Knowledge Domain

Pharmaceutical Quality & Role of Statistics

In the last two articles we discussed about desired “Performance Characteristics” (Quality Target Product Profile) and their association with “Quality Attributes” which are measurable product characteristics and thus can be used to ensure that end product meets laid down QTPP demands.
In pharmaceutical industry, assurance of safety& effectiveness of the product to patients is the fundamental requirement. To adhere to this dictate, it is imperative that the product remains consistent as developed because, understandably, the product safety & efficacy performance evaluation (biostudy) is doneearly on in its lifecycle. The underlying assumption is – if the product characteristics remain same then the product performance will be reproducible. Thus, consistency is the key feature of pharmaceutical quality. Pharmaceutical quality is notlimited to meeting specification. The emphasis on consistency as a dimension of quality brings in a set of challenges.
Our day to day experience tells us that variability is unavoidable. Any process, including measurement procedure, comprises of inputs (raw materials, reagents, solvents, catalysts, process aids etc.); operating parameters (temperature, mixing, pressure, concentration, pH etc.) and a process environment (humidity, ambient temperature, illumination, operator skills, etc.). We can clearly visualize that it is impossible to keep all of these invariable and as a result it is natural that the process or measurement output would be variable. If you consider a batch then the individual unit dosages are not identical, similarly batch to batch variation is observed. The variation is also observed in the measuring system output that is used to quantify quality characteristic. This implies that the manufactured product, output of the process, is variable. It is then imperative that we need to tightly control variability. This means we need to understand how to measure variability, be able to rationalize sources of variability, be able to partition total variability and assign it to its various sources. To accomplish this, we not only need good domain knowledge but also need fair understanding and application of statistical concepts.
Why should we use statistics? The uniqueness of statistics is in the fact that it deals with property of a group based on collection, analysis, interpretation of data on individuals from the group. Thus, based on a sample from a batch we can derive information about the whole batch; based on sample of batches we can derive information about overall behavior of the product over the time period.
To understand how statistics works, let us look at some basic concepts –
  • A representative sample adequately embodies characteristics of the population (group)
  • Data collected on sample is ‘statistic’ of the sample and corresponds to ‘parameter’ of the population which is unknown
  • In absence of exact value for population parameter we accept best estimate which is derived from sample statistic
To illustrate the concept let us look at an example – an assay result, performed in triplicate, on a sample is reported as an average of three observations. The reported assay value is 99.73%. The average assay value of the batch is unknown but the best estimate can be derived from the sample statistic and expressed as 99.73 + 0.38%. Here, the value 99.73% is called the point estimate and the 99.73 + 0.38% is called the interval which contains the best estimate of population saverage value.
Similarly, other population parameters can be computed. Since we test a sample but release a batch, since bio study results are utilized throughout product lifecycle, since same shelf life is used for all batches one can see that not only the point estimates but relevant population parameters and their intervals should be used to take quality related decisions. The width of interval is the measure of variability and should be contained within specification window.