Missing data are a common burden of epidemiological studies. When faced to such missing data, the assumptions with regards to their underlying mechanisms need to be considered cautiously and correctly to avoid biases and/or inefficiency in estimates of any exposure on the outcome. Accordingly, Little and Rubin’s classification of missing data is widely used to segregate their mechanisms, distinguishing three main types of missing data [30]. When the assumption of MCAR mechanism is violated but the MAR can hold, the use of multiple imputation approaches has been shown a valid and simple approach to deal with missing covariates and even outcome [11]. However, it is still seldom used and reported in epidemiological settings. Indeed, in addition to the incompressible time between any statistical innovation and its practical use, multiple imputation techniques require a good understanding and knowledge to be correctly applied. Notably, its implementation is not straightforward. Finally, complete case analysis method (i.e. excluding all subjects with missing value on at least one covariate) is the default method used by most of the statistical softwares, causing it easier to use and largely implemented in epidemiologic studies. We thus attempted to illustrate their use and the importance to be explicit about the multiple imputation procedure when assessing the impact of polyphenols on oxidative stress which is indeed a subject of major concern for epidemiologists. Actually, an adverse effect role of oxidative stress has been previously suggested in brain injury [31], carcinogenesis process [32], or cardiovascular diseases [33], and a protective role of polyphenols has been shown in cancers [34], or dementia [35].

We used data from SU.VI.MAX 2, which is a large cohort study conducted in the general population. The outcome was the TBARS concentration, which has also been recently used as an endpoint in clinical trials of selenium supplementation in patients with Type 2 diabetes [36], of exercise training in hemodialysis patients [37]. The association between catechins and biomarkers of oxidation measured with TBARS has been the focus of interest of many studies, particularly because of the abundance of catechins in the human diet. The impact of catechins on TBARS was mostly evaluated on animal studies while studies in humans were based on small samples, with conflicting results [38]. Studies on the relationship between catechins and oxidative stress are inconsistent [39] possibly related to the different amount of catechins ingested by subjects according to the study design. For example, Tinahones et al., in a study of 14 healthy women, showed that the consumption of green tea extract for five weeks was associated with a significant 37.4% reduction in the concentration of oxidized LDL (TBARS) (p = 0.017) [40]. Nantz et al. [41] showed, in a study on 111 healthy volunteers that after 3 weeks taking Camellia sinensis compounds twice a day serum malondialdehyde levels was 11.9% lower compared to baseline levels in the intervention group compared to the placebo group. On the contrary, Gomikawa et al. showed that TBARS contents in plasma were not changed after green tea consumption [42]. In our study, the relationships between catechins or acids hydroxybenzoic and TBARS were not linear, neither in univariate nor in multivariate analyses whatever the imputation model. Based on multivariate models from imputed datasets, high acids hydroxybenzoic intakes above the third quartile (Q3) were negatively associated with TBARS, while catechins intake higher than Q3 were selected as positively associated with TBARS; thus while the former subclass of polyphenols appears antioxidant, the latter appears to increase the oxidative stress. This result is quite unexpected since polyphenols have usually been reported as antioxidants. However, most of these studies were in vitro experimental or in vivo animal models studies with polyphenols at pharmacological doses, while the current study examines the role of polyphenols at nutritional doses in humans. Moreover, at high doses, polyphenols have also been shown to exert pro-oxidative effects (e.g., increased expression of phosphorylated histone 2AX and metallothionein, markers of DNA damage and response to oxidative stress, respectively). These prooxidative activities may be involved in hepatic and gastrointestinal toxicities observed in animals and humans [43, 44]. Nevertheless, the shape of the relationship between catechins and TBARS, should be stressed out. These results are driving interest in further explorations of the association between polyphenols intake and TBARS in humans.

Of note, in the complete case analysis, none of the polyphenol subclasses was found to be associated with TBARS. Moreover, the strength of association as measured by the estimated regression coefficients were affected by the handling of missing value approach, with for instance coefficients divided by two for the randomized supplementation group and the number of dietary records, while two-fold for others such as energy intake. At last, some participants’ characteristics such as sex, age, alcohol intake, zinc or selenium, differed according to the availability of a TBARS measure, suggesting that the probability of data being missing may depend to the observed data (that is, MAR). This mechanism excludes the complete case analysis as the basis of conclusive findings. However, it is not possible to further distinguish between MAR and MNAR (missing not at random, i.e. when the probability of missing data depends on unobserved data) from the observed data alone, although the MAR assumption may appear more plausible in this series due to the large collection of many explanatory variables included in the analysis. Otherwise, when the MNAR appear likely, other statistical approaches should be used [45–47].

According to previous recommendations, the imputation models included all variables planned to be in the analysis model including the outcome [11]. While it has been recommended to include the outcome in the imputation model, this point is somewhat delicate: as underlined by Moons et al. [48] it could seem, on the contrary, a self-fulfilling prophecy to use the outcome to impute data studying the existence of a potential association between the covariates and the outcome. As recommended, the TBARS outcome was systematically included in the imputation models whatever the sample of interest. Whatever the imputation model, the same predictors (except the hydroxybenzoic acids) were selected with close estimated effects, while differences in patient characteristics suggested some selected population from geographic criterion (Table 2). Thus, the close estimations of the two models can also be explained by the fact that these models were adjusted on those discrepancies. Moreover, the hydroxybenzoic acids were not selected when the imputation also applied to the outcome. The high proportion of missing outcome may have influenced these results, with about 50% of the outcomes that had to be imputed. However, Moons et al. [48] showed that imputation of such a high proportion of missing values still provided less biased results compared to complete case analysis. Thus, further studies are necessary to infirm or confirm this observation and the shape of the relationship.

Some limitations of our study could be advocated. First, the measurements of dietary intakes were performed at baseline whereas the outcome was measured about 12 years thereafter. Thus, it could be difficult to highlight the associations between polyphenols and TBARS due to changes in dietary intakes that may have confounded the estimation. Moreover, we used TBARS measure to explore the relationship between polyphenols subclasses and oxidative stress, which was the only oxidative stress biomarker collected in SU.VI.MAX2. Measure of oxidative stress is complicated and it is difficult to declare which oxidative stress biomarker is the best. TBARS represent an interesting marker of oxidative stress since they have been hypothesized to represent a composite number of oxidative damage products [49], however the assay of serum or urine isoprostanes as an oxidative biomarker is now frequently used as a gold standard. Further researches dealing with this association and using another oxidative stress biomarker than TBARS would be of great interest to confirm our results. Besides, the assessment of polyphenols intakes through dietary records is subject to self-reporting bias, despite the fact that repeating 24-h dietary records constitutes an accurate and efficient measurement of polyphenols intakes [50]. However, taking into account missing data with multiple imputations limit the over-selection bias issue analyzing subjects, regardless of the availability of missing covariates. Then, multiple imputation with chained equation procedure has some limitations among which are it lack of a theoretical justification, it MAR assumption sensitiveness increasing with the number of missing data, the possible non convergence insofar as it is an iterative procedure [11]. However, multiple imputation by chained equations, compared to other methods (CCA, median imputation…) remain a less biased methods to handle missing values. At last, the multiplicity issue should be pointed out that some false positive results could have occurred.