Hello Mahmoud Tarek Hefnawy. Do you have people's actual age in years? Or is all you know which side of 60 they are on? If you have age in years, I would advise you to include that in your model. Carving good quantitative variables into categories almost never makes sense. There are many articles discussing this issue. Some of them are mentioned in this conference presentation I put together several years ago.

Presentation Free Advice for Power-Hungry Researchers: Do Not Categorize ...

I hope this helps.

PS- I'll be curious to know if you still define "old age" as 60+ when you reach 60 yourself. ;-)

Dear Bruce Weaver . Thank you for your answer and for your recommended publication.

I was reading with interest this systematic review and meta-analysis:

Article Tooth loss and the risk of cognitive decline and dementia: A...

All the the included studies were of patients with median or mean age above 60 years old or more

the study investigated the role of tooth extraction on cognitive impairment, however all the included population are elderly. age is also a significant risk of cognitive impairment. The study for the first time in literature performed a regression analysis to limit the impact of age in cognition in order to get a clear effect Of tooth loss on cognitive function.

I mean that the sample doesn’t contain young and old, all the sample was old, So I wandered if the regression analysis here is of true impact on limiting the effects of confounding risk of age. because all the population was in the same category.

Thank you for your interest

Hi Mahmoud, that's a a very common situation.

Considering that your sample is composed mainly of elderly, performing regression won't fix the problem because you won't have a balanced sample with participants with different ages (those at risk and those who are not).

However, I feel like you can still go ahead and do your analysis after refining your research question. It should be "Efficacy of Intervention X in Cognitive Impairment in ELDERLY PATIENTS".

Many papers with a balanced sample size still perform a subgroup analysis based on an age cut-off. So it is as if you are targeting a specific subgroup.

If your sample size is large enough, you might try performing subgroup analysis based on different age cut-offs and examine your intervention efficacy and see what happens with increasing age. In that case, if you find that the effect size shows a pattern (increased / decrease) based on age subgroup, then your paper would be interesting actually.

You might try to visualize your data and get some descriptive statistics before running the regression.

Even if subgrouping doesn't yield interesting data, your paper might still be okay and you might mention the age as a limitation.

Hope that helps.

Thanks!

I think one cannot advise to include age or not into the regression without further considerations:

1) Is your intervention randomly assigned and a true experiment? If 'yes' then than age should not be correlated with your intervention, but only with the outcome/impairment. In this case you do not need to adjust for age, if you are interested in the total effect of intervention (see picture attached "no_age_bias"). If age is not correlated with intervention, but it is with the outcome, you MAY use it as covariable to increase power to detect the intervention effect, but the size of the total effect should not be biased in both cases.

2) Age does not only affect the outcome, but also the intervention (see picture "age_bias") then the total intervention effect will be biased and you need to adjust for age.

Of course I agree with Bruce Weaver concerning the age variable itself, you should not dichotomize or categorize metric variables.

Dear Rainer Duesing Thanks for your explanation, the attached figures are very informative and helpful

Thanks for your interest

Dear Youssef Soliman Thanks for your answer it is very helpful. I agree with you that adjusting the research question will be the best way in that scenario.

what if the study I am conducting is a meta-analysis and all the included studies have elderly populations defined by 60+ years old. Does conducting regression analysis on age may result in vanishing the effects of age as a confounding variable?

This is an example:

Tooth loss and the risk of cognitive decline and dementia: A meta-analysis of cohort studies

I think here the sample is not balanced as you mentioned

what is your opinion if the applicability of regression analysis in this scenario

Mahmoud Tarek Hefnawy

Hi Mahmoud, if you are doing a meta-analysis and you plan to conduct a meta-regression, then again, I don't think that would resolve the age issue since all included patients are +60.

However, as I explained above, you might find an interesting trend, which is your effect size significantly changes with age (even if they are all old). This can lead to the conclusion that the older the age, the higher/lower your effect size. This would be solid conclusion and consistent with your hypothesis.

If it is not significant, that can be due to issues such as:

1. You are conducting a meta-analysis on cohort studies that are extremely heterogeneous. Meta-regression tends to be non-significant in the meta-analysis of cohort studies, even if there is an actual effect.

2. Beyond 60 years old, age is no longer a covariate. People have similar risks, regardless of their age after that age cut-off. And that would take us to the first point: that you change your title to "risk of X in elderly",

Instead of meta-regression, you might pool effect sizes (i.e., odds ratios/risk ratios) that have already been adjusted for age. I would say this is more reliable than conducting meta-regression based on age, but this will be true only if the primary studies have conducted this analysis. The interpretation would be similar to the above (look at points #1 and #2).

Feel free to DM me if you need any help. Thanks.

