LAUSR

Dear Editor-in Chief, We read thepaper authoredby Imai et al thatwaspublished in Journal of SurgicalOncology,withgreat interest.Theauthorsaimedtodetermine the cure rate and its predictive factors in patients with colorectal liver metastases and concomitant extrahepatic disease (EHD) on the 5-year disease free survival (DFS) after surgery. They investigated two cohorts and the cure rateswere reported tobe13%and19% inpatientsof intention-totreat cohort and EHD resection cohort, respectively. Then, they applied univariable and multivariable logistic regression models to identify the predictors of studied outcome. Although an interesting study has been conducted, some methodological points need to be taken into account. First, the authors used logistic regression model and then the relative risk (RR) was reported as measure of association in their cohort study which is problematic. The logistic regression model can only provides odds ratio (OR) which is different from RR. In fact, the RR is superior thanORand theOR is only the appropriate estimates of the RR when the studieddiseases is rare;otherwise, the association reportedby ORmay be exaggerated. Hence, wewonder that why the authors did not used Cox regression model in their cohort study to estimate the hazard ratio (HR) as measure of association which is identical to RR. Hence, we respectfully suggest authors to re-analyze their data using the Cox regressionmodels such asCox proportional hazard regression or Extended Cox to obtain HR as robust measure of association. Second, the authors reported very large adjustedORwith considerably wide confidence interval (CI), on the association between the primary Tstageandstudiedoutcome in ITTcohort (OR=47.4;95%CI:7.7-439.0) and EHD resection cohort (OR=22.2; 95%CI: 2.53-510.5) which is questionable. It has been indicated that the very large measure of association with considerably wide CI can be resulted in sparse data. The sparse data meaning that the number of observations is rare in different strata of the Exposure and Outcome variables and this problem is exacerbated in the multivariable models since the number of strata would be increased. Hence, themeasure of association estimated in the sparse data is subject to sparse data bias. The penalization through data augmentation is one of the effective methods which decreases the aforementioned bias and provides more unbiased and valid measure of association. So, we respectfully suggest Imai et al to use penalized Cox regression models to provide more unbiased HR with narrow CI. As take home message for the readers is that the appropriate regression models should be used in the cohort studies to provide more robust measure of association. Also, the sparse data bias should be addressed and considered where it seems necessary.