Positive discovery rate

The complementary rates are obtained from the opposite conditioning the fraction of model-predicted hits that are observed hits (A A) and the fraction of model-predicted inactives (I /) that are observed inactives. We call these the positive discovery rate and negative discovery rate . It is important to look at these conditional probabilities a very clear example is in the analysis of gene chip microarray data where the false discovery rate is 1 minus the positive discovery rate as defined above and in Chapter 6 an excellent discussion is given by Benjamini and Hochberg (1995). 

Figure 8. Sensitivity, specificity, and positive discovery rate as a function of decision threshold the two reference lines correspond to two decision thresholds. The rates are estimated from predictions made for molecules not in the training set of the model.

SAM involves a modified t-test and computes a False Discovery Rate (FDR, representing the expected incidence of false positives) for each chosen differential expression (significance) cut-off. 

FDR False discovery rate, the expected proportion of rejected null hypotheses that are false positives. 

Outputs Sample size FDR for different Sample size Sample size Expected discovery rate, trae positive rate, sample size... 

False discovery rate Proportion of false-positive results among all the reported positive results. This is usually estimated through permutations in practice. 

Familywise error rate The error rate for one or more false positives among all the tests conducted. Controlling a familywise error rate leads to more stringent control than the false discovery rate control at the same nominal level. 

In the framework of a generalized linear model, linear model decompositions (contrasts) are done in the usual traditional way. For example, if one compares controls against each of the test compounds, this is an a priori linear contrast and sufficient degrees of freedom exist to avoid a multiple comparisons adjustment. However, if one also compares each compound to every other one, or against a deet positive control, then one is making more comparisons than allowed for with the degrees of freedom (the multiple comparisons scenario) and an adjustment, either on the test statistic or the p value, is needed. A Bonferroni adjustment is an example of an adjustment on the p value better methods exist—a contemporary one is to adjust for the false discovery rate. 

As ADME/PK has become incorporated into drug discovery it has become necessary to reconsider the purpose of the studies. If the science is really going to reduce the attrition rate in development, then it is essential for the studies to allow predictions of the PK in man to be made. This means predicting the likely size and frequency of the dose. A review of the top 10 medicines of 1999 (Table 6.1) shows all of them to be once-a-day compounds. It is clear that to be best in class , and to be able to maintain that position as follow-up compounds come along, it seems probable that a compound will need to be suitable for once a day dosing. 

Polymerisations in hexane. The study of the reaction in hexane at low temperatures showed that it would not proceed in the absence of moisture [22, 28], and this was one of the observations which lead to the discovery of co-catalysis. The rates and DPs obtained when moist air was blown into a quiescent solution of isobutene and titanium tetrachloride in hexane were not very reproducible, and the reaction curves were S-shaped. Both the initial and maximum rates increased with increasing temperature [9], with ER = 8 1 kcal/mole. The DP increased with decreasing temperature [22], such that EDP = -2 0.5 kcal/mole. The relatively large, positive ER was taken to represent mainly E-, which seems reasonable since micro-crystalline ice must have been involved in some way in the initiation reaction. 

The mechanism of initiation of cationic polymerisations by metal halides was clarified and systematized to some extent by the discovery of the phenomenon of co-catalysis or co-initiation. But, whereas there was, by the mid-1960s, good evidence that at any rate in many systems the halides of boron, titanium, and tin required a co-initiator, the position with regard to the best-known and most popular initiator, and the one which was of greatest economic significance, aluminium chloride, remained obscure. Of the vast number of published experiments on the system, aluminium chloride + isobutylene, hardly any could provide evidence concerning the initiation reaction, because they were almost exclusively concerned with measurements of yields and degree of polymerisation (DP). 

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