Statistical sampling is crucial for biopharmaceutical companies to ensure product quality, maintain regulatory compliance, and optimize manufacturing processes. But many organizations still rely on outdated methods that may not be suitable for the unique challenges of small lot sizes in biopharmaceutical production.
The FDA Group's Nick Capman spoke with Gary Ritchie about rethinking statistical sampling approaches and embracing more rigorous methods that can significantly improve cost efficiency, risk management, and regulatory compliance.
Gary Ritchie is a veteran pharmaceutical scientist with nearly 30 years of experience in the life sciences industry. He specializes in statistical sampling, analytical chemistry, and pharmaceutical waters. Gary's expertise spans various areas, including process analytics, quality control, and regulatory affairs. Gary’s held key positions at the United States Pharmacopeia, where he served for five years on expert committees for waters, statistics, and general chapters. His experience as a liaison allowed him to work closely with the FDA, industry leaders, and academia.
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Summary, Key Points, and Practical Takeaways
This interview has been edited for clarity and length.
Nick Capman: What are we going to be talking about today?
Gary Ritchie: We're going to delve into the idea of statistical thinking and acceptance sampling for biopharmaceutical raw materials. I've been thinking about the state of sampling today — from receiving shipments to sampling in the lab. In process analytics, one standard that's been relied upon for some time is the √N + 1 approach. We'll discuss the best practices used today and where I think they should rely on more formalized statistical testing.
What makes a statistical sampling plan valid?
First, let's talk about what √N + 1 is. It's generally been used for large lot sizes, with a history from the United States Department of Agriculture for sampling fields - very large populations with low-cost, often destructive testing. But in biopharmaceuticals, the requirements in 21 CFR 820.250 for statistical sampling are not met with this approach. That's why we need to discuss it in detail and explore better approaches.
A valid statistical sample plan needs several elements. First, any draw from a population must be representative of the whole lot. As population size increases, the frequency of getting a truly representative sample decreases. To address this, we use the ANSI Z1.4 attribute sampling method. This accounts for lot size includes an inspection level to manage the risk of drawing the wrong sample and incorporates an acceptance quality level (AQL). These three factors, plus representativity, are what make a valid sample plan.
Why is the square root of N+1 plus one rule not useful for small lot sizes, and what is a small lot size, statistically?
In biopharmaceuticals, we typically deal with small lot sizes - usually between five to 30 samples, sometimes even less. The √N + 1 approach isn't valid for these sizes. Small lot sizes need a defined inspection level, generally lower than larger ones. This ensures you're getting a more representative sample.
The problem with √N + 1 for small lots is that it doesn't account for the lot size or allow control over the inspection level. It also doesn't incorporate the AQL. These factors are crucial for ensuring valid sampling in smaller populations.
What is the solution?
The solution involves properly assessing the true data of the population value. This means selecting the right inspection level according to lot size, which then leads to selecting an appropriate AQL. Once you apply this correctly to different sample sizes, you can observe the effect on what we call the AQL curves. These curves help determine the most appropriate sample range for representation.
Interestingly, √N + 1 mathematically approximates an AQL curve for a narrow range of lot sizes. It becomes more accurate for larger lot sizes, but that's where we run into problems with biopharmaceutical samples. For instance, when dealing with reagents for mammalian cell growth, a company might only get one or two lots a year. If it's destructive testing, you can't test both. So, can you get away with just one? Yes, but what's the risk? You can't answer that with √N + 1.
The key issues are that √N + 1 doesn't accommodate the risk factor, and for smaller lots, you risk oversampling. If you're oversampling, your estimate will be wrong. Your risk approximation might be correct, but you could still fail the whole approach. So, it's crucial to manage the risk and use the appropriate sample size based on your lot size.
What does this all mean?
Ultimately, this impacts the bottom line of businesses. It's costly to continue using √N + 1 when we have ways to minimize costs. Moreover, patient risk is managed much better with correct sampling sizes and proper risk assessment.
