The whole study is a fairly detailed explanation of the results. They address variables in their testing:
We found that an increase in sugary drink consumption was positively associated with the risk of overall cancer and breast cancer. When the group of sugary drinks was split into 100% fruit juices and other sugary drinks, the consumption of both beverage types was associated with a higher risk of overall cancer. In contrast, no association was detected between artificially sweetened beverage consumption and the risk of cancer in this study. These results were robust after a wide range of sensitivity analyses."[My highlighting]
" Sensitivity analyses
Further adjustments for several indicators of the quality of the diet did not substantially modify the findings, nor did any other sensitivity analyses (appendix 11). Results remained stable when applying a bootstrap approach to account for extra variation (subdistribution hazard ratio for a 100 mL/d increase in sugary drink consumption 1.18, 95% confidence interval 1.02 to 1.34 for overall cancer; 1.23, 1.02 to 1.60 for breast cancer). Appendix 12 shows that cause-specific Cox proportional hazard models provided similar results."
There is much more discussion in the report of sampling, statistical modelling, sample sizes etc.
In regards to whole fruits and fruit juices they made note of this " Of note, despite their overall healthy and natural image in the general population, and some studies suggesting lower health risks compared with sugar sweetened beverages,55 56 57 58 100% fruit juices generally contain high levels of simple sugar (median=10.3 g/100 mL in this study, sometimes higher than regular soda),59 and their glycaemic indexes are higher than that of whole fruits.60"
They also reference a number of other studies which have found correlation between sugary drinks and cancers:
" Comparison with other studies
Except for pancreatic cancer (non-significant, six prospective studies, 2010),52 no meta-analysis was performed by the World Cancer Research Fund/American Institute for Cancer Research on the association between sugary drinks and the risk of cancer. A meta-analysis showed no link between the consumption of sweetened,29 carbonated beverages and the risk of overall cancer and specific locations, unlike our findings. However, this meta-analysis, funded by one of the biggest soda producing companies, did not show the isolated associations in sugary drinks and artificially sweetened beverages, which might have impaired the possibility to detecta potential role of sugar (main driver of the associations in our study). Genkinger and colleagues observed an increased risk of pancreatic cancer associated with sugar sweetened carbonated soft drink consumption in the framework of the Pooling Project (14 cohorts),24 and Navarrete-Muñoz and colleagues observed no association in the EPIC cohort.27
Data are scarce regarding other cancer sites, notably for breast cancer. The two published prospective cohorts were consistent with our findings; Hodge and colleagues observed an increased risk of breast cancer associated with sugary drinks (Melbourne Collaborative Cohort Study, participants aged 40 and over, 946 cases).22 This association was only observed for postmenopausal breast cancer. In contrast with our results, Makarem and colleagues observed no association with breast cancer (Framingham Offspring cohort), which might result from a lack of statistical power (124 cases).23
In line with our results, a recent meta-analysis observed no association for the risk of colorectal cancer,28 even though statistical power was limited for this cancer in our cohort. Results are contrasted regarding prostate cancer in the literature: in line with our findings, no association was observed for sugar sweetened and artificially sweetened sodas in a meta-analysis combining two prospective studies.29 Consistently, no association was observed in the Framingham Offspring cohort for sugary drinks,23 but an increased risk was observed for 100% fruit juices; however, statistical power was also limited in this study (157 cases). Sweetened beverage intake was associated with an increased risk of gallbladder cancer in the Swedish Mammography Cohort and Cohort of Swedish Men.25 Sugary drinks were associated with increased risk of endometrial cancer in the Swedish Mammography Cohort.26 The limited number of cases did not allow us to perform site-specific analyses for these cancer locations in our cohort.
Lastly, and in line with our results, two recent prospective studies observed an increased risk of obesity-related cancers and adiposity-related cancers associated with sugary drink consumption.2223 Furthermore, associations were observed between fruit juice intake and an increased risk of thyroid carcinomas,53 and in the EPIC cohort between citrus fruits and juices and increased risk of basal cell and squamous cell carcinomas of the skin.54"