# Proportional Reporting Ratios

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## Chapter: Pharmacovigilance: Statistical Methods of Signal Detection

Proportional reporting ratios (PRRs) compare the proportion of reports for a specific ADR reported for a drug with the proportion for that ADR in all other drugs

PROPORTIONAL REPORTING RATIOS

Proportional reporting ratios (PRRs) compare the proportion of reports for a specific ADR reported for a drug with the proportion for that ADR in all other drugs (Evans, Waller and Davis, 1998, 2001). The principles are not new, but were set out in a similar way by Patwary (1969) and Finney (1974) for ADR reporting with WHO data. The methods were not fully used subsequently, either in WHO or in the United Kingdom, and were effectively reinvented in 1995 at the UK MCA, where they have been used routinely since 1997. The PRR can also be seen as a numerical version of the ADR profile; this simply uses a bar chart for a particular drug giving the numbers in each system organ class (SOC). An implicit comparison is made with a bar chart derived from another group of drugs. A similar approach is used in classical epidemi-ology with death data – the ‘Proportional Mortality Ratio’ (see, e.g., Rothman and Greenland, 1998).

The calculation of the PRR is very simple in prin-ciple as shown in Table 19.1:

PRR = [ a/(a+b)] / [c/(c+d) ]

This is analogous to a relative risk. An obvious alter-native is to use an odds ratio (ad/bc) that may be regarded as a ‘Proportional odds ratio’ (POR). This has slightly more desirable statistical properties than a PRR, but will be very similar in magnitude since in most circumstances b >> a and d >> c.

When a reaction is new and rare, then a (in the 2 ×2 table, Table 19.1) can be one or a very small number, and it is possible that there are no other drugs with that exact reaction. This means that b is zero and the PRR or POR is not calculable. However, it is possible to use the table for practical purposes in a way that is not exactly statistically rigorous. The second row can refer to all drugs rather than ‘all other drugs’. This means that c is never zero and the POR or PRR is always able to be calculated, and the estimated values are less than they would be otherwise. This conservatism applies when the numbers are small and does no harm when using the PRR or POR for prioritisation.

A more general approach is to ask ‘What is the expected number of reports for this ADR and this drug?’ and then to compare the observed number with the expected number. A first attempt to obtain the expected number is to assume that the proportion of reports for this ADR with this drug will be the same as the proportion for this ADR in the database as a whole, PADR. The expected number can then be obtained using the total reports for this drug, Ndrug:

The deviation of the observed number from the expected number can be expressed as a ratio, that is, the PRR: