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That present BDI score is 12 and that for Mr Adams is buy 30gm v-gel with mastercard, the ith patient provides a value for either is 15. Mr Smith provides ask what would have been the effect of therapy Y (t 1) but not Yc(1), Mrs Jones provides Yc(2) offered if they had actually received it? Expressed the effects of different types of psychotherapy, mathematically: or to the comparison of a speciﬁc type of psy- chotherapy with, for example, a psychopharma- E[Y (i)t ] = E[Y (i)t |T = t] = E[Y (i)t |T = c] cological intervention such as a tricyclic antide- (3) pressant. If we are able to do this t c large population of eligible patients – the target then we have replaced an impossible-to-observe population about which we wish to draw causal causal effect on an individual patient with a inferences about the value of psychotherapy possible-to-estimate average of the causal effects or counselling. This is the ACE = E[Y (i)t ] − E[Yc(i)] (2) familiar problem of confounding. The difference in observed outcomes may arise from the fact that This simple formula shows us that information the patients with the best (or worst) prognosis, on different patients can be used to estimate on average, might be the ones that opt for E[Y (i)t ]andE[Yc(i)] separately and the differ- therapy. The observed outcomes in this situation ence between these two expectations (averages) might tell us something about the selection can be used to estimate the average of the dif- mechanism (treatment choice) but are not very ferences (i. All that we need is to be sure experimental design, might lead us to match that the observed averages for the treated (ther- or stratify the patients prior to estimation of apy) and untreated (control) patients are unbiased the treatment effects. But we cannot guarantee 300 TEXTBOOK OF CLINICAL TRIALS that we are aware of all possible confounders. It is a valid estimator of a ourselves that we have not missed an important causal effect but many investigators (particularly confounder, the only way we can ensure that we psychotherapists! Random allocation of the causal effect of receiving therapy the ensures that both E[Y (i)t ] = E[Y (i)t |T = t] and ITT estimate is likely to be biased. However, E[Yc(i)] = E[Yc(i)|T = c] providing that t and many other investigators might be convinced caretheallocated treatments (not, necessarily, that this is the estimator of real interest – it those actually received). Randomisation is the measures the effect of a decision to treat in only sure way of coping with all confounders, a given way and is therefore vitally important and it copes with them irrespective of whether for people involved in making these decisions we are aware of them or not. Our conclusion is that if we wish Drug Administration (FDA) and the UK National to be sure that we are estimating the desired ACE Institute for Clinical Excellence (NICE).
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