Biomedical Engineering Reference
In-Depth Information
Quantifying Randomness
From the earlier discussion, it should be clear that randomness—which refers not to the data, but
how they are obtained—is inherent in every measuring device. In general, the lower the randomness,
the better. Randomness is commonly quantified in the equipment's published specifications
document, which characterizes the equipment's performance in terms of accuracy, resolution
(precision), repeatability, stability, and sensitivity.
Accuracy—the degree to which a data value being measured is correct—is usually expressed as plus
or minus a percentage of the reading, as "± (0.2%)". The accuracy of digital systems is further
defined in terms of the number of counts of the least significant digit, such as "± (0.2% + 1 count)".
Resolution, sometimes referred to as precision, is the ability of an instrument to resolve small
differences. In a digital system, resolution is often expressed in terms of the number of bits available
to represent a signal. For example, in a 4-bit digital device, there are 2
4
or 16 discrete steps.
Consider an analog-to-digital (A-to-D) converter, a device that converts continuously variable analog
signals, such as the intensity of fluorescence emitted by a spot in a microarray, to digital values. If a
4-bit A-to-D converter has full-scale capacity of 16 volts, then the resolution is one volt. Signals are
rounded to the nearest integer, so that 0.5, 1.2, and 3.6 volts are represented as 1, 1, and 4 volts,
respectively. In general, the higher the resolution, the greater the accuracy of a device.
Sensitivity—the ability of a device to detect low-level signals—is a function of the resolution and the
amount of noise in the system. For example, continuing with the example of the 4-bit A-to-D
converter with a 16-volt full-scale capacity, the maximum sensitivity would be 0.5 volts, assuming a
perfect, noiseless system. However, as noise is added to the system, the sensitivity decreases as a
function of the amplitude and time distribution of the noise. That is, the higher the signal-to-noise
ratio, the higher the effective sensitivity of the device.
Repeatability is the ability of an instrument or system to provide consistent results. For example, the
initial intensity of a spot's fluorescence, as measured with a photomultiplier tube, should ideally agree
with a subsequent measurement. Repeatability is related to stability, which is the ability of an
instrument or device to provide repeatable results over time, assuming certain environmental
conditions, such as ambient temperature, are maintained within a certain range and the process of
photo bleaching is consistent. Repeatability is also affected by any changes in the data source caused
by the measurement process.
An instrument may provide highly repeatable results, but the results may be inaccurate unless the
instrument is properly calibrated. All instruments are subject to changes in accuracy over time,
whether or not they are operating. For example, an ordinary mercury thermometer is subject to a
change in accuracy because of changes in the glass housing, which crystallizes and contracts over
several years. Accuracy specifications are therefore stated in terms of time, such as within one year
of calibration. The accuracy of a calibration standard limits the maximum accuracy of the equipment
being calibrated.
In assessing the capabilities of a microarray experiment system, one measure of overall system
performance is the dynamic range of the system—the ratio of the maximum signal level to the
minimum signal level that can be measured or represented. The dynamic range of a microarray
system, which is typically expressed in terms of orders of magnitude, is a function of the scanner
electronics, the chemical dynamic range of the chemicals used, and the biological dynamic range of
the system under investigation. All else being equal, a system with a greater dynamic range is
capable of greater precision and accuracy in quantifying the relative gene expression. Furthermore,
the dynamic range of the system is limited by the element in the signal chain with the smallest
dynamic range.
Although the biological dynamic range is usually an unchangeable parameter, there is some latitude
in selecting reagents with the greatest dynamic range and even more choice in the microarray
