Sample size assurance calculation

According to Table 13, the cap was present for each bottle sampled however, the lip seal was not fully adhered in 16 instances. The proportion of defectives in the samples is 16/15,600 or 0.001 (0.1% or 1/1000). The maximum fraction defective for an incomplete lip seal in the population (production lots) is 0.0018 at the 99% confidence level. Stated another way, there is 99% assurance that the number of bottles with an incompletely adhered seal will not exceed two units for every 1000 produced. The value has been calculated for the other quality attributes to illustrate the impact of the sample size and the different levels of machine performance on lot defectives. 

Using these values, the total sample size for this raw material is 2.4 kg to be assured that the sample analysis is within 10% of the true assay of the lot 90% of the time. This entire 2.4-kg sample would need to be finely ground, and a representative sample for the marker analysis would need to be split out using a riffle splitter. These calculations also show that a sufficiently large preship sample must be obtained from the raw material vendor to accurately measure the expected marker content in a given lot. 

An appropriate approach to sample size determination is to calculate assurance... 

For this and other reasons, I am not particularly keen on the use of assurance as the primary criterion for designing a clinical trial, although it may well be useful to calculate it in addition. My own view is that if I am going to be Bayesian about sample size calculation I would rather be hanged for a sheep than a lamb and use the methods of section 13.2.15. 

An appropriate sample size, or number of replicates, can be calculated for the type of statistical test by using the a and P error, the minimal detectable difference between two test procedures, and the variability (standard deviation) of data determined from previous neutralization system validations. The statistical test chosen to detect if there was a significant comparative increase or decrease in microorganism populations is the two-tailed, pooled Student s f-test. Both and values have been determined, 0.05 and 0.10, respectively. The minimal detectable difference is the minimal difference between samples from two procedures that the researcher would consider as significant and would want to be assured of detecting. Minimal differences that have been published are 0.15, 0.20, and 0.30 log 10 differences between data from Phase 1 and those from other phases [4,19,20]. The 0.15 logic difference will be used for this validation, because it is the most conservative and is from a validation test that involves multiple samples (replication) and a statistical analysis [4]. The final requirement, variability of the data, will be difficult to establish, especially because many researchers will be performing this validation for the first time. If past data are unavailable, then an option is to use an excessive sample size (at least 10) and use the data from that validation to determine an appropriate sample size for future validation studies. 

The quality control and assurance measures for paternity testing are similar to those for other types of human identity testing. Positive identification of samples, prevention of DNA contamination, the use of control alleles of known size, and the validation of software employed for genetic analysis and calculation are among measures common to identity testing programs. Population distribution data for the systems used must be documented. In addition, mutation frequencies of the systems used must be dociunented and used appropriately. 

This procedure marks the end of the spatial component of the library synthesis. The resin beads in the wells identified to proceed in the library synthesis are mixed and then split out into a 96-well reaction block. All 96 reaction wells are indistinguishable and consist of compounds that have all possible A-B combinations. Monomer set C typically consists of 96 unique monomers, where one unique monomer C is coupled in each well for the third point of diversity. QC is conducted after completion of the final synthesis step by the selection of a minimum of 12 beads from each well. The sampling rate does not permit the calculation of relative synthetic yields for all compounds in the library however, a global assessment on synthesis for each monomer C is produced. A narrow bandwidth of mass spectral-relative yields of the final product is selected for assay and assures a tight-Ugand concentration band. Those monomers that fail after the last synthetic step are not forwarded to biological assays. This synthetic scheme can produce a 36,864 compound library that is characterized by approximately 4200 mass-spectral data points. Normally, the final library size is between 20 and 30K after removal of the identified synthetic failures during the QC process. 

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