* * * INSIGHT * * *
Role of Statistics in Lyophilization or Freeze Drying
By
Thomas A. Jennings, Ph.D.
There is little doubt, at least in my mind, that lyophilization or freeze drying (see INSIGHT Vol. 2 No. 1) is a very complex and often confusing process. In our efforts to understand such a complex process we will tend to simplify rather than treat the subject in a rigorous manner. Even so, the process continues to offer us a real challenge in our efforts to reach some kind of general understanding.
But our efforts to simply do come at a price which often is a source of even more confusion. Take for example when one finds that less that 1 % of the product in a batch is defective in some way, e.g., partial meltback (see INSIGHT Vol. 1 No. 5). If our product is in vials, it represents less than 1 in a hundred but if the batch size is of the order of 50,000 there could be hundreds of defective product that will have to be removed from the batch by inspection. Now the defective product not only represents a loss in revenue but is a constant source of irritation because the defects are generally randomly scattered throughout the batch and there does not appear to be any pattern one can attribute to the process or the freeze drying equipment that can account for the defects. What makes this even more frustrating is that attempts to eliminate these defects often proves to be an exercise in futility.
The answer to such problems may often lie in the fact that not even the most fundamental aspects of statistics were applied to the process. This INSIGHT will therefore address two key parameters that need to be examined on a statistical basis in order to improve the reliability of the process.
Given the nature of this topic and troubled state that now seems to grip the world, what better way to commence this first issue of the sixth volume of INSIGHT but with a smile or two by paying a visit to our dear friends at the Surcure Company. Especially when it is the last day of the year and preparations are underway for the Annual Surcure New Year’s Eve Party. So let us begin our story.
Since it is the last day of the year and minds are now more focused with anticipation on the big party that evening than on the work at hand and given the fact that the following day is a paid holiday, it is of little wonder that, by the time the afternoon has arrived, interest in working is rapidly waning. It is at times like this that Armondo will retreat to the safety of his office and invite his friend and associate to join him in his office while the last minutes of the year slowly tick by. Armondo is relaxing behind his desk and he has some regrets about consuming another one of those huge sandwiches so apply named an “Awful - Awful” for it seems that the sandwich is beginning to live up to its name as the afternoon wears on.
The room is quite for some time and it is Armondo who breaks the silence by stating “I think I should have passed up on the “Awful - Awful” at lunch. Especially since we will have a big meal tonight and I also guess I should not have eaten the apple pie but I do like apple pie so much.
“Especially when it is topped with two large scoops of ice cream” interjected the Novice.
“I guess I could have just taken one scoop to think about it but then my New Year’s resolution to lose weight does not technically start until after midnight so why not enjoy a little treat when I can?”
“That’s right.” chirped the Novice “enjoy it while you can.”
Sensing that even the Novice was in a mellow mood, Armondo thought he might just take this opportunity to review the successes of their validation program during the past year. “You know we have had a petty good year and certainly have things pretty much under control. Would you agree?”
But before the Novice can respond, the phone rings and Armondo picks it up and replies in a rather playful mood, “Armondo is here and is full of the Holiday Cheer!!!” There is a change in his expression and it becomes more serious. After a long pause he replies “I agree it was a bit unprofessional but......” There is another long pause when he continues “ No it won’t happen again and yes I will be in my office... all afternoon I will be here so come at your convenience.” With a quick “good bye” he hangs up the phone and looks at the Novice.
The Novice cannot help but have a smile on his face and say “Don’t tell me who it was. Let me guess - Miss Charm?”
“Who else would call on the afternoon of the last day of the year.” replies Armondo. “She has this uncanny way of being in the right place at the wrong time.”
The Novice still cannot refrain by replying with a smile, “Right place for her - wrong time for you!!! But just think that this will be no doubt the last you will see of her until next year.”
“Not quite.” answers Armondo “She will be stopping by later this afternoon - God help me!!!”
Now eager to change the subject in order to remove the sudden gloom that has seem to fill the room. The Novice tries to change the subject back to a more pleasant theme. “You were stating before the call that you were pleased with progress made by the Validation Department. Would you like to elaborate on that Sir?” asks the Novice.
Eager to get the phone call off his mind, Amondo is quick to respond. “Well like I was saying before getting THAT phone call, I think we have things pretty much under complete control when it comes to the manufacture of Surcure. Don’t you agree? asks a very confident Armondo.
The Novice is not fast to respond to the question and his delay troubles Amondo so he repeats his question “Don’t you agree???”
