Friends who are engaged in process development are no strangers to DOE. DOE is an experimental science. By making some purposeful changes to the input (X predictor variable) in the experiment and observing the changes in the output (Y response variable), so as to study some effects of changes in X on the output of Y, and establish a model for X Relationship and understanding with Y.
DOE is usually in process development, usually in three phases.
- First, the screening phase. What we need to understand is which predictor variables can significantly affect the Y output, and we need to quickly find these most important predictor variables.
- On this basis, the second step is optimization, including optimization of process applications, as well as PC experiments, process characterization research, etc. DOE can be of great help to the optimization of process development.
- The last one is robustness research, that is, how to produce quality products stably and efficiently. Whether the process capability is good and whether the process is stable, we can have a better understanding of the process through DOE.
These are the three main application aspects of DOE in the process development process. So, in the process development process, what problems are usually solved by applying DOE?
The first is cell culture, which can be cell culture or fermentation of material cells, and the production of polypeptides often requires some enzyme digestion, and DOE can also be applied in the process of enzyme digestion. In addition, DOE is also a very useful tool in the process development of chromatography in downstream processes, and even the development of analytical methods, such as HPLC method development. In some processes, we need to do crystallization and precipitation processes, and DOE is also relatively common. If it is expanded to the entire production process, DOE is also widely used in the preparation process.
Therefore, it can be seen that DOE is widely used in the whole process development process. Everyone also understands the importance of DOE, but in fact, when using DOE for process development, there are some precautions or unexpected points that are easily overlooked. Today we will take a look at some of those in the process of using DOE Key factors, or considerations that are often overlooked by everyone.
The first one is the range of Input, that is, the selection range of X.
Generally speaking, we want the X range to be set wider. As shown in the following two figures, when the experimental system error is a fixed value, the range is set narrower, and the fluctuation of the obtained model will naturally be large. If the range is set wider, the stability of the model will be better. So people usually tend to choose a wider range when choosing a range. But what needs to be reminded here is that, especially when doing biological experiments, the range width of X needs to be selected to a suitable point. If set too wide, some problems may arise.
For example, the graph range on the left is more appropriate. If you choose the low-value and high-value center points, you can make a model through these three data points to try to understand what the real world is like. It can be seen that the obtained model fits the actual situation better. However, if the range is selected too wide, the second situation may occur, that is, the low value, high value, and center point are selected. But in the real world, when its peak appears in a relatively narrow range, that is, the black line in the figure, if it is the real situation, the fitted red line will be distorted. What does it mean? It could be that this predictor variable probably doesn't affect Y very much because the low, median, and center points don't differ that much, but you might actually be missing a very important parameter.
So how to find a more suitable range? It is suggested that you can use your own biological knowledge, for example, first have a preliminary understanding of the experiment you want to carry out, so that you will not choose a particularly inappropriate range when you come up. For example, when doing anion and cation chromatography, you choose pH for chromatography at the upper and lower isoelectric points at the same time. When the protein crosses the isoelectric point, many of its behaviors are different during the chromatography of. At this time, the range of selected results may be too wide, and this result will make people feel difficult to explain. When sometimes the results are completely contrary to your biological understanding, then you may need to go back and check where it is not appropriate, one of which is the selection of the scope.
The second is the evaluation of the model.
When we use DOE, especially for practitioners who lack statistical background, sometimes it is easier to over-rely on software, directly put the data in, and use it directly after fitting a model. In fact, can this model be used, and is the model effective? If you don't think more about this place, you may get a conclusion that is a little bit wrong. Therefore, first of all, it is necessary to evaluate whether the model is good, and then adjust the model and re-fit, which is actually a progressive process.
For example, how reproducible is the original data? Are there any outliers? Is this model a model worth testing? If there is an outlier, is this outlier a pure outlier, or is it a meaningful rational point? Sometimes it may be because the range is selected differently. Some outliers are repeatable. It may really mean something. If you see outliers and simply delete them, you will miss the discovery. Opportunities for some unknown, new information. Also, are there any key parameters missing? If this parameter has not been found, the data that may be produced may have adjusted a lot of X but have little impact on Y. This may be because some parameters that have a large impact on Y have not been found. Also, with the X you choose, is there any interaction between the different parameters? Whether they have curves and so on are all factors that must be considered in model evaluation.
JMP provides a very rich model evaluation tool. The following figure is a relatively common one. In fact, it is far more than that. It is recommended that you complete the model evaluation before doing further data analysis.
The third is the selection of the output (Y).
When it comes to the choice of Y, you may think that what needs to be studied, just define it as Y, this is very simple. But in some cases, you need to think carefully about how to choose Y.
For example, if we want to develop a chromatography process, we hope that the target protein and impurities can be separated better, and we hope to choose a chromatography method with a good separation effect. The separation effect is good, in fact, there are different Ys that can be done.
- The peak area percentage of the main peak. If the impurities are well separated, the peak area percentage of the main peak should be low, the lower the better. It's a dimension.
- The resolution between different peaks will be provided on the chromatography interface. The larger the resolution, the better your resolution. This is also a dimension.
- Another is the height of the trough. That is, what is the height of the trough between the two peaks. The lower the height, the better it separates.
