an individual's genotype, such as vitamin D receptor polymorphisms (Li et al., 2007), modulates its association with the vitamin D status.
In addition, the comparatively small sample size together with the incompleteness of data did not allow us to investigate the relationship of 25(OH)D with different tumour stages. Rectal examinations and prostate-specific antigen tests at baseline would have improved the reliability of our inclusion criterion, that is, no evidence of disease.

| CON CLUS ION
Our findings proposed a direct relationship between circulating 25(OH)D concentrations and the risk of prostate cancer incidence.
The findings did not support the hypothesized explanation for this relationship that longer life expectancy due to higher 25(OH)D levels leads to a higher probability of prostate cancer incidence. The competing risk analysis did not eliminate the relationship between 25(OH)D and prostate cancer incidence but rather strengthened it.
Prospective studies of prostate cancer should consider a competing risk approach, specifically, when the follow-up time exceeds 20 years.

CO N FLI C T O F I NTE R E S T
Authors have no conflict of interest.

DATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the Institute of Public Health and Clinical Nutrition, University of Eastern Finland, upon reasonable request.