Immunological dosages: modeling and statistical inference

This dossier presents statistical methods for analyzing immunoassay data. These are essentially methods of estimation and statistical inference for non-linear regression models.

Two typical examples serve as a basis for methodological developments. The aim of the first example is to determine the interferon gamma content of a plasma sample by estimating a calibration curve. The second example compares antibody levels in two bovine plasma samples, based on response curves obtained for each sample. The questions posed by the experimenter are essentially the following:

• how to estimate a calibration curve?

• how to estimate the variability of a dose estimate?

• how can you compare the response curves of two samples that have been diluted several times?

• how can we make the most of the observations available to us?

The relevant methods are described intuitively and implemented on examples. For example, estimating the precision of estimators is equivalent to calculating confidence intervals or performing hypothesis tests. Classical methods such as the Wald test or the likelihood ratio test are presented, along with methods based on resampling procedures such as bootstrapping. The last paragraph deals in more detail with the calibration problem: how can we take into account the different sources of variability when calculating a calibration interval? In fact, there are two sources of variability:

• that due to the estimation of the calibration curve ;

• variability in response observation.

Another important question is how to take advantage of observations made in several dilutions of a sample to best estimate the concentration of products contained in that sample?