Probability-based forecasting for U.S. generic drug sales

Introduction

Although they may not be consciously aware of it, marketers and market forecasters tend to think in terms of continuous variables. For example, when someone asks the value of 1, 5, or 10 share points, they are operating on an unstated assumption that a product’s share can take any value between zero and one. This assumption holds true in markets made up of many independent, incremental customer buying decisions, each of which is too small to substantially affect total sales. With some caveats, it is a reasonable representation of the brand drug environment where activity is composed of numerous, independent prescribing decisions made by a large number of physicians, any one of whom represents a small portion of the overall business.

There are, however, many situations where the assumptions required for continuous variable modeling do not hold up. One relatively well-known example is the market for large passenger airliners where manufacturers compete for just a small number of high-value contracts from the handful of global airlines that need and can afford new airplanes. In such cases, rather than using a continuous variable approach, market share needs to be modeled as the combined outcome of n binary (yes/no) decisions where n is the number of potential contracts available.

Based on our experience, the market for generic drugs in the United States is, if anything, more binary in nature than the commercial airliner industry. The reason for this is that, while physicians choose which active ingredient gets prescribed, the company whose product gets dispensed at the pharmacy is a function of decisions made by a very small number of large wholesalers and pharmacy chains. A single one of these buyers might control 25% or more of a market and, with the exception of very high-volume generics, these purchasers tend to select a single primary supplier who will get all or nearly all of that company’s business.

As a result, models suggesting that generic business can be won or lost in single or half share point increments are unrealistic. They are also potentially dangerous in that they underestimate the importance of every single purchase decision: a brand drug company that lost the business of the category’s highest prescribing physician would not suffer nearly the same impact as a generic company that lost a major distributor contract. To ensure that this reality is represented, forecasters need to construct models that accurately simulate a small number of binary rather than a large number of continuous buying decisions.

Standard spreadsheet models are problematic for binary modeling of this type. For example, think of a situation where buying decisions are made independently by five distributors, each of which controls access to a different percentage of the market. Each distributor will also award a primary and secondary contract meaning that there are a total of 10 contracts being put out for bid (again, with each representing a different level of business for the winner). Even in a relatively simple example like this, the generic supplier faces 1024 potential primary–secondary/win–loss outcomes. When we consider that a forecaster using a regular spreadsheet would have to change each variable individually and record the results of each permutation, we can start to see why handling the bidding process as a continuous variable is a more common approach; it is much easier to judge the outcome of an additional share point than to run through all the binary permutations. Fortunately, the use of probability-based techniques such as Monte Carlo analysis (MCA) allow forecasters to construct the model and then rely on computing power to calculate the outcomes of the various permutation. To illustrate how vast the differences between a continuous and binary variable approach can be in markets that have a small number of buyers, our company did just that. The results are discussed below.

Structure of US pharmaceutical distribution

Figure 1 below shows US pharmaceutical wholesaler market share as of 2011. It clearly demonstrates the disparity between the conditions for use of a continuous variable-based forecast (i.e. many independent, incremental buying decisions, each of which is too small to substantially affect total sales) and the reality faced by generic drug companies (i.e. three wholesalers controlling almost 90% of the market and large number of very small companies servicing the other 10%). OPEN IN VIEWER

Modeling generic drug sales

Based on the data in Figure 1, we constructed a standard spreadsheet model with the following parameters:

There are 13 wholesalers in total.

Other parameters of the model are as follows:

The generic molecule under consideration has combined (all entrants) sales of US$100 million annually.

Table 1 provides a summary of the basic (pre-Monte Carlo) model from the perspective of a single generic manufacturer. (This version has five entrants but we will vary this in the MCA.) As shown, based on the probabilities and other conditions outlined above, the company’s expected sales value is US$20 million, which is also the same amount that would be expected by the other four entrants. Even before we proceed to the probability-based approach, we can see that not only is this unlikely—it is actually impossible under the outlined parameters because the smallest of the primary Big 3 wholesaler contracts is worth US$23.75 million and, without a Big 3 contract, a supplier could not earn more than US$14.5 million, even if they won all other available bids. In other words, our generic company can get no closer to the expected value than US$9.25 million less or US$3.75 million more.

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Table 1.

