Frontiers in Statistical Quality Control 5

Frontiers in Statistical Quality Control 7

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Building Intuition Dilip Chhajed. Lean For Dummies Natalie J. The Phoenix Project George Spafford. The Toyota Way Jeffrey K. Dr Deming Rafael Aguayo. Warehouse Management Gwynne Richards.

Hans-Joachim Lenz (Author of Frontiers in Statistical Quality Control 9)

Project Planning and Scheduling Gregory T. Operations Management Andrew Greasley. Essentials of Inventory Management Max Muller. Training Design Basics Saul Carliner.

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Design for Operational Excellence: Operations and Process Management Nigel Slack. Custom Nation Emily Flynn Vencat. Markets of One B. Pharmaceutical Microbiology Tim Sandle. Within the field of molecular pathology and molecular diagnostics, qualitative assays often suffer from a limited repertoire of methods for monitoring process performance over time. This is quite the opposite to high-throughput departments such as clinical biochemistry which run controls throughout the day and plot the performance of these controls on Levey-Jennings charts or an equivalent form of monitoring chart in a process termed statistical process control SPC Levey and Jennings, The characteristics of clinical biochemistry that render it suitable for SPC are twofold; firstly, the laboratories have the throughput to generate statistically relevant data and can add run controls to routine work; secondly, clinical biochemistry tends to generate quantitative data which lends itself to plotting on control charts.

With the emergence of targeted therapies in hematological malignancy and solid tumors, many molecular assays are now processed in numbers sufficient to permit some form of SPC and this has been achieved for quantitative molecular assays Liang et al. However, the literature regarding SPC or an equivalent technique for qualitative molecular diagnostic assays is scant and those wishing to apply statistically valid monitoring to qualitative assays have a limited range of techniques to choose from.

While some articles in the field of quality control do make reference to qualitative observations Spanos and Chen, these approaches may be difficult to translate directly to the clinical laboratory. A relatively simple approach that may be applied to any laboratory with sufficient throughput is the monitoring of mutation frequencies in tested samples.

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By combining point estimates of mutation frequency with statistically informative confidence intervals the laboratory can monitor process variations and performance relative to a known reference point over time. In this article we assess the applicability of SPC to qualitative molecular pathology assays. It is our contention that a confidence interval of the observed mutation frequency may be compared to an expected value to give a reliable indicator of process performance.

If a laboratory finds the mutation frequency confidence interval to lie outside of an expected value or range of values, this would trigger further investigative action and troubleshooting and may permit earlier detection of assay or protocol deviations that may be detrimental to patient care. By using statistical models we highlight the strengths and weaknesses of this approach and use modeled data to demonstrate how this may be applied in a routine laboratory. Significantly, we are also able to calculate minimum sample numbers necessary to apply this technique in a given clinical scenario with clear implications for laboratories seeking to implement high standards of process control.

The approach taken for this analysis used a point estimate of mutation frequency and a confidence interval to guide the interpretation of the point frequency estimate relative to a prior frequency estimate. Based on this approach, should the confidence limits of the point frequency estimate fail to overlap the prior frequency estimate, this would act as a trigger for further investigative action. The Clopper—Pearson confidence interval estimate is used to calculate binomial confidence intervals using the cumulative probabilities of the binomial distribution.

The calculation is written in Equation 1 below. Sample numbers from 10 to per annum were used for model building with a statistical power of 0. Matlab scripts used for all calculations have been made available in the supplementary data file. Calculations were performed using the parameters specified above for all combinations of the deviation size and prior frequency estimates. The relationship between deviation size and mutation frequency was plotted using a series of subplots Figure 1 , and minimum recommended sample numbers were summarized using a quick reference table Table 1.

Statistical process control sample number requirements. This figure illustrates the non-linear relationship between sample number and applicability of the calculations to laboratory monitoring.

The figure highlights the clear requirement for greater sample numbers to detect deviations where the prior frequency estimate is lower or the required detection level is lower. Estimates of sample numbers required to detect deviations from an expected cut-off. A uniform sampling interval was determined assuming equal sample distribution throughout a year and this was applied in a non-overlapping schema to weeks of modeled data. Detection of mutation frequency deviations using frequency plots.

The modeled data used as described in the materials and methods is highlighted in the color bands along the lower boundary of each plot. Analysis of the modeled data for sample throughput, proportional deviation from the expected mutation frequency and number of samples per annum shows that as sample numbers increase the time taken to identify a deviation of a particular magnitude decreases, often markedly Figure 1. Moving in increments of samples, the most pronounced decrease in time is noted at the lower end of the scale i.

The size of the deviation too has a definite effect on the ability to detect the deviation and the time taken to do so. For example, by comparing the subplots of Figure 1 , it is evident that the identification of a deviation of 10 percent would require much greater sample numbers than one would require to detect a deviation of 40 percent.

This observation holds true for all prior frequency estimates tested with this model. In order to forecast the required number of samples necessary to allow a laboratory to detect a deviation of a given percentage from an expected mutation frequency also referred to as a prior frequency estimate , a quick reference chart was generated. This chart compares the expected frequency of a mutation with a percentage deviation cut-off to suggest the number of samples that might be required to detect this deviation with a power of 0.

It is also possible to use this table to calculate the number of individuals likely to be unnecessarily affected by under or over treatment as a result of suboptimal service capacity. In the case of an increase from 35 to The laboratory would be able to detect a similar level of under treatment if the mutation detection frequency decreased.

Laboratory B examines samples per annum. The applicability of point frequency estimates with control data to monitoring and detection of laboratory processes is illustrated in Figure 2. The modeled data used for this chart show the type of variability one might expect from a process that is in control i.

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The utility of SPC is hard to deny, it permits a broad overview of an entire analytical process. In the context of molecular pathology and molecular oncology this means that assay deviations leading to over or under treatment of patients can be identified and any process faults may be corrected within a clinically relevant time frame.

As a quality control technique SPC is in common use in many laboratories but a lack of suitable methods to apply it to qualitative data have meant that it is more often applied to quantitative methods. Using a characteristic such as a point estimate of the mutation frequency for comparison to an expected frequency gives an estimate of the performance of a clinical laboratory testing process.

However, calculations such as this are fraught with scope for mis-interpretation or inappropriate usage. For example, should one calculate such a figure with too few samples it would not be reflective of the true frequency in the population being tested. Similarly, a failure to calculate confidence intervals would give the observant little room to qualify a deviation from normal as being clinically or analytically relevant.

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The opposite effect might also be observed if one used too many samples for the calculation and thus delayed an opportunity to detect a process deviation. By pre-defining an optimal sample number and prior frequency estimate for a given mutation detection assay, it is possible to use mutation frequency calculations coupled with confidence interval estimates to assess whether a process is performing as expected.

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