Repeated measure design with missing values I have data from a repeated measure design, as follow:

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*Each subject is measured under 10 differente experimental conditions

*For each experimental conditions, 2 physiological caractéristics are measured.
==> I want to compare the means/see if there is any effects on the experimental condition of both physiological measurements.

If no data is missing, which means 2 * 10 measures are available for each subject, then a tow-way repeated measure ANOVA is applicable to evaluate if there is any effects (or interaction effect).
But in my case, there is missing data. Some subjects were not measured under all 10 conditions and these conditions are always the same. Actually, 65% were measured under all experimental conditions, and 35% were measured under the first 5 experimental conditions. When a subject underwent a condition, the 2 phsyiological measurements were always measured.
repeated measure ANOVA would still be applicable, but it would simply delete all incomplete cases (i.e 35% of the subjects), which would results in possibly huge bias. It seems from here that a linear mixed model could be an option. So my questions are:

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*Is a linear mixed model really a good choice in my case ?

*What about post-hoc analysis / paire-wise comparisons ? when no data is missing, paired t-test is applicable, but does linear mixed model can still hold here or is there any other options ?

EDIT: data are missing because the next 5 experimental conditions were added during the study. So the first 35% of subjects were just not aware of the 5 extra conditions. Also, we can fairly assume that the order of arrival of the subjects has no effect on the measurements, as each subjects are independent.

I linear mixed model (e.g. mixed effects model for repeated measures aka "MMRM" as available via e.g. the mmrm R package or the latest version of the brms R package, or PROC MIXED in SAS with the REPEATED option etc. or similar) would implicitly impute the data. I.e. you fit the model without doing anything about the missing data and it behaves as if you had imputed the data under a multiple imputation that assumes missing at random.
As you would expect from the preceding sentence, if you make sure to match the mixed model and the multiple imputation (MI) up, doing MI with a large number of imputations such as, say, 2500 (followed by a simple analysis of each of the 2500 datasets as if there were no missing data and combining estimates +- SE about the parameter using Rubin's rule to get a single overall results) should give essentially identical results (there's again, a lot of software that would let you implement that kind of analysis, e.g. PROC MI in SAS, the Amelia R package which is a bit more flexible in terms of being able to deal with continuous, categorical and ordinal data etc.). The advantage with MI is that it tends to be a little easier to be very flexible in your imputation model, while making a mixed model very flexible can sometimes be a bit harder (and if you don't, you end up making assumptions you may not have wanted to make).
With either approach, the main question is whether the assumptions make sense for your case (and some implementation details such as how flexible a correlation structure you want to allow for). Problematic scenarios include:

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*When missingness occurs due to something you know (or don't know) about and it correlates with outcomes, but you don't include it in the model (e.g. younger people are more likely to drop out and tend to have worse scores, but you didn't even record age).

*Another version of the previous point is where subjects learn what the next experimental condition is going to be and decide to drop out, because e.g. they worry they'll perform badly under it, they are scare of it or something like that. Unless you somehow appropriately model this, your imputation wouldn't capture that they likely would have done badly.

*Either of the points above can (if you collected the right data) usually be addressed by jointly modeling multiple things or including all these other things in your multiple imputation model.

*I think this doesn't apply here, but in clinical trials sometimes people leave a trial (and as a result also stop their treatment). If you want to impute what really happened to them, you can't do it by modeling the values from other that are still on the treatment, because you would be imputing the data as if they had remained on treatment (on the other hand, the strategy makes sense, if you want to know what would have happened, if they had stayed on treatment).

In terms of modeling assumptions, to keep things very flexible, you may want to ensure to use an unstructured covariance matrix across all the observations for a subject, ensure to include main effects for each condition, what physiological caracteristic is being measured and relevant subject characteristics, as well  as interaction interaction terms between these. You'd also want to allow for different variances for the physiologic characteristics (and possibly even for these to depend on the other main effects). These choices would depend on your understanding of the situation.
