P test for trend v. Odds ratios and 95% confidence intervals

[Omer Gersten]

Hello everyone.

I’ve been reading some epidemiological papers and I’ve been confused about interpreting results that display both point estimates for odds ratios (ORs) with accompanying 95% confidence intervals (CIs) and p test for trend. My confusion stems from seemingly different conclusions from the two different sets of statistics. Often, based on the presentation of ORs and 95% CIs, the results don’t seem to be statistically significant, but the p test for trend is statistically significant. In these cases, which result do I favor?

Here’s an example (slightly simplified) from “Maisonneuve et al. (2016). Dietary inflammatory index and risk of lung cancer and other respiratory conditions among heavy smokers in the COSMOS screening study. Eur J Nutr, 55: 1069-1079”. The question of interest in this example is whether among heavy smokers the Mediterranean diet is protective against emphysema. Compliance with the diet can go from 0-9, with 9 being the most compliant. Since the Mediterranean diet is thought to be very healthy, especially in comparison to the Western diet, one might reasonably hypothesize that higher Mediterranean diet scores are associated with reduced risk of emphysema (i.e., an odds ratio less than 1 when compared to the comparison group which has a low Mediterranean diet score).

The results:

Mediterranean diet score OR (95% CI)^a
0-1 1.00
2-4 0.93 (0.70 – 1.23)
5-7 0.76 (0.57 – 1.01)
8-9 0.83 (0.55 – 1.27)

p trend 0.02
^a ORs and 95% CIs obtained from multivariable logistic regression model adjusted for baseline risk probability (based on age, sex, and other covariates)

The way I would interpret this is that there isn’t a relationship between Mediterranean diet score and better outcome on emphysema. My reasoning is that although the point estimates of the odds ratios are below 1 when higher Mediterranean diet scores are compared to the baseline, the confidence intervals all overlap with 1, meaning the result is not statistically significant. Nevertheless, the p trend is 0.02, which crosses the threshold for statistical significance for whatever this test is. The authors state “p values for trend were calculated using the quartile median values” and that they used SAS to carry out the analysis.

In my mind, wouldn’t it be better to just have emphysema as the dependent variable in a logistic regression with Mediterranean diet kept as a continuous variable? For the most part I think it’s better to keep variables continuous if you can, otherwise you throw out useful information. It seems that to generate the odds ratios the authors did use logistic regression, but with dummies for different values of Mediterranean diet score with the score 0-1 left out of the model.

So, in the example above, would you conclude that the Mediterranean diet is helpful in reducing the chances of getting emphysema or not? Do you go with the ORs and CIs or the p test for trend?

Thanks so much for your help,
Omer

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Omer Gersten, Ph.D.
University of California, San Diego (UCSD)

[Clyde Schechter]

In my mind, wouldn’t it be better to just have emphysema as the dependent variable in a logistic regression with Mediterranean diet kept as a continuous variable? For the most part I think it’s better to keep variables continuous if you can, otherwise you throw out useful information. It seems that to generate the odds ratios the authors did use logistic regression, but with dummies for different values of Mediterranean diet score with the score 0-1 left out of the model.

Yes, you are absolutely right here. Don't let the widespread bad practice in epidemiology of turning everything into categories infect your brain. You have this right. Now, the counter-argument is that the categorization enables you to represent all manner of non-linear relationships. But continuous variables can be transformed in ways that represent non-linear relationships flexibly as well--they're just a little more complicated to implement and interpret. I think it is this desire to avoid mis-specifying non-linear relationships as linear that leads epidemiologists to frequently discard information in this way. But I agree with you that it's not the right thing to do.

The use of a test for trend partly undoes this. While a test for trend is not specifically a test for a linear relationship (or, at least, not all test for trends are based on linearity), a test for trend is a test statistic that is more powerful at detecting monotone relationships. So whereas the use of indicator variables will detect any departure from all of the effects being 1 (in the odds ratio metric), it is unfocused. A departure from this null hypothesis in which the OR's follow some serpentine trajectory as we increase adherence to the Mediterranean diet will be found statistically significant by using indicator variables. By contrast, a test for trend will not find such an irregular pattern significant, even if it is very strong, but it will detect much subtler departures from the omnibus null provided they are monotone in the adherence variable. If it helps, you might think of it as somewhat analogous to the difference between a 1 and 2-sided test. The 1 sided test is oblivious to half of the space of estimates but is more sensitive to the tail on the other side, whereas the 2-sided test treats both sides similarly, but is more difficult to "trigger" in either end. The test for trend is, in this sense, like a 1-tailed test, and the category variables are more like a 2-tailed test.

I hope this helps.

[Omer Gersten]

Hi Clyde.

Thanks so much for your detailed and thoughtful response. Your comments are helpful. If you don’t mind, could you also give me your thoughts about the appropriate interpretation when all the CIs overlap with 1, but the test for trend is statistically significant? Would you say that overall there’s a statistically significant relationship in this case? Since I don’t know how to interpret the results for test for trends yet, in my mind if the CIs all overlap with 1 the relationship isn’t statistically significant. In my readings so far it seems that when the ORs are going in the same direction and the CIs don’t overlap with 1, the test for trend is (nearly?) always statistically significant. However, it is often the case that the tests for trends are statistically significant but the CIs overlap with 1.

Also, it is not clear to me in reading these epidemiology articles what test for trend measure they are using. My understanding is that there’s a number of them. Is there a standard test for trend in the epi literature?

In your response you said “But continuous variables can be transformed in ways that represent non-linear relationships flexibly as well--they're just a little more complicated to implement and interpret.” Do you mind elaborating on the types of transformation? One that I believe is pertinent is adding a quadratic term to the model. Do I have this right?

Thanks so much,
Omer

[Clyde Schechter]

For these purposes, at least, (and for many others) the confidence interval for the OR containing 1 is equivalent to not having a statistically significant result. What your results as described in #1 show is that a test that is specifically focused on identifying a monotone relationship between the score and the outcome, and that will be "oblivious" to patterns that oscillate up and down, has concluded that your data are supportive of the existence of such a monotone relationship. That is, the data suggest that the probability of the outcome decreases as you move to categories of mediterranean diet score that are higher numbered. However, when each outcome category is considered in its own right, there is not enough information in the data to determine whether the OR is greater or less than 1. So the data do suggest that these OR's differ from each other and do so in a way that orders them in inverse order of the Mediterranean diet scores the categories represent. But the data are not to determine with desirable levels of precision by how much, or even in which direction, any of the individual OR's differs from 1.

There is no "standard" test for trend. You are correct in noting that several are available, and that authors frequently neglect to report which one they have used. If it is important to you to know what has been used in a particular study, you should contact the study's author(s).

[Omer Gersten]

Thanks so much for your explanations Clyde!