Proper analysis of partially matched, randomized design I apologize that I can't be completely explicit because this is for review of an unpublished article.
The design involved a cluster randomized trial of a new procedure to monitor an illness.  Health care centers were randomly assigned to treatment or control.  They were also matched on two relevant conditions - but there could be many other relevant factors.  Then patients were followed.
For one continuous measure, the authors used a matched t-test.  For survival, they used Cox proportional hazards but stratified by site pair and fit a separate model for each site pair, with a constraint of equal coefficients but different baseline hazards.
This seems intuitively wrong to me; this doesn't really seem like proper matching for a paired t-test and I don't really see how they can do Cox PH regression that way.
But I'm not certain, so I wanted to get thoughts from experts.  
EDIT: The t-test was on an individual measure and the sites were randomized in pairs. 
 A: Regarding the Cox PH model portion of your question:
It seems entirely plausible that constraining coefficients to be equal across sites in their survival model may not be an accurate reflection of the data. At the very least, they should offer both theoretical and empirical support for making this, potentially non-trivial, modeling choice. Absent additional details about the data and model, my instincts would be to include the coefficients as random effects rather than constrain them to be equal. See this article for a more comprehensive discussion. 
*Edited to address t-test portion of question: 
The estimation of treatment effects in matched-pair randomized clusters has been a bit of a controversial topic. One option is to take something of a meta-analytic approach to the problem of integrating differences across study pairs. Though some have argued for a more sophisticated approach that involves calibrating differences within each pair based on covariates. My understanding is that the former approach is more commonly employed, but this remains an active area of research, if only among a few passionate statisticians. 
In any event, your instincts are right that they may need to consider a more sophisticated modeling approach than a simple paired-samples t-test. 
A: I would consider the t-test largely invalid, as it disregards clustering and matching features. I would recommend instead a GLM or a GEE analysis (I favor the latter). Both can be easily implemented in Stata or R (eg http://www.stata.com/features/generalized-estimating-equations/).
For the survival analysis, I would also consider the chosen approach incorrect or at best inefficient and requiring excessive assumptions. I would instead recommend a Cox proportional hazard analysis for survey data. This can also be easily implemented in Stata or R (eg http://www.stata.com/features/survey-methods/).
GLM, GEE and survey Cox models can all include several clustering features as moderators.
