Analysis options

The following options are available for the linear model in QuBAS:

Transformation of the dose

The estimation of the relative potency in the linear model assumes the dose will be analysed on a log scale. If the data for dose levels are not already presented on the log scale, the following log scale transformations are available:

log base 2
log base e
log base 10

Transformation of the response

A log transformation of the response can often result in more stable variance across the range of dose levels in the assay. The response can be transformed as follows:

log base 2
log base e
log base 10
square root
square

It is also possible to apply a linear transformation to the response. This allows an offset to be added to the recorded dose, and a constant multiplier to be applied.

Weighting of the response

Another approach to achieving stable response variance across the range of dose levels in the assay is to apply weights to the responses which vary across the dose groups. When the variance at a mean response value of Y is A * Y^B, the appropriate weighting is:

Weight =

QuBAS allows the user to select the values of A and B.

For example, if the variance is proportional to the mean response value, then A = 1 and B = 1 and the weighting is 1/response.

Outlier identification and removal

QuBAS allows for examination of the data for outliers, and the option to exclude the outliers. There are two options for the identification

Grubb’s test: significance level fixed at p = 0.05

Ref: Grubbs, Frank E. (1950). "Sample criteria for testing outlying observations". Annals of Mathematical Statistics. 21 (1): 27–58.

Studentised residuals: outlier if > 3

Allen J. Pope (1976), "The statistics of residuals and the detection of outliers", U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Ocean Survey, Geodetic Research and Development Laboratory, 136 pages

Method for ratios

There are two generally used methods for calculating confidence limits for ratio values.

Delta Method: based on a truncated Taylor series expansion (generally applicable to any function of random variables).

Fieller Method: developed specifically for ratios of random variables.

Generally the methods give very similar results, but Fieller's can sometimes create nonsensical intervals (see https://en.wikipedia.org/wiki/Fieller%27s_theorem).

Variance estimate

There are several possible approaches to the estimation of the variance, σ², which is needed for the calculation of confidence intervals. The variance can be based on:

Residuals: the distances of each response from the fitted model (default)
Lack of fit: the distances of the mean response per dose group from the fitted model
Pure error: the distances of each response from the mean in its dose group

Note that for the estimation of the variance of the RP and parameters, the correct selection is ‘Residuals’. The other options are provided for comparability with other bioassay software.

All p values and confidence intervals are calculated using the same selected variance method.

Selecting the linear part of the dose response curve

If the data are expected to exhibit some curvature, perhaps for very high or low potency test samples, it may be required to exclude dose groups at one end of the dose range in order to achieve a linear dose-response. QuBAS allows for the sequential exclusion of dose groups, starting either at the top end or at the bottom end, whereby dose groups are excluded in turn until the test for linearity is passed. The user selects:

Low dose end
High dose end
Both dose ends
P value for linearity (default p = 0.05)