Log-odds ratio

If the treatment effect in each of the individual trials is the difference in the mean responses, then d represents the overall, adjusted mean difference. If the treatment effect in the individual trials is the log odds ratio, then d is the overall, adjusted log odds ratio and so on. In the case of overall estimates on the log scale we generally anti-log this final result to give us a measure back on the original scale, for example as an odds ratio. This is similar to the approach we saw in Section 4.4 when we looked at calculating a confidence interval for an odds ratio. 

Equation (5.22) is referred to as the log-odds ratio or logit of the event occurring. The term in the brackets of Eq. (5.22) is referred to as the odds ratio. In the case of x itself being a binary variable, the log-odds ratio has a simple interpretation it approximates how much more likely the event Y occurs in subjects with x = 1 than... 

It would be quite wrong in my opinion to conclude that that what therefore needs to be done is to abandon the usual additive scales of analysis, such as log-odds ratios and log-hazard ratios, in favour of risk differences and differences in median survival. There is every reason to suppose that these will not transfer well from one trial to another and hence, of course, from clinical trial to clinical practice. 

Log-odds ratio. The logarithm of the odds ratio. A transformation very frequently used for modelling binary data. See logistic regression. 

Under Hanemann s (1984, 1989) well known linkage between random utility maximization and the functional form of econometric models with a binary dependent variable, a logit model has been estimated on SB-CVM data. It explains the log-odds ratio as a linear function of several household attributes (including income level as a covariate) and of the percentage premium price proposed (Franses and Paap, 2001 Gourieroux, 2000). Median WTP and truncated mean WTPs (both only at zero and between zero and 100%) have been calculated according to Hanemann and Kanninen... 

Defining as the log odds ratio between treatment k and placebo, with di = 0, the mean of can be replaced by - d. That is, we can assume an independent normal specification for the such as... 

In this model, we assume homogeneous variance across all k treatments. For a three-arm trial, having two 5,2, we would further need to consider correlation between them. In this case, we would assume the 8 vector follows a mulfivari-ate normal distribution, typically with common correlation of 0.5 between two log odds ratios (a consequence of the usual assumption of consistency between direct and indirect evidence), as suggested by Lu and Ades (2006). 

RE Bayesl and RE Bayes2 are examples of contrast-based models, which use log odds ratio for inference on relative treatment effects. In this section, we introduce an arm-based alternative model (denoted by RE AB), which seeks to capture absolute effects (say, log odds) in its model parameters (Dias et al., 2011a Salanti et al., 2008). The arm-based model can be written by respecifying model (12.2) as... 

We calculate the empirical frequency that Drug C is selected as least safe based on Safel probabilities or log odds ratios for a Bayesian or frequentist model, respectively, over 1000 simulations. We call this the empirical probability of correct decision (i.e., that Drug C is the worst drug). Tables 12.2 and 12.3 present the probability of correct decision with various parameter... 

The above represents the log odds ratio of the posterior probability given the data M. To implement this hierarchical Bayes procedure, calculation of the posterior probability is... 

One more example of a "modified" t-statistic is derived from a Bayesian approach, which has become popular in statistics. For example, the B-statistic, the log odd ratio of the... 

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