Actually a confounder is something very specific, I would not say that "covariates are sometimes called confounders"... for the rest, I agree with Eric.

"Adjustement", for instance, is done when you put covariates in a regression model, or something like that. You are looking at the effect of something, corrected for the effect of something else: thus, you are taking into account the fact that two independent variables can contemporarily have independent effects on the same dependent variable. In this situation, you can also include confounders (but they should be handled with care...)

For subgroup analysis, I think you mean "stratification". It may be appropriate when effects are not independent: for example, in a regression, if you find a significant interaction term between X1 and X2 (let's say, for instance, "exposure" and "sex"), you have to stratify your analysis for sex, splitting your group in males and females, and then for sure you can compare the effect of exposure between the two groups.

Anyway, stratification isn't costless: each stratified analysis will have a relatively low statistical power, so if you're planning to stratify an analysis this will impact on the needed sample size. In fact, if it's not really necessary to split your sample in separate groups, I would avoid it.

Covariates are sometimes also call confounders - these are variables that are related to both the dependent and independent variable but are not in the causal pathway. E.g. you control or adjust for variables such as age, gender, race in most adjusted logistic or linear regression models.

Subgroup analysis is when you split or divide participants/patients/respondents data into subgroups, often so as to make comparisons between them. E.g. you can perform an analysis for say males and then females and you can compare the results among the 2 groups. In this case, males is one subgroup and females are the other subgroup.

I hope this helps, let us know if you need more explanation.

Actually a confounder is something very specific, I would not say that "covariates are sometimes called confounders"... for the rest, I agree with Eric.

"Adjustement", for instance, is done when you put covariates in a regression model, or something like that. You are looking at the effect of something, corrected for the effect of something else: thus, you are taking into account the fact that two independent variables can contemporarily have independent effects on the same dependent variable. In this situation, you can also include confounders (but they should be handled with care...)

For subgroup analysis, I think you mean "stratification". It may be appropriate when effects are not independent: for example, in a regression, if you find a significant interaction term between X1 and X2 (let's say, for instance, "exposure" and "sex"), you have to stratify your analysis for sex, splitting your group in males and females, and then for sure you can compare the effect of exposure between the two groups.

Anyway, stratification isn't costless: each stratified analysis will have a relatively low statistical power, so if you're planning to stratify an analysis this will impact on the needed sample size. In fact, if it's not really necessary to split your sample in separate groups, I would avoid it.

Thank you all for your comments.

Would it be correct to affirm that, in Covariate adjustment, you're aiming to achieve the most appropriate p-value for the treatment difference and to improve the precision of the estimated treatment difference, thus increasing the statistical power of the trial? On other words, when you are performing covariate adjustment, you are not interested in learning how groups respond to treatments, only to increase efficiency.

You NEVER want to "achieve a p-value". P-value is just a measure of how likely an effect is a random phenomenon. What you want to adjust is the estimation of the effect.

Marco Gnesi, I believe you got it wrong. 

It was said "achieve the most appropriate p-value" and "to improve the precision of the estimated treatment difference". 

The p-value represents the probability that the observed outcome was the result of chance. If you can find a more precisely p-value, why not do it?

I agree that the most important is "to improve the precision of the estimated treatment difference", as I said before.

However, other benefits of adjustment include protection against chance imbalances in important baseline covariates, and maintaining correct type I error rates when the covariates have been used in the randomization process.

 1- Kahan et al. The risks and rewards of covariate adjustment in randomized trials: an assessment of 12 outcomes from 8 studies. Trials. 2014; 15: 139;

Sorry Allan, but you don't "achieve a p-value". Definitely not. You achieve an estimation, which can be more or less precise and whose accuracy can be improved. The p-value only tells you how likely the estimated value is different from something else by stochastic processes. You do not improve the p-value, you improve the estimation and this (obviously) may affect the p-value.

The difference seems so subtle, but actually there is an entire world of research metodology behind it, and being so p-value-centric is a huge bias that affects the results of scientific research (see, for instance, the paper by Regina Nuzzo published in 2015 on Nature, vol 506).