Guidance on Significant Figures and Rounding of Result.

In Pharmaceutical Industries, it's is very important to know the guidance for significant figure and rounding of results.
USP and ICH has given some guidance on this topic.
The drug analyst should be thoroughly familiar with thease topic.
Some highlights on this topic are summarized below-

1. Numerical limits specified in a monograph include the extremes of the values and all values in between, but no values outside these limits.
This statement should be applied after proper rounding of numericalr results, for example, a properly rounded result is found to lie exactly
at the extreme of a limit .
(e.g. limits 98.0-102.0% of declared; found
102.04%, rounded to 102.0%) then the monograph limits are met. If the
result lies outside the numerical limits (e.g. 98.0-102.0% of declared;
found 102.05%, rounded to 102.1%), then the monograph limits are not met.

2. Numerical result should be reported to the same number of decimal
places as the limit expression stated in the monograph. For example, if
limits are stated as 90.0-110.0% of declared, report results to 1 decimal
place (e.g. 98.3%, 101.8%), after applying USP rounding rules.

3. The USP has slightly different rounding rules:
USP rounding conventions are as follows:
a. Retain only one extra digit to the right of the rightmost digit of the monograph limit expression.
b. If the extra digit is less than 5, drop the digit.

c. If the extra digit is greater than 5, drop it and increase the previous digit by one.

d. If the extra digit is exactly five, then drop it and (always) increase the
previous digit by one.

4. An explicit statement is made for titrimetric procedures: essentially all
factors, such as weights of analyte, should be measured with precision
commensurate with the equivalence statement given in the monograph.
Examples in the significant figures section above illustrate the
importance of this for all analytical work.

Few examples are given in the following -
For Assay:
If limit is 95.0 to 105.0%.
Result-1: 94.94%----Reporting as per rounding rule:94.9%----Doesn't comply. 

Result-2: 94.95%----Reporting as per rounding rule:95.0%----Complies.

For Related Substances:
If limit is NMT 0.20%.
Result-1: 0.206%---Reporting as per rounding rule:0.21%----Doesn't comply. 
Result-2: 0.203%--Reporting as per rounding rule:0.20%---Complies.

If limit will 0.2% instead of 0.20%, then both the cases are complying to the specification. 

OOS Investigation case study-5 (Dissolution)

In Pharmaceutical Industries OOS investigation and root cause identification is very important topic. If you are not able to identify the exact root cause, then your effort should be looked in your investigation.

Here I am sharing another case study to understand it in a better way-

Description of Event:

OOS result observed in dissolution test for capsules analysis.
One unit result is 58% and other 5-units are well with in limit (about 98%) -Limit is NLT 85%(Q).

Preliminary investigation:
During preliminary investigation no obvious error is identified, but out of six units, one unit weight is about 40 mg less (subjected unit) in compare to other units weight (about 100mg) .

Re-measurement:
Re-measurement from same solution (same vial, refilled vial) is found in line to the initial result. Hence instrument error and vial filling error is ruled out.

Root cause:
From above investigation, it's seems that as lower weight of capsule is the reason for lower result. It's may be the our first root cause. But how such lower unit capsule has been packed. We have to find out second root cause to make this investigation more adequate.

In such case Phase-II investigation is required.
The manufacturing facility is fully automated and having different check points including sensor to reject the unit of less or higher weight of Pre-defined setting in machine.

But now the question is how such lower weight unit has been packed, if we have sufficient technology to avoid such incident.
If we unable to identify the second root cause then the whole system is questionable.

My take:
In capsule filling it's general observation that many Capsules are rejected due to lower or higher content filling.

But if capsules having lower content but weight is with in range then it will not rejected by the machine.

But the question is how it's possible.. .. It's possible only when lower content capsule have double capping (it's observed when capsule rejected by machine due to higher weight is some time it's double capping) .

So if the above mentioned case is correct then why QC analyst had found lower weight of subjected capsule... .. .. It's may happen the second capping is detached during packing due to vibration which occured during packing for movement of capsules.

If we can do such negative challenge by video recording, then only we can justify the above probability to make this investigation more adequate.

OOS vs OOT vs OOE

For OOS, USFDA published a guidance in October-2006 and MHRA published OOS investigation guidance in August-2013.