All of the above dimensions can help us evaluate whether the chromatographic effect is good or not, and which is better between different chromatographic methods. When faced with different separation goals, which one to use as Y is not the same. For the first case on the left, it doesn’t really matter which one you choose as Y, because they can better reflect the advantages and disadvantages of the chromatographic separation effect. But for the second case, we will find that which standard is used as Y, the separation effect, that is, the deviation calculated from the data is relatively large. In this case, it is actually more appropriate to use C to separate and analyze the data. So this is especially reflected in dominant chromatography method development. When we develop HPLC analysis methods, many companies are also using DOE methods, and there are often discussions about which one is better as Y.
To sum up, I would like to remind everyone that no matter which one is used as Y, do not give up mining the original data, and see which Y is really suitable, so that the validity of the data will be better. Let's look at a small case.
These two tables record the different conditions tried during process development, including PA1-PA3, PA4-PA6. If you only look at the results, you will find that there is not much difference, indicating that the process is very stable. Is this really the case? Let's look at the original data. From the perspective of peak shape, the results of 123 are not much different, and 3 is slightly higher. Looking at the peak shape of 456 again, the peak shape of 6 is completely different from that of 4 and 5. In the end what happened? This requires you to dig your own experiments. In many companies, R&D is one team, and testing is another team. Sometimes, when the experiment is not carried out by the process developers themselves, the original data may be ignored and only the conclusion is looked at. If you don't look at the source material, you'll miss a lot of questions. Regardless of whether the original material is "surprise" or "scare", you have to read it early and know it.
Fourth, regression and model complexity.
When we are doing fitting, we all hope that R 2 The higher the better. Must be higher the better? Not necessarily.
Let's look at a famous case (Anscombe's quartet), there are a total of 4 graphs, all with the same R 2 , it can be seen that they are different. We picked up 2 here. If the real situation is linear, the first graph uses the least square method to make R 2 It is more realistic and linear. But if the software is used to fit the second graph with the least square method, the R of this graph 2 To be better. If you don't look at the original data, don't do model evaluation and just look at R 2 , the second graph will be used to make predictions, and the predicted results will deviate greatly. Therefore, R 2 It's not that higher is better. Secondly, we must pay attention to the outliers, and then judge whether to eliminate them.
So, is the more complex the model, the better?
The same data, if the real situation is linear, the first way to fit the R 2 yes 0.96. If excessive pursuit of R 2 , can do X 6 , forcefully fit each point to the best, that is, R 2 close to 1.So which one is more predictive? Obviously the former. Because the former is more reflective of the fluctuations in the real situation. So don't pursue R 2 Forced fit is better, apparently better, but actually less predictive.
Fifth, distinctiveness and equivalence.
When we make a model, we usually hope to find 1 or 2 significant predictor variables that can affect Y. Sometimes we find, for example, 1 center point, 3 repetitions, and the condition. Analysis of significance reveals that all predictor variables and their permutations are less significant. The relationship between X and Y is not too strong. Does this mean that the information is wasted? Not necessarily.
First of all, we must see whether the three repeatability is good or not. From the understanding of the experiment itself, can we see whether the three repetitions should have fluctuations? That is to say, first of all, it depends on whether the repeated fluctuations in the experiment are similar to the expected fluctuations. If the fluctuation this time is much higher than the expected fluctuation, it means that the experiment was not done well and the experiment needs to be repeated. If the three experimental deviations are relatively close to the expected deviation, is such fluctuation acceptable? Can regular and meaningful data be found under such fluctuations? If you can still find it, then carry out the experiment; if not, it means that the system fluctuation itself is relatively large. At this time, it is necessary to consider that this experiment is not suitable for a system with such large fluctuations to find the law through DOE. In other words, whether this fluctuation is still suitable to find the law through DOE.
If it is still a good fit, the data is still the same, indicating that the number of X's studied does not significantly affect Y. There may be two situations. One is that there is still a significant X, but it has not been found, and the ones found so far are not important; the second situation is that several predictor variables that may most affect Y in the process have been found out. None of them affect Y that much. Congratulations, it shows that this process is very robust.
Therefore, we do not necessarily say that R 2 How high it must be, and the significance must be found, this experiment is a good experiment. When you exclude the previous problems, even if no significant X is found, then this experiment is also a good experiment. Of course, when you don't know much about the system, you may need to confirm some extreme points before judging the validity of the data.
Finally, let's look at the equivalence evaluation. When doing equivalence evaluation, we usually hope to get equivalent conclusions. Taking the following as an example, the recovery rate was tested for 3 times and the results of 200L production were compared with the TOST method, and it was found that it met the judgment standard, so it was judged to be equivalent. Sometimes we also find that the results are not equivalent, but not all inequalities are meaningless data.
For example, the three results of 2000 L produced by monomer and the three results of the reduced model, if judged according to statistics, it is found that the results are not equivalent. Let's go back to the source material to see what happened. In fact, from the perspective of process developers, the differences between the six data and the detection methods are very close, indicating that there is no significant difference between them. But if you just log the data into the software, the software does not understand the process behind it, and does not understand the fluctuation error of the analysis method, so the calculation will not be equivalent. Therefore, when we find that the results are not equivalent, we should not draw conclusions lightly. We should interpret these results in combination with our own professional knowledge background to get more objective conclusions and judgments.
DOE is widely used in process development, and it is also an extremely powerful tool. However, there are also the above-mentioned misunderstandings that are often overlooked in the application, and you need to pay attention to it. I hope this article can inspire and learn from you.
