# Validation Case Study – Resource Allocation

Summary

This table summarizes the differences in forecasting accuracy between PBE’s models and the naïve models across the 118 cells. The table shows the weighted-average absolute percent errors for both models. Scripts were used to weight the errors for each cell.

PBE was able to reduce the naïve model error by 75% . We have undertaken a total of 14 such validation exercises and have in each case reduced the naïve model error by 75% to 85%. In other words, this Case Study is far from our best example. As of this writing, we are aware of no one else being able to reduce the naïve model error at all, much less challenge PBE’s standards.

Forecast vs. Actual Filled Rx’s Weighted-Average of 118 Cells
 PBE Models 3.1% Naïve Models 12.4%

A Blinded Forecasting Test To Objectively Determine if it is
Possible to Quantify the Relationship Between Amounts of
Details/Samples and Rx’s at the Individual Doctor Level

Call Value Targeting

Introduction

Pharmaceutical companies are constantly focused on improving the productivity of their detailing and sampling. This is not surprising, since an organization’s sales force is normally its second largest expense item after R & D. Additionally, details and samples are such potent generators of Rx’s that the opportunity cost of failing to fully exploit their potential is enormous.

Companies are increasingly relying on mathematical models that their creators claim quantify the relationship between details and samples on the one hand and filled Rx’s on the other, for each individual doctor. In theory, such models could show how 1,000 representatives might detail and sample with the effectiveness of 1,200 or more — without making more calls.

However, there is a question every user of models should want answered: “Do these models really do what they claim to do?” How does a company know if its models actually quantify the cause and effect of personal selling? Specifically, do the models quantify cause and effect well enough so that, if representatives follow the resulting plans, they will be more productive than they would have been on their own?

In order to determine if anyone could actually quantify cause and effect, an interested party sponsored a shoot out among organizations that claim to be able to forecast at the doctor level. The test was designed to determine if anyone could backup their claim. Five organizations agreed, including PBE, and one later dropped out. Other invitees declined to participate from the outset.

PBE won the shoot-out “hands down”. According to the sponsor, none of the other participants was able to account for the impact of details and samples at all! The Validation Methodology Section of this Case Study explains how the sponsor reached these conclusions. In short, they created a placebo.

The sponsor of the shoot-out has released very little detailed information. However, the Case Study that follows presents highly detailed information from a blinded validation test conducted by a leading pharmaceutical company. This exercise involved only PBE, but the protocol was the same as in the shoot-out. This protocol (which was reviewed by a leading academic) enables any company to quickly determine if and how well a model building methodology finds the relationship between numbers of details and samples on one hand and total filled Rx’s on the other at the individual doctor level for an established brand.

Validation Methodology

A pharmaceutical company provided PBE with monthly, doctor-level detailing and sampling data for 30 consecutive months for one of its brands. The company also provided the corresponding doctor-level prescribing data for only the first 24 of those months. PBE’s mission was to tell the company how many Rx’s each doctor had had filled during the remaining six months that were withheld from PBE. This way, the company was able to immediately validate PBE’s forecasts for each doctor by comparing them to the actual audited Rx’s for these same doctors. By taking advantage of existing data, the company was able to avoid the time and expense of a test market – which would also have forced representatives to adhere strictly to specific call plans.

For purposes of analysis, the doctors were grouped into 120 cells. This was done by segmenting the doctors by 12 levels of market share and 10 levels of prescribing volume. Forecasts were made for each doctor within each cell and these forecasts were then summed to produce a single forecast for each cell. The absolute percent difference between forecasted Rx’s and actual Rx’s was calculated for each cell.

The doctors were grouped into 120 cells for two reasons. First, although 120 numbers are a lot to look at, this is far better than looking at forecasts for tens of thousands of doctors. Second, there is a tremendous amount of random variation in the number of scripts individual doctors write for a brand from one period to the next. This variation is primarily due to the luck of the draw in terms of the number of patients showing up in the office that the doctor considers to be appropriate for a specific drug. Grouping the doctors eliminates most of the effect of this random variation.

Prior to the exercise, it was agreed that the accuracy of PBE’s forecasts would be compared to the accuracy of forecasts produced by a naïve model, i.e., the placebo. The naïve model simply stated that each doctor’s filled Rx’s would increase at the national rate. In this case, Rx’s were flat, so the naïve model assumed that each and every doctor’s prescribing would remain constant.

The naïve model assumes, in effect, that detailing and sampling have no impact on filled Rx’s. Both the client and PBE agreed that any methodology that cannot at least beat the naïve model is worthless at best — and counter-productive at worst.

The sponsor of the shoot-out used this naïve model to determine that PBE had indeed quantified the cause and effect of personal selling which none of the other participants was able to do.

TABLES 1- 4

These tables show the period-to-period changes in detailing and sampling for the brand used in the exercise. PBE has had the opportunity to examine the detailing and sampling of scores of brands. We have consistently observed that there is a large amount of period-to-period variation in detailing and sampling at the individual doctor level even when the national numbers are stable. Such was the case with this brand.