Now forced to respond the Novice hesitates at first and then says “But we still are stuck with doing that 200% inspection and if we really had things well under control we would not be forced to perform such an inspection twice just to be sure.”
It is a rare treat for Amondo when he can use the Novice’s own words to make a point. With another thought he fires back, “You know full well why we must do a 200% inspection. It was you who pointed out that variations in the banana skins due to the season where they are grown and even variation in climate all are factors that effect the final composition of Surcure. So while we may well be able to control the concentration of the active ingredient, it is the variation of the numerous other compounds which are present that results in different thermal properties. In fact, it was you who stressed the need for a thermal analysis prior to running each batch. You seem to forget how I had to go before the budget committee and justify the need to perform 30 thermal analysis on each batch (see INSIGHT Vol. 2 No. 5) and they thought I was really crazy when one analysis would have been adequate.”
“Would one have been adequate Sir?” responds the Novice.
“Of course not!!!” explains Armondo. “You need to know the frequency distribution of the thermal properties and in particular the “collapse” temperature [1].
“And how does knowing the frequency distribution of the collapse temperature help us?” asks the Novice in a soft but firm voice.
“Well we will know the mean value of the collapse temperature and the standard deviation.” replies Amondo with a bit of hesitation in his voice.
“And how do knowing those values help us with the lyophilization process?” presses the Novice.
Looking a bit like a fish out of water, Amondo tries to find an answer. But before he can answer, the Novice is asking yet another question, “Does knowing the frequency distribution of the thermal properties of the Surcure alter in any way how we conduct the lyophilization process?”
“No the process always stays the same. Now I have been meaning to ask you why in the world are we wasting all that time and money performing all those thermal analysis when we continue to use the same process each time?” demands Armondo looking rather stern.
“What did we do with batch 1313?” responds the Novice.
Armondo pauses for a moment trying to recall what happened to batch 1313. He struggles until the Novice comes to his aid and states “Why did we immediately discard the batch after formulation?” presses the Novice.
“Marketing didn’t like to have a batch number that was doubly unlucky.” is Amondo’s weak response.
“No!!!!” the Novice replied with a bit of chuckle. “That was not the reason although I didn’t hear too much opposition by marketing when you made the decision to discard the batch.”
“That was because you talked me into it.” answered a now bewildered Amondo desperately trying to search his memory for the reason why batch 1313 was discarded.
“It was because of the frequency distribution” replies the Novice in an effort to help his colleague recall the rationale behind discarding the batch.
“You are absolutely right!!! It was because of the frequency distribution of the collapse temperature that formed the basis for discarding the batch!!! answers a somewhat relieved Armondo.
“What about the frequency distribution?” questions the Novice.
Amondo has taken all he can stand and shouts “ I don’t remember why we discarded the Batch, I don’t remember why we did it based on the frequency distribution, all I know is that you talked me into it. It was your idea to discard the batch not mine and in fact I happen to like the number 1313.”
Realizing that he may have pushed Armondo a bit too far, the Novice steps in to assist his friend. “Sir, I think you must have forgotten that you recommended discarding the batch because the frequency distribution of the collapse temperature was too broad.”
“I did?” asks a bit puzzled Armondo.
“Yes Sir” continues the Novice and it was you who showed the Review Committee that because the broad frequency distribution would have generated such a large number of defective final product that we would have had to find and then throw out perhaps more than 20% of the final product.”
“I did?” asks Armondo once again with a grin on his face.
“So you see Sir, had it not been for you insisting on the thermal analysis of a statistically significant number of samples of the batch, there would have been some question regarding the quality of the product even if we would have released such a batch.” continued the Novice in a reassuring voice.
“Yes, I remember it now” recalls Amondo as he gazes at the ceiling as he does so often when he is deep in thought. “And I do remember that I had to call you in to explain it to the Review Committee in more simple terms because they found my explanation to be a bit too academic or far too complex for them to understand. And what was the point that you made that surprised them into accepting our recommendation?”
“That the collapse temperature would not be the same in each container and from the distribution we would have expected a very large number of the vials to collapse or even meltback.” replied the Novice.
“Yes, Yes” answered Amondo “We really did convinced them when we brought out that point. Yes, I remember it quite well now and thanks for helping to clarify that point with the committee.”
The Novice could only grin for he was glad to see that Amondo was calmer now and really didn’t mean to up set him and so he added “You know your memory astonishes me at times.” In an effort to maintain the pleasant mood, the Novice continues with “I wonder what they will be serving for a salad this evening?”