As such there is no official guidance for OOT and OOE results.(ECA meeting will held on 23 and 24 October-2019 for OOT/OOE Results)  

But we can and we are investigating OOT and OOE results in the similar way as OOS investigation.

Now, how we can categorize the investigation in OOS/OOT/OOE.

For OOS: I think,there is no confusion to any one, as any generated result is not with in the Pre-defined specification limit is OOS result and the event should be investigated through OOS procedure.

Few examples;

For Assay, if Pre-defined limit is 98.0% to 102.0% and result is 97.9% ----it's OOS result.

For Dissolution, if Pre-defined limit is NLT 75%(Q) and result is 81(48-94) %---only one unit is failed-48%--Out from the S-3 stage criteria.

But for OOT and OOE there is no any written guidance till date to confirm that which result is OOT result and which one is OOE.

Many organizations have no separate SOP for OOE (Out of Expectation)  , they have Clubbed OOE concept with OOT .

So organization has made OOT/OOE -SOP and fix the criteria on basis of his own scientific knowledge and reasons. 

As per my recommendations OOT criteria should be as (Some one may have change of openion) --

For Assay: 

Fixed limit for release (if less than 30 batches data available) and for Stability--- +/-3.0% of labelled amount. If 30 or more batches data are available then based on statistical tools uses limit should be definede. g. LCL/UCL.

For Related Substances test;

For unknown impurity and known impurity (Non degradation impurity) :
For release: Fix limit is 50% of specification limit and if sufficient number of batches data available then define the limit based on statistical calculation.
For Stability:

If limit is less than 0.1% then no need to investigate. 

If limit is between 0.1 to 0.5% then 50% variation to be investigated. 

If limit is between 0.5 to 1.0% then 25% variation to be investigated. 

For more than 1.0% limit: 80% or more of the specification limit result to be investigated.
For Dissolution:
Any thing not complying in S1/L1/A1/B1 criteria.

OOE:
The results or neither OOS Nor OOT  but result looking questionable should be handle through OOE.
For example;
Dissolution result is complying S-1stage criteria - 83(80-86) %---Limit is NLT 75%Q.
Last 10 batches mean results are between 94% to 97%.
So this batch result is complying in S1 stage but out of Expactation.

For other test , you can ask my opinion.

CAPA (based on Risk based approach).

In Pharmaceutical Industries, in most of the cases investigator has fixed many CAPAs without identifying the actual root cause.
Our investigation and CAPA should be like that to avoid the re-occurance of event with the same reason.
Here the case study...

“Fixing problem “is the main activity at pharmaceutical industry now a days, Rather than manufacturing medicine, we are focusing on the failure investigations, root cause identification, CA-PA implementation & effectiveness verification. When a facility or a product is designed, the risk based approach not followed. Maximum problems happed during tech transfer from R&D to commercial manufacturing. Failure is happened due to higher variability in utility, machinery & area maintenance, operation and control. This is the time when we start taking support with short cut (quick-fix solutions).

Suppose the problem stated as “Mr. Y. have fallen down in the bathroom due to slippery floor”,
Then what will be the thought process of CAPA as a pharmaceutical professional. 

·  We will fix the first cause is Human error / person does not know how to move in bathroom –Blame on Training adequacy

·  After that, we will propose extensive Cleaning of bathroom – Inadequate Process

·   Then, change the detergent of bathroom cleaning will be additional control – Blame on the external supplier and material use.

·  Increase frequency of cleaning to avoid the slippery floor – Inadequate maintenance program

·   Training how to move in slow motion in bathroom – Inadequate process control

·  Visible board mentioned “Wet floor, move slowly” and mention Ambulance number in case of emergency  – Additional control to make process more complex and to satisfy auditors

·  Increase the lighting for better visibility – Additional budget investment and increase annual maintenance cost

·  Installed telephone to take help from neighbor – Involves of external consultant to fixed internal problem

· One person will stand outside of bathroom to support in case of emergency -  Proposal of increase of manpower to management

But we did not think for permanent solution. 
In current scenario change in bathroom floor tiles with Rough Surface new tiles can be an appropriate CAPA. 