This variation in promotion at the doctor level makes the validation protocol discussed earlier a true test of someone’s ability to model cause and effect well enough to create plans that find hidden profits.

Tables 1, 2, 3 compare detailing activities (Primary, Secondary and Reminder) during the forecasted six months (Period 2) versus the previous six months (Period 1) for every doctor who wrote a script or received promotion during either period. For example, Table 1 shows that 3,939 doctors received exactly three Primary Details during Period 1. (This number is shown in the far right column.) Looking across the corresponding row, one sees that of the 3,939 doctors who received 3 primary details in Period 1 — 1,807 were not detailed at all during Period 2. In fact, fewer than 10% (298) of the doctors who received three primary details during Period 1 received that exact same number in Period 2.

TABLE 5

This table shows the results of PBE’s forecasts versus the naïve model forecasts. For purposes of the exercise, the doctors were grouped 12 ways according to their initial shares and 10 ways according to their prescribing volumes. We then added all the forecasts for doctors within each cell to produce 118 forecasts (2 cells were empty) rather than 134,000 forecasts. The data were looked at the cell level for two reasons. First, grouping the doctors into cells greatly reduces the impact of random variation created by patient visits. Second, aggregating the data makes it much easier to see what was going on.

Here is how to read the table, starting by reading across the first line on Table 5 (CELL 1). This cell has the doctors in the lowest share and volume groups – Group I in both cases. There were 2,404 doctors in this cell and they wrote a total of 2,404 scripts during Period 1. During Period 2, the forecasted period, their scripts jumped to 12,549. PBE had predicted 12,626. PBE’s forecast was off by 0.06%. The naïve model (Period 1 vs. Period 2) which assumed no change, was off by 80%.

