Here are some comments, which don’t apply to all but may be of interest and usefulness to 
others who may have avoided them by accident. 
 

(1) If you have strong evidence of an interaction between two factors but the 
coefficients for the main effects of those factors are small in comparison with 
their standard errors (so the partial z-test for that coefficient produces an 
insignificant result) then it is false/incorrect/a mistake/misguided/an 
error/untrue/a blunder/just plain WRONG to say that the factor has ‘no effect’ 
or that there is no evidence that the factor as an effect. There most certainly 
is evidence that it has an effect and moreover that the nature of that effect 
depends upon the value of the other factor with which it interacts. Most 
people got this wrong, despite the warning in the notes and the repeated 
warnings in lectures.

(2) If you have an interaction in a model then it is essential to retain 
the main effects as well, even if the coefficients for these are small by 
comparison with their standard errors. You can (and indeed actually definitely 
will) go seriously wrong in interpreting the results from a model with only 
interactions and no main effects.

(3) Interaction itself does not ‘have an effect’ and certainly you cannot 
interpret the sign of the coefficient of an interaction term in the same 
way as you can of a main effect in the absence of any interaction. It 
doesn’t make sense to say ‘as the interaction increases …’. More generally, 
I think that really the only things that can ‘have an effect’ are things that 
are administered in a general sense. So treatments have an effect; stage of 
disease does not ‘have an effect’ in the same way. If the coefficient for ‘stage’ 
is significantly large then it indicates that there is a difference between the 
stages, a significantly large coefficient for interaction means that the effect 
of treatment is different for different stages (or equivalently that the 
difference between stages depends on the treatment group). All of this 
applies to any form of regression model and I am sure it is covered in 
the Linear Models course.

(4) When there is an interaction term there is no substitute for considering each 
combination separately; you cannot make global statements about the effect of a 
factor if it is involved in an interaction with some other covariate. This 
means that it is sensible to calculate (in this case) the hazard ratios of 
the five combinations relative to the sixth and provide confidence intervals 
for these and then comment upon them. Not many people did and of those

(5) a few should note that e.g. s.e.(beta1+2beta3)=sqrt{[s.e.(beta1)]**2+4[s.e.(beta3)] **2}, 
many omitted the 4. 

(6) A few people noted that the factor stage was essentially a discrete factor and so 
ought to be coded with two binary dummy variables. However, it is actually an ordered 
categorical variable and coding as two dummies looses this --- one way of handling this 
is to give some numeric score to the categories (in this case 0, 1 and 2) and there are 
ways of determining a ‘natural’ set of values. For stages of cancer it is not uncommon 
to see them coded in this simple [simplistic] way.

(7) In question 2 many people did not focus on the question asked which was whether 
there was a difference in survival prospects between the two treatment groups, 
making any due allowance for covariates. Instead, many people answered unasked 
questions on whether the Gleason index/tumour size/... ‘had an effect’ [see 
comment above also]. If you do not answer the question posed then your client 
will not pay your invoice at the end of the day, nor will they give you any 
marks in an examination. If you answer questions that you think they should 
have asked but didn’t then they won’t pay you any extra unless you had the 
foresight to insert this into the original contract (or protocol), nor will 
they give you extra marks. My two comments are that you should answer the 
question asked and not any other and that you need to be cautious about 
claiming evidence of relevance of covariates, especially when not specifically 
asked about those factors. The first comment has wide applicability. We have 
now covered the multiplicity section but you hadn’t before then.

(8) A few people approached question 2 as a model building exercise and started 
worrying about interactions. I hadn’t intended this question to be about interactions 
(that was Q1) and as well as noting that this will not answer the question posed I 
have reservations about the principle of this in general. If working on a project 
with a client I myself would not consider investigating interactions between 
covariates (e.g. between Gleason index and serum level) unless specifically 
warned that these were likely to be relevant by the client, the rationale 
being that the client has selected which covariates are worth considering 
from perhaps a much larger set of those available --- I might prompt the 
client to consider the possibility of interactions as well as othe covariates 
which they hadn't considered (e.g. time of day of teh reading of blood pressure) 
but once the contract has been drawn up (or the exam question printed) I wouldn’t 
consider them. I might investigate interactions between the treatment and the 
covariates since that might be outside the client’s experience (especially 
in cases where there is a trial of a new treatment). I myself have not 
investigated this data set particularly, but somebody did produce an analysis 
that shewed strong evidence of an interaction between serum and treatment, 
which is interesting (especially noting that when fitted as a main effect alone 
there is negligible evidence of any dependence ----- this illustrates the hazards 
of dropping such factors from consideration, I think somebody else looked at 
interactions between treatment and covariates but had already discarded serum). 
Incidentally, if working on a model building exercise it is dangerous to drop 
more than one variable at a time on the grounds that they all have large p-values 
--- the p-value only reflects the partial z-test of the corresponding coefficient 
presuming all other terms are included. 

(9) Some people did not interpret 'effect of treatment making allowance for 
other covariates' as calling for a regression analysis and looking at the 
partial z-test (t-test) for the treatment factor ---- I am sure this has 
been covered in linear models or regression modelling courses and Survival Regression 
is just another form of regression model appropriate when the response is a survival 
time rather than a normally distributed variate. Survival models also easily handle 
censored data but of course any form of statistical model, including Normal theory 
linear models, can easily handle censored data (it just arises more commonly in 
Survival contexts). 

(10) A couple of people tested statistically for a difference in means of the 
various covariates between treatment groups. This is illogical since it is a 
randomized trial. Therefore if you obtain a 'significant result' and declare 
there to be a difference in population means you KNOW you are committing a 
Type I error --- i.e. you KNOW you have a false positive. This contrasts 
with the situation in multiple testing, e.g. the Zodiac example --- there 
declaring a difference ont he pasis of a nominal p-value of 0.016 when you 
have done 12 tests makes you only SUSPECT a false positive. Even if you find 
no apparent difference between the groups on the copvariates it still is sensible 
to include those terms in a regressiona analysis. Sadly you will find 
some non-authoratative books which recommend including covariates only 
if there appear to be 'significant differences between them'. 
These texts are incorrect.


(11) Some people did not offer any more interpretation than ‘so this covariate is 
significant and so must be included in the model’ or ‘this term is insignificant’ 
--- a LARGE amount of credit is lost if you do not turn this into a real world 
interpretation and say something like ‘the data do not provide evidence that 
there are differences in survival prospects for those born under the sign of 
Aries compared with those under Taurus. A 95% confidence interval for the hazard 
ratio is (0.32, 1.15)’. This is especially true in formal examinations and in 
whether your client decides to pay your invoice.