Making inferences from summary data: Can one relate chi squared tests to output from a Cox PH models?

Question

This might be a silly question, but I've been asked about interpretation of a paper and have a query on how much one can ascertain without access to the raw data used, illustrated by example here. In this paper, the authors report finding that artificial sweetener use is associated with increased risk of cancer. They used a Cox PH model for this on a predominantly female cohort, with a minimally adjusted model with age and gender as covariates, and a more complicated one with many others. Here's some of the results they report:

Without any raw data, I simply did a chi-squared test looking at the proportion of cancers per consumer group, and found that the reported trend seems to be driven by the lower consumer group in the all cancer subsection: if I compare non-consumers to higher consumers, the result is insignificant (p = 0.195). The authors however report a HR of 1.19 for higher consumers, though I'm not sure precisely what this was compared to as again, it is significant versus lower consumers, not versus non-consumers, at least by chi-squared testing. If this is the case, it might suggest a non monotonic dose response, indicating either weird biology or spurious findings.

The problem is, I don't have access to the raw data to run a Cox PH, and I'm wondering the limitations of what I can ascertain from summary statistics like the above. I also looked at breast cancer (presumably almost entirely female) to eliminate at least one variable (gender) and found the same trend in the reported data, the low consumption group driving the seeming significance. The question is without access to the raw data from a Cox PR model, can analysis of the summary statistics like this tell you anything conclusively, or do you need the raw data itself to make inferences?

Answer 1

Simply evaluating the fraction of cases with events, via chi-square or other tests, is inappropriate when there is "censoring" of the event times. In this type of study there are people who will eventually experience the event but haven't yet done so at the last observation times. For those, all you have is a lower limit for the time of the event: a right-censored event time.

Proper survival analysis takes that censoring into account, in a way that just counting up the events and dividing by the number of cases doesn't. Also, just counting up events doesn't take into account possible differences in other outcome-associated predictors, as a regression analysis can.

Thus you can't reliably evaluate this study in the way that you propose. Raw data are needed to reproduce the results and to evaluate the quality of the modeling.

In the data table you show, the hazard ratios for the "Lower consumers" and "Higher consumers" are the ratios versus the "Non-consumers" in the same analysis. For the "All cancers" analysis, the 95% confidence intervals don't cover the null-hypothesis value (a hazard ratio of 1), the usual evaluation of "statistical significance." Without a reference to the paper, I can't say what the "P-trend" values are supposed to represent.