 Results of PBE’s Forecasts vs. Naïve Model Forecasts Actual Rx’s Actual Rx’s Predicted Rx’s PBE Error Naïve Error Cell Share Group Volume Group Freq Period 1 Period 2 Period 2 Predicted vs.Actual Period 1 vs.Period 2 1 1 1 2404 2404 12549 12626 0.00613 0.80843 2 1 2 1659 3904 13352 12640 0.05331 0.70763 3 1 3 596 2611 6574 6810 0.03599 0.60281 4 1 4 408 2743 5611 5878 0.04756 0.51113 5 1 5 245 2393 4466 4197 0.06029 0.46421 6 1 6 236 3340 5045 5590 0.10811 0.33793 7 1 7 178 3927 5425 5069 0.06565 0.27613 8 1 8 107 3790 5294 4742 0.10421 0.28409 9 1 9 25 1414 1734 1393 0.19689 0.18454 10 1 10 5 460 516 388 0.24736 0.10853 11 2 1 1865 1865 6307 6762 0.07215 0.70432 12 2 2 2248 5436 13623 13594 0.00215 0.60099 13 2 3 1328 5887 11813 11094 0.06082 0.50163 14 2 4 1292 8863 14859 14226 0.04260 0.40353 15 2 5 868 8580 13165 13516 0.02670 0.34826 16 2 6 923 13063 18757 17485 0.06781 0.30356 17 2 7 846 18681 23953 23004 0.03959 0.22008 18 2 8 898 32204 39452 37278 0.05511 0.18371 19 2 9 671 40776 45465 43848 0.03557 0.10313 20 2 10 298 33128 35724 33806 0.05368 0.07266 21 3 1 998 998 2819 3015 0.06938 0.64602 22 3 2 1745 4258 8620 8980 0.04170 0.50607 23 3 3 1209 5362 8810 8241 0.06464 0.39138 24 3 4 1450 10080 14061 15698 0.11643 0.28308 25 3 5 1068 10582 13991 13659 0.02374 0.24366 26 3 6 1399 19932 25147 24842 0.01213 0.20740 27 3 7 1237 27294 31880 32440 0.01758 0.14384 28 3 8 1299 47023 53566 52420 0.02139 0.12215 29 3 9 1372 84595 90745 87971 0.03057 0.06778 30 3 10 1417 180655 185594 178636 0.03750 0.02662 31 4 1 948 948 2354 2586 0.09867 0.59726 32 4 2 1308 3192 5928 5870 0.00971 0.46161 33 4 3 1021 4544 6342 6729 0.06101 0.28348 34 4 4 1371 9570 11361 11604 0.02136 0.15772 35 4 5 1033 10193 12157 12310 0.01258 0.16161 36 4 6 1387 19842 22829 22421 0.01786 0.13081 37 4 7 1470 32283 35298 33460 0.05206 0.08542 38 4 8 1467 52945 56969 53180 0.06651 0.07063 39 4 9 1429 88134 91007 84928 0.06680 0.03158 40 4 10 2237 328011 323316 311589 0.03627 0.01452 41 5 1 588 588 1149 1538 0.33828 0.48823 42 5 2 951 2326 4082 3697 0.09436 0.43010 43 5 3 812 3602 4776 5141 0.07633 0.24583 44 5 4 1146 8028 8928 10088 0.12989 0.10089 45 5 5 949 9407 10023 11298 0.12715 0.06145 46 5 6 1310 18850 19577 21193 0.08257 0.03714 47 5 7 1392 30751 31044 30838 0.00664 0.00946 48 5 8 1514 54428 53871 53045 0.01534 0.01034 49 5 9 1321 80697 78533 75885 0.03373 0.02755 50 5 10 2280 376893 358270 347064 0.03128 0.05198 51 6 1 323 323 576 720 0.25070 0.43915 52 6 2 743 1878 2918 3118 0.06875 0.35625 53 6 3 604 2697 3171 2977 0.06114 0.14952 54 6 4 866 6006 6543 6878 0.05122 0.08206 55 6 5 682 6759 6702 7040 0.05047 0.00855 56 6 6 1114 16037 17102 16828 0.01602 0.06227 57 6 7 1242 27607 26499 26773 0.01031 0.04181 58 6 8 1248 44517 42100 41535 0.01343 0.05742 59 6 9 985 59863 55760 54668 0.01957 0.07359 60 6 10 1937 354250 332732 320256 0.03750 0.06467 61 7 1 752 752 1449 1393 0.03892 0.48106 62 7 2 1376 3322 4773 4479 0.06169 0.30412 63 7 3 1107 4939 5542 6121 0.10447 0.10867 64 7 4 1456 10156 9492 10310 0.08621 0.06995 65 7 5 1196 11830 10892 11489 0.05479 0.08609 66 7 6 1817 26007 23952 25236 0.05363 0.08580 67 7 7 1958 43195 38686 39996 0.03386 0.11656 68 7 8 2025 72930 65817 65655 0.00246 0.10809 69 7 9 1651 101016 93518 90301 0.03439 0.08019 70 7 10 2696 523590 488898 475539 0.02732 0.07096 71 8 1 450 450 763 710 0.06958 0.41038 72 8 2 1422 3591 4257 4306 0.01136 0.15665 73 8 3 1333 5941 5475 5587 0.02045 0.08522 74 8 4 1773 12386 10753 10870 0.01088 0.15185 75 8 5 1460 14390 11591 11949 0.03086 0.24147 76 8 6 1962 28239 23687 25043 0.05724 0.19216 77 8 7 2205 48433 41165 41708 0.01318 0.17655 78 8 8 2258 80507 66902 68912 0.03004 0.20335 79 8 9 1682 101828 89116 87985 0.01268 0.14265 80 8 10 2684 588252 538877 525613 0.02461 0.09163 81 9 1 1220 1220 1774 2230 0.25722 0.31224 82 9 2 1658 4065 4445 4488 0.00970 0.08542 83 9 3 1520 6714 5556 5204 0.06320 0.20848 84 9 4 2100 14620 10620 10466 0.01444 0.37671 85 9 5 1454 14307 10565 10696 0.01239 0.35425 86 9 6 1864 26569 19885 20219 0.01678 0.33615 87 9 7 1718 37746 28869 29031 0.00559 0.30749 88 9 8 1630 58176 47091 47927 0.01776 0.23541 89 9 9 1179 71621 58923 58759 0.00278 0.21550 90 9 10 1540 358936 324675 324880 0.00063 0.10552 91 10 2 629 1481 1313 1141 0.13081 0.12841 92 10 3 589 2588 2035 1812 0.10941 0.27178 93 10 4 892 6154 3683 3700 0.00460 0.67086 94 10 5 624 6164 3609 3776 0.04633 0.70781 95 10 6 739 10548 7091 6276 0.11485 0.48755 96 10 7 587 12802 8734 9170 0.04994 0.46576 97 10 8 445 15980 11442 11588 0.01276 0.39662 98 10 9 281 16966 14729 13045 0.11430 0.15188 99 10 10 282 54733 46965 45232 0.03690 0.16540 100 11 2 264 792 662 595 0.10088 0.19617 101 11 3 514 2349 1325 1244 0.06129 0.77269 102 11 4 716 4998 2854 2879 0.00878 0.75113 103 11 5 390 3807 2135 2233 0.04585 0.78334 104 11 6 403 5711 3187 3445 0.08106 0.79198 105 11 7 257 5596 3443 3389 0.01582 0.62529 106 11 8 153 5310 3869 3973 0.02681 0.37243 107 11 9 70 4137 3774 3331 0.11735 0.09619 108 11 10 39 7842 5948 6804 0.14386 0.31843 109 12 1 2986 2986 3443 3270 0.05030 0.13270 110 12 2 3434 8197 5872 5659 0.03626 0.39591 111 12 3 1854 8109 4411 4379 0.00715 0.83859 112 12 4 1710 11724 5267 5292 0.00487 1.22597 113 12 5 823 8063 3929 3927 0.00063 1.05216 114 12 6 591 8127 3822 3813 0.00247 1.12633 115 12 7 186 3935 2012 2099 0.04308 0.95581 116 12 8 68 2288 1222 1396 0.14251 0.87229 117 12 9 14 830 603 540 0.10473 0.37647 118 12 10 5 822 685 710 0.03591 0.20000