Cramér Ráo Lower Bounds - dwong263/MAGIQ GitHub Wiki

The lowest expected variation of an estimated model parameter is quantified using a value called the Cramér-Rao Lower Bound (CRLB). Put another way, the CRLB is the minimum expected error associated with modelling the data. CRLBs decrease in proportion with the level of noise, meaning that better SNR results in more precise estimates of model parameters and a lower variability of calculated metabolite concentrations. Increasing the spectroscopy voxel size and the number of averages will increase SNR and decrease measurement variability.

CRLBs are also affected by the linewidth of the metabolite peaks. Increased linewidths causes increased overlap of adjacent peaks of different metabolites (e.g. peaks of glutamate and glutamine) that results in greater uncertainty of estimated model parameters and increased variability in calculated metabolite concentrations. Since linewidths are driven by the quality of the shim, a high quality shim can ensure narrow linewidths and reduce metabolite measurement variability.

It is important to note that the CRLB is not the error of the measurement. Although it is often reported as a percentage, it is not the same as a percent error. That is:

Another important point to make is that the CRLB is often used as a metric to judge whether or not a certain dataset should be thrown out. For example, suppose we are interested in measuring glutamine concentrations. One dataset might have high glutamine SNR, and a CRLB of 10%. Another dataset might have a lower glutamine SNR, and a CRLB of 25%. We might be inclined to attribute the high CRLB of this dataset to high noise in the measurement, resulting in an "inaccurate" model fit. Thus, we could perhaps justify throwing out any datasets that have CRLB over 20%. However, it is also possible that the second dataset has a low glutamine SNR, because of a truly low glutamine concentration. Thus, by using CRLB as a "data-quality" metric, you run the risk of skewing your sample distribution and distorting your statistics. See this article for more details. A quote from the linked article's abstract drives home the point:

It is shown that such quality filtering with widely used threshold levels of 20% to 50% CRLB readily causes bias in the estimated mean concentrations of cohort data, leading to wrong or missed statistical findings—and if applied rigorously—to the failure of using MRS as a clinical instrument to diagnose disease characterized by low levels of metabolites. Instead, absolute CRLB in comparison to those of the normal group or CRLB in relation to normal metabolite levels may be more useful as quality criteria.