# Deriving INRs with customized tables.

AFTER A SLOW START, more and more laboratories in this country are reporting prothrombin time results in the form of the international normalized ratio (INR).|1-3~ Some limitations of the system, however, are becoming evident.|4,5~ Ideally, a lab's coagulometer or the laboratory information system (LIS) calculates the INR automatically, but this is often not feasible in smaller rural hospitals, such as the Columbus Community Hospital at which I serve. Budgets are limited; this year's finances did not allow replacing our 8-year-old manual coagulometer, and an LIS is not as necessary for us as it is for larger institutions. Manually calculating INRs at the bench seemed the only solution. * Defining INR. INR is defined as:

INR = |(Patient PT/Average normal PT).sup.ISI~

where the PT is the prothrombin time and the ISI is the international sensitivity index. Note that the average normal PT is the geometric mean of approximately 20 normal people--not the normal control's average PT.|6-9~ The geometric mean is used because the INR model uses a linear relationship between the logarithms of PTs measured with different reagents. Practically, the geometric mean is so near the arithmetic mean that this distinction is not always specified.

While the calculation is not difficult, calculations conducted at the bench should be kept to a minimum to save time and avoid errors. Dividing two numbers and then raising the quotient to a fractional exponent is not something you can easily calculate or verify in your head.
```Figure 1

Manufacturer-supplied INR conversion table

With this method, the PT ratio must be calculated manually.
Rounding is increasingly evident at higher ISI values.

PT ratio ISI ISI ISI ISI ISI ISI
R 1.1 1.2 -- 2.6 2.7 2.8 2.9

1.0 1.00 1.00 -- 1.00 1.00 1.00 1.00
1.1 1.11 1.12 -- 1.28 1.29 1.31 1.32
1.2 1.22 1.24 -- 1.61 1.64 1.67 1.70
1.3 1.33 1.37 -- 1.98 2.03 2.08 2.14
1.4 1.45 1.50 -- 2.40 2.48 2.57 2.65
1.5 1.56 1.63 -- 2.87 2.99 3.11 3.24
1.6 1.68 1.76 -- 3.39 3.56 3.73 3.91
```

* Drawbacks of methods. Calculating each patient's INR with a scientific calculator is one approach. A programmable model minimizes data rekeying. Printed output helps to catch keying errors and provides documentation. Unfortunately, low-cost, printing calculators are usually not programmable and are incapable of fractional exponentiation. A programmable scientific calculator including the optional printer is relatively expensive.

Thromboplastin reagent manufacturers provide a second approach: INR conversion tables. Using a table, however, requires several steps. First, you must divide the patient PT by the average normal PT. Then you must find the table's ISI column value closest to your lab's thromboplastin. Finally, you must look up the approximate INR. These tables eliminate fractional exponentiation, but keying errors are no less likely than with a programmable scientific calculator. Furthermore, reading an INR value from this type of table rounds a patient's INR to an approximate value unless both the quotient of the two PTs and your reagent's ISI match the table exactly. This rounding is particularly noticeable with higher ISI reagents; for ISIs over 2.3, our manufacturer's table gives only two or three INR values in the usual therapeutic range (INR between 2.0 and 3.0). Rounding all therapeutic values to only two values and then reporting them in three digits invites skepticism from clinicians and may result in values outside the acceptable range for both proficiency survey results and future CLIA limits.

Nomograms are a third approach.|10~ They also require dividing patient PT by average normal PT, allowing keying errors. Interpolating more exact values for the PT ratio and ISI is easier than with a table, but the process is more cumbersome, and reading the scale comes with its own potential for error.

* Custom tables are key. Confronted with these drawbacks, I considered creating either a spreadsheet or a dedicated INR program to run on a lab microcomputer. Doing so would have made it easier to catch keying errors, and results could have been printed. Our PCs, however, are not located near the coagulometer and extra training would have been necessary.

Instead, I used a spreadsheet program to print an INR table customized to our lab's average normal PT and thromboplastin's ISI. This eliminated data rekeying and bench calculation.

Further, this system simplified training and makes it easy to look up a PT in seconds given an INR. We use a second customized table when a clinician requests an INR calculation from a PT determined with our previous thromboplastin. This table is marked distinctly and located in another area to avoid confusion with the current table.

Creating a customized INR table is straightforward and can be accomplished with any modern spreadsheet software. Our version has several refinements. The ISI and average normal PT cells print in a larger font to emphasize their critical nature for a customized INR table. INR values are rounded to the nearest decimal. A separate cell located outside the print range sets the amount to increment the prothrombin times. There are several columns on one page, each boxed with lines to enhance readability. Finally, there is also a version that consolidates the prothrombin times column, listing a range of PTs for extremely high INRs.

