PRR computations

When specifying data mining parameters for a run, you can perform PRR and ROR computations. For information about ROR, see ROR computations.

The Proportional Reporting Ratio (PRR) computation relates to drug-event combinations, only, in two-dimensional data mining runs. If you specify a dimension of 3 for the run, the application computes PRR only for the 2D pairs; that is, the drug-event combinations, but not the combinations of one drug and two events, two drugs and one event, three drugs, or three events.

Default PRR computations

If you check Base counts on cases rather than drug-event combinations but no other PRR options, the application computes PRR as follows. If you select a subset variable for the run, the application computes PRR separately for each subset.

1. Assume that observed counts of cases with drug-event combinations are named a through d as follows:

   Type of event	Specific drug	All other drugs
   Specific event	a	b
   All other events	c	d

   • a is the number of cases with the specific event and the specific drug.
   • b is the number of cases with the specific event but not the specific drug.
   • c is the number of cases with the specific drug but not the specific event.
   • d is the total number of cases with neither the specific event nor the specific drug.
2. The PRR for the combination of a particular drug and particular event is computed as follows:

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

   If b=0 (and the Include drug of interest checkbox is not checked), then the formula is adjusted to avoid the possibility of division by zero:

   PRR = ((a+0.5) / ((a+0.5) + (c+0.5))) / ((b+0.5)/((b+0.5) + (d+0.5)))

3. For each cell in the table in step 1, the application computes the expected count as follows:

   Event	Specific drug	All other drugs
   Specific event	E(a) = ((a+b)(a+c))/(a+b+c+d)	E(b) = ((a+b)(b+d))/(a+b+c+d)
   All other events	E(c) = ((c+d)(a+c))/(a+b+c+d)	E(d) = ((c+d)(b+d))/(a+b+c+d)

4. The application computes the chi-square of PRR (PRR_CHISQ) for the combination of a particular drug and particular event as follows, where E represents the expected count under the assumption of no relationship between drugs and events:

   PRR_CHISQ = ((a-E(a))²)/E(a)+ ((b-E(b))²)/E(b)+ ((c-E(c))²)/E(c)+((d-E(d))²)/E(d)

   The P-values for Chi-square values are also computed. The P-value is the probability that Chi-square would be as large as the value for PRR_CHISQ by chance alone if there were no causal relationship or consistent association between the drug and the event.

   Note:

   If any of E(a), E(b), E(c), or E(d) is zero, the Chi-square and P-value cannot be computed and are defined arbitrarily as -1.

Counts based on drug-event combinations

By default, the PRR computation counts the occurrence of cases. On the Data Mining Parameters page, if you clear Base counts on cases rather than drug-event combinations , then a through d represent counts of drug-event combinations. If a case has more than one drug or event, the case supplies several drug-event combinations to the computation. This option is not recommended, especially if data mining results include custom terms or Standardized MedDRA Queries (SMQs).

If you select stratification variables for the data mining run, the application checks Base counts on cases instead of drug-events combinations automatically and cannot be cleared. The PRR calculator also always bases counts on cases.

Drug of interest in comparator set

On the Data Mining Parameters page, if you check For PRR, include drug of interest in the comparator set, then PRR is computed as:

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

Yates correction

On the Data Mining Parameters page, if you check Apply the Yates correction in computing the value of chi-square, then PRR_CHISQUARE is computed as:

PRR_CHISQ = ([max(0, |a - E(a)| - 0.5)]²)/E(a) + ([max(0, |b - E(b)| - 0.5)]²)/E(b) + ([max(0, |c - E(c)| - 0.5)]²)/E(c) + ([max(0, |d - E(d)| - 0.5)]²)/E(d)

Note:

|a - E(a)| = |b - E(b)| = |c - E(c)| = |d - E(d)| for every 2x2 table. This formula can also be expressed as:

PRR_CHISQ = (1/E(a) + 1/E(b) + 1/E(c) + 1/E(d)) [max(0, |a - E(a)| - 0.5)]2

If you select stratification variables for the data mining run, this option is available only if you do not check Use stratified computation for PRR and ROR.

Stratified PRR computation

Even if you select stratification variables for the data mining run, Oracle does not recommend using stratified computation for PRR and ROR. However, on the Data Mining Parameters page you have the option to check Use stratified computation for PRR and ROR. The PRR computation is performed as follows.

If there are K strata, then for stratum k (k = 1, 2, .., K), let ak, bk, ck, dk be the four cell counts in stratum k, and let

• M1k = ak + bk
• M0k= ck + dk
• N1k = ak + ck
• N0k = bk + dk
• T = M0k + M1k = N0k + N1k = ak + bk + ck + dk

PRR = (ΣKakN0k/Tk) / (ΣKbkN1k/Tk)

Note:

If the run uses subsetting, only those strata that contain cases for a given subset are used in the PRR computation for that subset.

The Chi-square statistic for stratified PRR is computed as:

PRR_CHISQ = ΣK(ak - N1k*M1k/Tk)² / ΣK((N0k*N1k*M0k*M1k)/((Tk-1)*T²))

Note:

For instances where the denominator in the PRR or the chi-square formulas would be zero, the computation adds 0.5/K to ak, bk, ck, and dk, where K is the number of strata.