In fact design and installation of bathroom should to be with rough surface tiles only as part of risk based approach. But here the attitude which comes that is it's ok. Because to fix the actual problem productivity can be temporary decrease but in future same problem will not be happened.

OOS Investigation case study-4(Water content by KF)

Here we will discuss about an OOS of destructive test (Water content test by Karl Fischer) . In other case of OOS we can do the many of hypothesis testing to identify the root cause, but in distructive test we can not produce the same situation again.
Description of Event:
OOS result observed in Water content test.
Result: 4.9% . 
Limit: NMT 4.0%.

Preliminary Investigation:
During preliminary investigation, checked all the possibilities of higher water content result like any leakage in vessel, graph pattern, delay in analysis after crushing of tablets etc., but no any error is identified from preliminary investigation. 

Re-measurement:
Destructive test , hence not possible. 
Trend evaluation:
Reviewed all batches data which are manufactured in last 2years, and all water content results are found between 1.5% to 2.0%.
So there is no trend of higher water content. 
Re-analysis:
Can we perform the re-analysis based on trend ?, and if result is with in the specification limit and trend of other batches, can we release the batch? 

My Take:
Yes, we can perform the re-analysis based on trend data, and release the batch. 

But, what is missing in this investigation, what additional we can do to make this investigation more adequate. 

As per my opinion, in above investigation if we perform a protocol base study as an  expanded hypothesis I. e. Prepare a protocol to perform sample analysis in 3-sets and maximum variation between lower and higher results should not be more than 0.5%.(why 0.5%--In last 2years data the variation in results are only 0.5% it means product give very consistent results) .
If any set of result is failed or near to 4.0%, then we can not perform the re-analysis and send the investigation for Phase-II. 
But if results are complying to our Pre-approved acceptance criteria of protocol then definitely we can perform the re-analysis. 

Re-analysis results found well with in specification limit and trend. 

So what is the root cause for initial higher result. 
Now we can compare graph pattern of initial, hypothesis and re-analysis results, is there any difference in the pattern of initial analysis. 

Call and Discuss the case with Technical person (Technical engineer) of Instrument with all these data, definitely you will get the root cause or the most probable root cause. 
In this case we have to perform the phase-II investigation to check  variation (if any) from previously manufactured batches. 
Our above efforts will give confidence to auditor. 

OOS Investigation case study-3 (Assay)

OOS observed in Assay test. .. 
During investigation when you found any root cause in Preliminary or hypothesis testing, before planing of re-analysis, Review it thoroughly and plan the negative experiment if required to make the investigation more adequate. 
Description of Event:
OOS result observed in Assay test.
Result: 92.0% 
-Limit: 95.0 - 105.0%.
Preliminary investigation:
During preliminary investigation checked all possibilities for lower Assay results like calculation error (wrong weight, wrong potency etc.), Standard preparation error (recovery factor of standard and control standard is 99.2%) and all other possible causes for lower result, but no error is identified in preliminary investigation. Hence hypothesis testing is planned. 

Re-measurement:
Hypothesis testing is performed to rule out instrument error, vial filling error, dilution error etc.
Same vial result is found similar to initial result, hence Instrument error is ruled out. 
Refilled (101.9%) and re-dilution (99.1%) results are found well with in specification limit. 

Now most of the investigator will plan the re-analysis  as vial filling error is identified. 

Now the question is , 
Is above investigation and hypothesis outcome is sufficient evidence to plan the re-analysis? 
Yes ,we can . 
But this may not be acceptable to many of the Auditors. 
So what is the additional investigation and efforts are missing. 

My take. 
In above investigation re-fillled from final sample solution result is with in specification limit and  re-dilution from stock solution is also with in limit(slightly lower- about 3% from re-fillled vial) . So there is no issue with the product quality and no error in sample preparation. 
There is something happened during sample vial filling. 
How final solution gives lower result during initial analysis and with in specification result from same final solution in re-measurement. 

So we can say that the analyst might had not mixed the sample solution after make-up the volume with diluent to make it homogenous solution and filled the solution from upper layer which is having less drug concentration in compare to lower solution in volumetric flask. 
So the root cause may be the Non-homogeneous same solution instead of vial filling error. 
But this is the actual reason for initial lower assay result, we have to perform the negative experiment to proove that this is the actual root cause. 