Initial generic drug sales forecast (expected value method)

Parameters
Generic market size in $			100,000,000
Number of entrants			5
Probability of winning primary supply contract			20%
Probability of winning secondary supply contract			20%
% of each wholesaler business to primary supplier			95%
% of each wholesaler’s business to secondary supplier			5%
Wholesaler	Market share controlled (%)	Value of primary position	Value of secondary position	Expected value of primary supply contract	Expected value of secondary supply contract	Total expected value
Wholesaler 1	35.00	33,250,000	1,750,000	6,650,000	350,000	7,000,000
Wholesaler 2	30.00	28,500,000	1,500,000	5,700,000	300,000	6,000,000
Wholesaler 3	25.00	23,750,000	1,250,000	4,750,000	250,000	5,000,000
Wholesaler 4	3.50	3,325,000	175,000	665,000	35,000	700,000
Wholesaler 5	2.50	2,375,000	125,000	475,000	25,000	500,000
Wholesaler 6	1.25	1,187,500	62,500	237,500	12,500	250,000
Wholesaler 7	1.00	950,000	50,000	190,000	10,000	200,000
Wholesaler 8	0.75	712,500	37,500	142,500	7,500	150,000
Wholesaler 9	0.40	380,000	20,000	76,000	4,000	80,000
Wholesaler 10	0.30	285,000	15,000	57,000	3,000	60,000
Wholesaler 11	0.15	142,500	7,500	28,500	1,500	30,000
Wholesaler 12	0.10	95,000	5,000	19,000	1,000	20,000
Wholesaler 13	0.05	47,500	2,500	9,500	500	10,000
Total	100.00	95,000,000	5,000,000	19,000,000	1,000,000	20,000,000

About probability-based forecasting

Having seen why the continuous variable and expected value approaches are unsuited for generic drug sales forecasting, we will now demonstrate why probability-based methods are more appropriate for the task. Toward this end, a little background on MCA is in order. Readers who are more interested in how the structure of the wholesaler system affects generic sales than in the mechanics of the modeling process may wish to skip ahead to the “Forecast results” section.

As we know, standard spreadsheet models provide a single figure or figures representing what is believed to be the most likely outcome. No matter how well-built the model or how high the quality of data used, the probability of getting the same results in the real world is extremely low (and sometimes, as we have seen in the preceding example, mathematically impossible). In recognition of this, many models also include best- and worst-case scenarios. However, the boundaries for these scenarios tend to be arbitrarily selected and assume that everything will go right or everything will go wrong—again, a rare outcome in reality.

Unlike these techniques, MCA replaces single-point estimates with probability distribution functions, thereby allowing for realistic incorporation of risk and uncertainty into forecasting models. After probability distributions have been assigned to the parameters, the model is then calculated and recalculated hundreds or thousands of times, with each iteration having a different set of randomly generated values derived from the probability functions. As these randomly generated distribution values interact with each other, they ripple throughout the model showing outcomes for the entire spectrum of possible outcomes. The results provide decision-makers with a wide range of feasible outcomes and their probabilities of occurrence.

Expressed a little differently, spreadsheets allow us to change one variable at a time in order to assess its impact on the model: for example, “what happens if we raise the price 5%?” In contrast, MCA changes all the variables simultaneously on each iteration: for example, “what happens if we raise the price 5% and price sensitivity is 2% higher than we expected and the economy enters a recession?” The next iteration might answer the question: “what happens if we raise the price 3% and price sensitivity is 10% lower than expected and the economy experiences flat growth?” This process is repeated over and over again until all feasible values and combinations of values have been tested and recorded for analysis.

Simple MCAs can be performed by using Microsoft Excel’s RAND and RANDBETWEEN functions in combination with other standard formulas. For example, the binary analysis described below could be performed by using RAND to generate a random number between 0 and 1; in a separate cell, an IF statement could be written that returns a value of 0 or 1 depending on the value of the randomly generated number. Assuming that there is a 25% probability of winning a contract, then the IF cell would return 1 if the randomly generated value was less than or equal to 0.25 and 0 if the value was greater than 0.25. Similar formulas would be constructed for each of the available contracts, the 0 and 1 contract win values would be multiplied by the value of each contract, etc. Additional IF statements could be added to reflect the modeling rules that allow for suppliers to win only one contract per wholesaler and preference for larger over smaller contracts.

This approach would represent a single iteration of the model which is of limited value in a Monte Carlo context; it is akin to determining the probability distribution of a coin toss by flipping the coin once. This problem can be overcome by copying the formulas hundreds or thousands of times and then analyzing the results in the aggregate. Although this would not be particularly difficult with the current scenario, commercially available software packages that work as spreadsheet add-ins are recommended for more complex modeling scenarios.