Youssef Soliman Thanks dear friend. I got your point and your explanations are very reasonable and informative. Thanks for your time

First let's take a look at the simple regression equation:

y = b + x1 + x2+.... +xi

if x1 is age, x2 is cognitive test score and x3 is sex etc... and let's assume an equation that looks like this:

y = 3 + 2*x1 + 5*x2 + 4*x3

if age is equals 60 in all patients in your sample then the equation for the first patient and the last patient in your sample will be like this:

first patient: y = 3 + 2*60 + 5*x2 + 4*x3

last patient: y = 3 + 2*60 + 5*x2 + 4*x3

which means basically the two equations are the same then we can remove x1 and add its weight to the intercept like this: 3 + 2*60 = 123

then the final equation must be like this:

y = 123 + 5*x2 + 4*x3

Eventually this means that age in this case is not a confounding factor because you already have stratified and selected a homogeneous subsample from the population regarding this factor (age)

Either adding it or removing it will not change the final equation for the model and it may add some bias and overfitting in your case so removing it is the best practice and you can confirm this if you are using linear regression using the adjusted R square comparison between the two models or using AIC or AUC or any other metric if you are using a different model

Best luck

Dear Colleagu, Ahmed Shaheen Thank you for this excellent, simple and comprehensive explanation of how it goes in Simple Regression analysis equation, and for simply explaining why age in this case is not considered a confounding variable and hence performing a regression analysis is useless.

I totally agree with you but let me explain more details,

This question is based on my reading a recent published article:

“Tooth loss and the risk of cognitive decline and dementia: A meta-analysis of cohort studies”

In which Li et al is trying to find the relationship between Cognitive decline and Tooth loss

One of the problems he faced is that the population of the included studies are old (60+) and age is a known risk factor for dementia, he made a regression analysis to limit the effects of age as confounding variable ( As mentioned in Methodology, Strength & Limitation sections )

So I wondered, Does he really limit the confounding risk of age by performing regression analysis in that case ?

According to my conclusion from you and my colleagues replies;

1) Age may not be a confounding variable in this case, because all the population included is old ( have the same risk ) but this doesn’t mean that age is not a confounding variable in cognitive decline in other population ( young - middle aged ) and this takes us to the next conclusion

2) Whether the regression analysis in this case is conclusive or not; it is better to adjust the research question to be (The relationship between cognitive decline and tooth extraction in “Elders“ )

3) If we need to get the real answer to the relationship between cognitive decline and tooth extraction regardless of age we should include a balanced samples from all ages groups and perform a Subgrouping analysis and regression analysis in a sample containing balanced population from all ages categories

4) The above study of Li et al contains one category of population (+60) most of them are from observational studies; cohorts and cross sectional studies ( non- balanced samples from a single category ), and hence regression-analysis on age is of less value.

Thanks again for your reply and let me know if you have further comments.

Yes of course, adjusting by age will remove the confounding factor of age. Actually, adjusting the model by a confounding factor is one way of two to remove its effect when checking the effect of another variable.

Look at this example:

if the equation of model with only cognitive score as x and the outcome as y is like this:

y = 1 + 5*x1

and equation of a model with only age:

y = 2 + 3*x2

Assuming that both variables have additive effect (which is may not be true)

then the final equation should be something like this:

2*y = 1 + 5*x1 + 2 + 3*x2 = 3 + 5*x1 + 3*x2

and it can be written like this: 2 * y/2 = (3 + 5*x1 + 3*x2)/2

y = 1.5 + 2.5* x1 + 1.5 * x2

And adding more and more variables to the model will definitely affect the coefficients

The other way is by stratification: you can just select homogeneous sub sample and fit a model and so on as I mentioned in the previous comment

There is another way "propensity score matching/ propensity weighted analysis" which is using the same model of the previous regression and adding weights to the patients which can be used in weighted analysis or scoring analysis ( but I don't encourage it in most cases it doesn't work unless you have a large sample )

This in general, but the question remains:

Is there results conclusive? Absolutely not, the only way that can eliminate the confounding factors is controlled randomized trials or a very big sample of the population like big clinical registries or census

In my opinion and from experience most studies group patients like this: ">18", "18-45", "46-65", "> 65"

In your case it deserves a good letter to the editor to criticize and obvious mistake and I would as the authors to send me their data to replicate their results.. there is a very big mistake if they did so.

>> Tooth loss and age are correlated variables and can't be included in the same model as they will produce a collinearity problem, it must do so.

Thanks again dear colleague Ahmed Shaheen for your clear and comprehensive explanations, currently I am preparing a manuscript discussing the gaps and the recommendations in this area and I am planning to cover this point ISA. Your efforts and opinions are highly appreciated, thank you !