Negative Experiment:

Plan the expanded hypothesis in a similar manner I. e.prepare final sample solution as per STP and do not mix it after make up the volume with diluent. Fill the vial without shaking the final solution and inject all the solution like blank ,SST ,standard and sample as per STP. 

It will definitely give lower result, may not be exactly the same ,but near to the initial result. 
This experiment will support to our initial root cause. 
Our such efforts in investigation will give confidence to auditor. 

Deviation vs Incident

In pharmaceutical industries specially in Quality control laboratory, it is very difficult to decide that the event should be handle through Deviation or Incident, it is always debatble.

So we should have a clear cut SOPs where it should be clarify that event should be handle through which QMS documents.
From my view, any deviation of SOP Should be handle through deviation. 
Apart from SOP deviation all laboratory events should be handle through Incident. 

And in any laboratory events, if results are not with in limit, then it should be handle through OOS only. 

For example,
Case-1:

Analyst had selected wrong wave length.i.e.254 nm instead of 354 nm) , but all results are well with in limit.

Case-2:

Analyst had frogot to inject the bracketing system suitability injection (for resolution), while injected diluted standard for bracketing RSD% (It is part of SOP for bracketing injection). All results are well with in limit.

Case-3:

Bracketing System suitability parameters are failed due poor column efficiency, and due to poor peak shape (its look like principal peak split) sample is failed in unknown impurity.

My take
For case-1 ,
Analyst was not followed the STP, hence it should be handle through Incident.
For case-2,
Aanalyst had not followed the SOP , So it should be handled through Deviation.
For case-3
Here result is Out of Specification, hence this case should be handled through OOS only.

In any case ,if result is OOS then it should be handle through OOS Only, either STP devation or SOP deviation. Even though, result may be 0% due peak not eluted, It should be handle through OOS only.

OOS Investigation case study-2 (RS)

OOS observed in Related Substances test.
Description of Event:
OOS result observed in RS test.
Result: 0.27%  (Suppose at RRT 0.4)
-Limit is NMT 0.20%.

Preliminary investigation:
Checked pressure graph📈,System suitability parameters etc. and No laboratory error is identified from preliminary investigation.
Re-measurement:
Hypothesis testing is performed to rule out instrument error, vial filling error, dilution error etc.
But no any error is identified and all above possibilities are ruled out.
Reviewed the trend of previous 10 released batches and stability trend data of Validation batches and no any impurity peak observed at about RRT 0.4.

Now what is the next step. . .Based on trend data it  looks like that, this is not a true failure.
But we can not perform the Re-analysis by saying that this is an erratic result.
Then what is our next step as an investigator.
Step- 1
Inject same subject sample on PDA detector and record the spectra and peak purity of the subject impurity (it helps when in expanded hypothesis any other standard peak observed at same RRT, then we can match the spectra of both peaks) .
Step-2
Review the force degradation chromatograms to check any peak at RRT .4.
If there is no degradation peak at RRT  0.4.
Then it's confirmed that this failure is not a product failure, further we have to rule out that this peak is come due to any product contamination during manufacturing to support this statement further follow step-3.
Step-3
Inject all product standard (about 10 ppm) which are used in manufacturing before this product (cover all equipment) in same chromatographic condition.
If there is no peak at RRT 0.4, then there is no product contamination is proved.
Step-4
Again re-look in laboratory investigation and rule out all probabilities i. e. filter interference (if sample required high pressure during filtration), Is analyst taken glassware from cleaned glass room Or he cleaned glassware himself and used due to unavailability of cleaned glassware. Rule out all possible reasons through "SYSTEMATIC ROOT CAUSE ANALYSIS TOOLS " and perform all expanded hypothesis testing to identify the root cause and take proper and effective CAPA for future Re-occurence.
If required keep sample for stability study with reduce testing (3, 12 and 24 months) , which data help you to convince auditor that initial failure was not  product quality issue.
Always try to apply systematic approach of investigation.

By all these efforts, if we will do the Re-analysis and release the batch. It will give confidence to auditor that there is no any issue with the product quality.