Statistics in Analytical Chemistry: Part 51–Internal Standards With Electrospray Mass Spectrometry

In modern scientific laboratories, the electrospray mass spectrometer is being used extensively. The instrument is highly specific and for many applications is quite sensitive. However, the electrospray process is subject to greater variability than, e.g., conductivity or flame-ionization measurements. The analyte’s signal may be suppressed (or enhanced) by other compounds in the matrix. Thus, internal standards (ISTDs) typically are added to samples and standards, in an attempt to improve precision via a scaling of the analyte’s response. In other words, for each analysis, a ratio (R) is calculated, where the response of the analyte itself is divided by the response of the ISTD; a calibration curve is generated by using R as the response. Ideally, an isotopically labeled version of the analyte is used as the ISTD, since the analyte and the ISTD should coelute and presumably behave similarly in the electrospray interface.

This installment will investigate, from a statistical standpoint, the above use of ISTDs. To accomplish this goal, the following questions will be addressed:

  1. Does the presence of the ISTD affect the signal of the analyte itself?
  2. Does the presence of the analyte affect the signal of the ISTD?
  3. Are any such effects proportional to concentration?
  4. How well does the use of an ISTD reduce the day-to-day noisiness in the data?
  5. How does the width of the prediction interval (at a chosen confidence level) compare between the scaled and unscaled data?

A specific analysis (i.e., the determination of perchlorate in deionized water) will illustrate a protocol for answering the above questions. U.S. EPA Method 332.0 was chosen, using triple-quadrupole (MS/MS) detection and a 100-μL sample loop.

Two sets of standards were prepared; one set contained the ISTD and the other did not. Each time a specific level was analyzed, the with-ISTD solution was injected first, followed immediately by the without-ISTD preparation. This arrangement minimized instrumental fluctuations between the two analyses. When used, the ISTD was an 18O-labeled perchlorate, added at a concentration of 5 μg/L; the analyte and the ISTD did coelute.

Calibration studies were performed. The concentration range used was 0.25 to 200 μg/L (blank; 0.25, 0.5, 1, 5, 10, 25, 50, 75, 100, 150, 200 μg/L). Five replicates of the range were run (in random order within each set) each day analyses were made; this design was executed on two separate days. Peak areas (PAs) were used as the raw instrumental responses. The chosen confidence level was 95%.

Question 1

Answering this (and only this) query involved the results not only from the with-ISTD analysis, but also from the without-ISTD injections. Each concentration’s raw data were compared (via the t-test) to see if there was a statistically significant difference between the two sets of PAs. In no case was there a difference, meaning that the presence of the ISTD did not affect the response of the analyte.

Questions 2 and 3

For each analysis day, the PAs of the ISTD were plotted vs the true concentration of the analyte itself. A straight line was regressed, using ordinary least squares (OLS) as the fitting technique. The p-value of the slope (which was negative) was the coefficient of interest and was significant (<0.0001) on both days. (Figure 1 shows both plots.) Thus, the PA of the ISTD decreased as the analyte’s concentration increased, meaning that the response of the ISTD did depend on the concentration of the analyte. Such a situation is undesirable, since the ISTD’s purpose is accounting only for fluctuations in instrumental conditions.

Figure 1 – For each analysis day, a plot of the response (PA) of the ISTD vs the true concentration. In each case, a straight line has been regressed, using ordinary least squares as the fitting technique. See text for further details.

Question 4

One way to answer this question is to compare the values of R among the various analysis sessions. In this study, there were two testing days. At each concentration, a t-test was conducted to detect any statistically significant differences between the two days’ ratios.

For seven of the 11 concentrations in this study, there was such a difference between the Rs on Day 1 vs Day 2. Thus, from a statistical perspective, noisiness was not totally eliminated. The important issue, though, is whether this result was practically important. Answering Question 5 can help address this inquiry.

Question 5

For each of the two days, two types of calibration curves were generated: 1) PA vs true concentration and 2) R vs true concentration. For all four curves, no model was found to be adequate; between a quadratic and a straight-line model, the better choice was the former for PA data and the latter for R results. Since bias remained with these fits, the prediction intervals had to be adjusted to account for the problem. (See Part 16, American Laboratory, May 2005 for details on the adjustment procedure.)

Figure 2 shows both types of curves; in each diagram, overlay plots have been constructed. To assess the precision available among the various curves, the user can compare the half-widths of the four prediction intervals (all of which have been adjusted for bias). Keep in mind that once these graphs have been drawn, the statistical analysis is complete (i.e., it has provided the information needed for making practical decisions). Only the user can decide whether the PA or the R approach delivers adequate precision, and if any improvement R may provide is worth the increased cost (both time and money) that using ISTDs entails.

Figure 2 – Plots of calibration curves and their associated prediction intervals where the responses were: 1) the ratio, R, and 2) the peak areas, PAs. For each type of response, the figure shows the overlay of Day 1 and Day 2 results. Legend for each graph: 1) red, green, blue = calibration line, upper prediction limit, lower prediction limit, respectively, for Day 1; 2) gold, aqua, purple = these same lines, respectively, for Day 2.

While the above results are applicable only to the perchlorate study that was conducted, the protocol outlined provides a path to assessing the need for and effectiveness of an ISTD. Such an approach should be utilized any time an electrospray method is being developed so that informed choices can be made.

Lynn Vanatta is an Analytical Chemist; e-mail: The author would like to thank Rosanne Slingsby of Dionex/Thermo Fisher for conducting all of the laboratory work needed to generate the data for this study. For more details on this research, see J. Chromatogr. Sci.2009, 47, 498–504; for information on a follow-up investigation of perchlorate in simulated drinking water, see J. Chromatogr. Sci.2011, 49, 570–2.