Log-odds

Web search sites allow the user to choose among several. Their easy interchangeability means that substitution and gap score combinations are readily compared in performance. Over the past several years, results of numerous comprehensive tests have appeared. Some of these evaluation studies have confined themselves to log-odds matrices made from alignment data, whereas others have included matrices that are based on amino acid properties. 

Johnson and Overington (1993) measured alignment accuracy and found good performance for structure-based, BLOSUM, and Gonnet matrices. As in other studies, log-odds matrices performed the best. 

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. 

Pain relief is a categorical variable that can take a value of 0 (no pain relief), 1 (a little pain relief), 2 (some pain relief), 3 (a lot of pain relief), or 4 (complete pain relief). The log-odds that Y, is greater than or equal to the score m (m = 1,..., 4) is given by... 

The GOR method phrases a very similar approach in an information theoretic framework, computing not only preferences for individual residues but aiming at the delineation of preferences for short stretches of amino acids. Since the given data set will generally not supply sufficient data for estimation of the log-odds for every k-tuple certain approximations have to made [23]. At the same time it has become clear that even this approach is unlikely to give perfect predictions because, in known crystal structures, one and the same 5-mer of residues will be found in different secondary structures [24]. Other approaches like the one due to Solovyev and Salamov [25] assemble different characteristics for a short stretch (singlet and doublet secondary structure preferences, hydrophobic moment) of amino acids and apply linear discriminant analysis in order to derive a predictor for the secondary structure of a region. 

A log-odds score for a pairing of residue types a and b is derived ... 

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... 

The PAM250 scoring matrix in the log-odds form [Dayhoff 1978], Each element is given by S,j — 10(/og2o My/fi), where M j is the appropriate element of the mutation probability matrix (Appendix 10.4) and f is the frequency cf occurrence of amino acid i (i e the probability that i will occur in a sequence by chance). 

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. 

A further problem has to do with the nature of clinical trials. As has been explained elsewhere, these are comparative rather than representative and one of the tasks for analysis is to find a scale of measurement upon which the treatment effect is additive. If this can be found for adverse events, then even for quite different populations it may be applicable. Unfortunately, the sort of measure which, a priori at least is most likely to be additive is the log-odds scale and this is not easy for the amateur to interpret. The question then arises whether, in order to increase interpretability, the raw rates should be used, although possibly not applicable where we wish to apply them. This issue was also discussed in Chapter 8. 

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... 

LOD score For log odds, a statistical estimate of the linkage between two loci on the same chromosome. 

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