The message for businesses is to understand that while the FDA has accepted √N + 1 for a long time, it's not actually compliant with 21 CFR 820 for statistical sampling. By sticking with it, you're leaving yourself open to FDA scrutiny of your sampling plans.
An ANSI mechanism for continuous sampling could also be applied to continuous, online batch manufacturing. But again, you wouldn't be compliant with the FDA. So, in a nutshell, we're dealing with three main issues: cost, risk to the patient, and compliance.
What would you like to leave the audience with?
People first want to know where to learn about this approach. You can go to the ANSI standard, which is available online for purchase. My approach was to do a literature search; that's always a good place to start.
Learning ANSI has been a barrier to adoption. As soon as you say "statistics," I've seen everyone from CEOs to lab analysts roll their eyes. But I want to demystify the idea that ANSI is complicated. It's not; you just need to learn how to use the table. The more you work with different samples and lot types, generating those AQL curves, the more you'll understand how the statistics work as you increase or decrease lot size.
Two papers I found particularly helpful were Dan O'Leary's "Attributes Acceptance Sampling: Understanding How It Works" from 2009 and Ron Snee's "Solving Statistical Mysteries: What Does the FDA Want?"
The FDA wants compliance, plain and simple. But just because √N + 1 is widely used doesn't mean it's the right approach. As we move towards smaller lot sizes and see more issues in the biopharmaceutical area, reflected in increased FDA 483s and warning letters, the industry will need to address this. I think this solution — adopting proper statistical sampling — is a way for the industry to get ahead of the curve.
Gary's key takeaways:
Understand the limitations of the "square root of n plus one" approach. While commonly used, this method is not suitable for small lot sizes typical in biopharmaceutical sampling (5 to 30 samples). It doesn't meet the statistical requirements outlined in 21 CFR 820.250 for biopharmaceuticals.
Adopt the ANSI Z1.4 attribute sampling method for more accurate results. This approach accounts for lot size, includes an appropriate inspection level, and incorporates an Acceptance Quality Level (AQL). These factors are crucial for ensuring valid sampling in smaller populations.
Consider the impact on cost and patient safety. Using more appropriate statistical sampling methods can minimize costs and better manage risk to patients. It provides more accurate information based on correct sampling size and improved risk assessment capabilities.
Be aware of potential compliance issues. While the FDA has accepted the √N + 1 approach, it's not actually compliant with 21 CFR 820 for statistical sampling. Using this method may leave companies open to FDA scrutiny of their sampling plans.
Understand the importance of lot size in sampling. The effectiveness of sampling methods can vary greatly depending on lot size. This consideration is particularly crucial for biopharmaceutical samples, which often involve small lot sizes.
Learn to use and interpret AQL curves. These curves are essential for assessing the appropriate sample range for representation. Understanding how these curves change with different lot sizes is key to effective sampling.
Consider the applicability to continuous sampling. There's an ANSI mechanism for continuous sampling that could be applied to continuous, online batch manufacturing. This shows the versatility of more advanced statistical approaches.
Overcome the barrier of perceived complexity. While statistics may seem daunting, the ANSI approach is not as complicated as it might appear. Learning to use the tables and understanding the underlying principles can greatly improve sampling practices.
Stay informed through literature and industry standards. Refer to the ANSI standard and relevant literature to learn more about these approaches. Key resources include Dan O'Leary's paper "Attributes Acceptance Sampling: Understanding How It Works" and Ron Snee's "Solving Statistical Mysteries: What Does the FDA Want?"
Anticipate industry trends and regulatory changes. As the industry moves towards smaller lot sizes and faces more scrutiny (as evidenced by increased FDA 483s and warning letters), adopting proper statistical sampling methods can help companies stay ahead of regulatory expectations.
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Small Lots, Big Risks: Rethinking Statistical Sampling in Biopharma