* Less time, fewer errors. An INR table customized to your laboratory's average normal PT and ISI saves time, eliminates manual calculation at the bench, and simplifies training. The INR table, together with medical and laboratory staff education, made the change to reporting the INR using a lower ISI thromboplastin easier at Columbus Community Hospital.

Even if you are fortunate enough to have a coagulometer or an LIS that automatically calculates the INR, a customized table may be helpful. A customized INR table is also useful when you use an older coagulometer for backup, when your LIS goes down, or when you are asked for the INR from a PT measured before you reported INRs.

INR spreadsheet templates are available for Quattro Pro (Borland International Inc., Scotts Valley, Calif., .WQ1 file format), Excel (Microsoft Corp., Redmond, Wash., .XLS file format), and Lotus 1-2-3 (Lotus Development Corp., Cambridge, Mass., .WKS, .WK1, and .WK3 file formats) for MS-DOS ("IBM")-type computers. If you do not have access to a spreadsheet, I can provide you with a custom table. Please specify disk size and density, and provide your thromboplastin's ISI for your instrument and the geometric mean PT of at least 20 normal people. Include \$5 for shipping and handling. Make checks payable to Wisconsin Pathologists, S.C., 36 S. Brooks St., Madison, WI 53715.

References

1. Ansell JE. Imprecision of prothrombin time monitoring of oral anticoagulation. Am J Clin Pathol. 1992; 98: 237-239.

2. Brigden ML, Preece E. INR: A better way to report prothrombin times. MLO. 1991; 23(12): 25-27.

3. Check W. The INR gaining recognition. CAP Today. March 1993; 7(3): 1, 19-23. 4. Swaim WR. Prothrombin time reporting and the international normalized ratio system--improvements are needed. Am J Clin Pathol. 1993; 99: 653-655.

5. Triplett DA. International normalized ratios--Has their time come? Arch Pathol Lab Med. 1993; 117: 590-592.

6. Foster PA. Problems with the international normalized ratio. Blood. 1992; 80: 2690-2691.

7. Kirkwood TBL. Calibration of reference thromboplastins and standardization of the prothrombin time ratio. Thromb Haemostas. 1983; 49: 238-244.

8. Kirkwood TBL. General aspects of thromboplastin calibration. In: van den Besselaar AMHP, Gralnick HR, Lewis SM, eds. Thromboplastin Calibration and Oral Anticoagulant Control. Boston, Mass: Martinus Nijhoff; 1984: 11-23.

9. Hall R, Malia RG. Medical Laboratory Haematology. 2nd ed. Boston, Mass: Butterworth Heinemann; 1991: 677.

10. Poller L, Hirsh J. A simple system for the derivation of international normalized ratios for the reporting of prothrombin time results with North American thromboplastin reagents. Am J Clin Pathol. 1989; 92: 124-126.

Figure 2

Customized INR table

This table is valid ONLY IF:

* 1.99 = ISI of reagent used in the lab's instrument

* 12.29 = seconds for average normal PT with this reagent and instrument
```Patient PT
(seconds) INR

11.0 0.80
11.1 0.82
11.2 0.83
11.3 0.85
etc. etc.
Patient PT
(second) INR

15.0 1.49
15.1 1.51
15.2 1.53
15.3 1.55
etc. etc.
Patient PT
(seconds) INR

19.0 2.38
19.1 2.40
19.2 2.43
19.3 2.45
etc. etc.
Patient PT
(seconds) INR

23.0 3.48
23.1 3.51
23.2 3.54
23.3 3.57
etc. etc.
```

Figure 3

Customized INR table covering a range of higher prothrombin times

With low ISI reagents, this covers a wide range of PTs in a small table. This table is valid ONLY IF:

* 1.99 = ISI of regent used in the lab's instrument

* 12.29 = seconds for average normal PT with this reagent and instrument
```Patient PT range
(seconds) INR

11.0 0.80
11.1 0.82
11.2 0.83
11.3 0.85
etc. etc.
Patient PT range
(seconds) INR

15.0 1.49
15.1 1.51
15.2 1.53
15.3 1.55
etc. etc.
Patient PT range
(seconds) INR

23.6-23.8 3.69
23.9-24.1 3.79
24.2-24.4 3.88
24.5-24.7 3.98
etc. etc.
Patient PT range
(seconds) INR

38.2-38.5 9.63
38.6-38.9 9.83
39.0-39.4 10.06
39.5-39.9 10.31
etc. etc.
```

James M. Thornbery, M.D. is a pathologist at Columbus Community Hospital, Meriter Hospital, and General Medical Laboratories, Madison, Wis.