We also used the studentized version of the test, which is more robust to non-Gaussian variation (Koenker, 1981), and the results remained identical to at least two decimal places. Once the power transformation has been selected, the regression is not used further. For the 20 pools, the selected powers ranged from 0.23 to 0.31, mean 0.27. In other words, the optimal transformations were close to fourth root (power = 1/4). Fig. 1 Obeticholic Acid cost shows the Bland and Altman plots for the first haemagglutinin pool, and the second neuraminidase pool. These plots
also show i) the test wells positive on the T-SPOT criteria (see Introduction), and ii) the control wells which would have been positive on the same criteria, had the test and control status been reversed, hereafter referred to as pseudo-positive. For haemagglutinin, the T-SPOT-positive test wells greatly outnumber the pseudo-positive control wells (247:46), but this is not the case for neuraminidase (58:59). By quartile on the horizontal axis, the proportions positive on the T-SPOT criteria are: 0, 23, 26 and 32% for haemagglutinin and 0, 0, 6 and 16% for neuraminidase. To select a threshold
value for defining positive wells, we use the principle that test minus control values should, on average, be larger than control minus test. Otherwise, there Caspase inhibitor is no evidence of a ‘signal’ over the ‘noise’ of control variation, and any positivity threshold is dubious. To select the threshold we compare the empirical cumulative distribution functions (ECDFs) of i) test–control for those plates with test > control and ii) control–test for those with control > test. The ECDF of a sample is simply the proportion of the data points which lie at or below a given value. The difference between ECDFs can be used to discriminate between a mixture of two distributions. In particular, the value which maximizes the difference in ECDFs also maximizes the probability of correct classification (Stoller, 1954). Hence, for the current purpose, we choose the threshold to be the value which maximizes the difference between the above two ECDFs. Pools whose difference over
control exceeds this value are declared positive. In principle it is possible for this maximum difference in ECDFs to occur at more than Sirolimus manufacturer one value on the horizontal axis. Hence we define the threshold, more precisely, to be the lowest such value on the horizontal axis. This is shown in Fig. 2 for the two selected pools. Greater data values shift the ECDF to the right, making it lower at any given point on the horizontal axis. For haemagglutinin, the ECDFs of test-minus-control and control-minus-test are much more widely separated than for neuraminidase. For haemagglutinin, the maximum difference in ECDFs is 0.22 and occurs at a transformed test-minus-control value of 1 (i.e. a value greater than 1 is considered positive).