With a bit of scowl on his face, Armondo replies, “No doubt if Miss Charm has anything to do with it will be fruit salad mainly made of bananas.”
“Well that won’t be too bad for a change.” replies the Novice with a grim.
“Too bad!!!” storms Amondo “What do you think they serve here every day in the cafeteria. Why I am almost forced to order the “Awful - Awful” just out of self-defense. But that is not what scares me this evening” he continues.
“What is that Sir?” asks the Novice with a bit of surprise.
“Its the drink they are going to use to toast in the New Year that bothers me.” replies Armondo.
“Are they going to have Champagne this year?” asks the Novice eagerly.
“Surcure serve Champagne?. “You have really got to be kidding - no its going to be HBB wine that will be on the menu.” replies Armondo in a rather sarcastic tone of voice.
Looking somewhat perplexed the Novice states “Never heard of HBB wine before. What does the HBB stand for Sir?
This brings a smile and a laugh from Armondo as he replies “My boy HBB wine is good old Home Brew Banana wine [2] - straight from the Research and Development Laboratories under the careful guidance of Dr. Promises. Didn’t you ever wonder why lately there were so many white coats running around after hours?”
‘No, I never did give that much thought but I did find the giggling of late coming from that department each afternoon to be a bit strange” answered the Novice shaking his head.
“So now you can see why I feel that this department has things very much under control” states Amondo.
“Well we are sober for the most part if that is what you are implying” answers the Novice “But very much under control - I hardly think so. There is still room for improvement.”
“In what ways???” demands Amondo.
“Well for one thing we still have not taken the time to determine the frequency distribution of heat transfer coefficient (Co ) for each lot of vials that we receive” replies the Novice.
“I don’t see where that is a problem that we are facing today?” asks Armondo.
It is not a problem at the moment but we may receive a lot of vials which also has a broader frequency distribution of Co and we suddenly find that we have an increased incident of partial meltback as a result of the vials and not the formulation” answers the Novice.
“If that happens we could then go back and check the Co distribution vials at that point?” offers Amondo as a alternative measure.
“So you advocate wasting a few batches before we suddenly realize that we have accepted a lot of vials that are not suitable for our process? asks the Novice.
It does not take Armondo long to reply and he meekly has to admit that the prudent course of action would be to check the Co distribution of each lot of vials [1]. But he is quick to add “Of course you are right and we have always advocated a statistical approach to the lyophilization process. In addition.......” But before he can answer there is a knock at the door and before Armondo can even reply the door swings open and Miss Charm walks in carrying a bag under her arm and a big smile on her face.
The Novice is glad to see Miss Charm in such a good mood, especially when confronting his manager but Armondo seems to be of a different opinion and there is a look of concern on his face as his nemesis for the past few years strolls up to his desk.
It is Miss Charm who speaks first by saying “So glad that the Validation Department has decided to do its part in the New Years Eve Party tonight by playing a major role in the Surcure Players production of “Welcome to the New Year”.
The Novice is both thrilled and a bit naive when he says “That is wonderful and I am sure that Amondo will fit the role. By the way, who wrote the script?”
There is another moment of silence before Miss Charm speaks out while looking right at Armondo, “Why I wrote the script - and Armondo will be such a key player I personally brought down his costume for this evening.” Handing the package to Amondo, she continues with “Well Sir aren’t you going to try it on to see if it fits? I picked it out for you and I was told that one size fits all but I would love to see if it needs any adjustments.”
Armondo does not look at all pleased as he accepts to package and less thrilled at Miss Charm’s words. “No thank you I think it will be just fine!!” he says in a strangely meek voice.
“Well, I will be looking forward to your grand entrance at the stoke of Midnight” and having said this she leaves the room with the same happy expression that she had when she entered.
The Novice is confused by what he has just heard and especially Armondo’s lack of enthusiasm for his role to tonight’s play. He tries to cheer up his friend by asking “Sounds like you will have a real important part in tonight’s play and you do our department proud Sir. And what role do you actually have in the play?
“The New Year!!!” Armondo replies glaring at the Novice.
The novice can’t understand the reason for this friends behavior so he quietly asks, “And just what costume did she give you?
“A DIAPER!!!!” comes the loud response.
The Novice knows when it is time to leave the office.
Reference:
1. T. A. Jennings, Lyophilization - Introduction and Basic Principles, Interpharm Press, Buffalo Grove, IL 1999.
2. Recipe by Alwyn Jones see http://www.hookerycookery.com/banana21.htm
Volume 6 Number 1 January 2003