Creating the probability-based model

The modeling parameters are left unchanged in the MCA. To incorporate the probability element, we employed a commercial software package (Palisade Software’s @Risk, which works as an add-in to Microsoft Excel) but the process is similar to the one described above: i.e. a column simulating the binary outcome of each contract was added; the cells in this column can take win (1) or loss (0) values based on the probability of winning each contract. These win/loss results are multiplied by the value of the contract in question, and the sum of contracts won equals the company’s total sales.

To ensure that the probabilities associated with the range of contract win/loss combinations were captured, the model was then run through 10,000 iterations. (Note that each time these iterations return a distinct set of contract wins and losses is equivalent to the results that would be generated by a forecaster manually running through possible permutations of the variables.) Total sales as well as number and type of contracts won were captured as output variables. This process was repeated for scenarios with two contracts and 3, 4, 5, and 10 generic entrants. In addition, we performed a similar analysis for scenarios where there are three contracts, and each wholesaler’s business is allocated 80% to the primary, 15% to the secondary, and 5% to the tertiary supplier.

Forecast results

Percentile breakdown of generic drug revenues with 2 and 3 wholesaler contracts

The preceding charts demonstrate the market’s binary nature but it is difficult to evaluate the actual probabilities of achieving a certain revenue level using the charts alone. This shortcoming is addressed by the percentile breakout in Table 2, which shows probabilities of earning up to a certain level of revenue based on the number of contracts and competitors present in the market.

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Table 2.

Percentile breakout of generic drug revenues by number of wholesaler contracts and competitors

Percentile	3 entrants	4 entrants	5 entrants	10 entrants
2 Contracts available
10th	3,548	1,773	963	20
20th	5,742	3,210	1,947	145
30th	23,953	4,770	3,089	505
40th	29,118	7,677	4,440	1,250
50th	32,023	27,351	7,273	1,820
60th	35,220	30,471	27,209	2,935
70th	38,838	34,011	30,796	4,826
80th	57,581	37,240	34,591	27,090
90th	63,768	58,037	52,466	33,265
99th	90,080	87,400	67,421	60,708
3 Contracts available
10th	9,394	3,598	2,115	165
20th	12,168	6,027	3,935	585
30th	24,439	8,526	5,752	1,328
40th	28,897	12,612	7,842	2,162
50th	31,808	24,906	12,980	3,785
60th	34,322	28,321	24,812	5,339
70th	37,501	31,061	28,228	8,542
80th	51,082	34,921	31,095	24,125
90th	55,888	50,909	44,223	28,363
99th	76,163	73,098	59,289	52,173

Discussion

To fully appreciate the value of MCA in this application, it may help to note that there are theoretically more than one million possible win/loss permutations with the two-contract scenario and more than one billion with the three-contract scenario. In practice, the condition that requires generic suppliers to always take the best contract available would reduce these numbers but tracking allowed permutations one by one would still be well beyond the capabilities of a standard spreadsheet model (or the patience of the spreadsheet modeler).

There are some limitations to the preceding analysis. First, the wholesaler share data on which the analysis is based are derived from the overall US pharmaceutical market and, as a result, includes brand and specialty drug distribution, which may differ somewhat from generic-only distributor share figures. Of greater importance is the fact that our model is not a perfect reflection of the environment it seeks to represent. For example, we have not accounted for the impact of price on probability of contract wins or revenues. Price is of paramount importance in actual wholesaler decision-making. In practice, optimal pricing strategy can be readily incorporated into a probability-based model but addressing it here would add an additional layer of complexity to this discussion, the primary purpose of which is to demonstrate the binary nature of the US generic market and the forecasting implications of this.

Aside from ignoring prices, the most notable difference between our model and the real world may be the model parameter that competitors have an equal chance of winning contracts. In the real world, some firms possess advantages arising from quality, reputation, service, and personal relationships between the wholesaler and the generic company, as well as other possible points of competitive differentiation. Our company’s experience, however, suggests that these factors are of modest importance; in general, once the FDA has approved the drug, generics are viewed as commodity products where price is the deciding factor and other considerations only come into play in “all other things being equal” situations.

In addition, the figures shown here are based on the results from 10,000 iterations of the MCA model, collectively known as a simulation. Because there is variability at the iteration level, there can also be variability at the simulation level, as a result of which another simulation of 10,000 iterations might return slightly different probabilities. This is more of a problem with models that have higher inherent variability and when the simulation is based on relatively few iterations. Because our choices are constricted to yes/no contract wins and the simulation consists of 10,000 iterations, the variability between the results shown here and another simulation would be very small.

Despite these limitations, we believe that both the model parameters and results are a reasonable representation of the situation facing generic drug manufacturers in the United States. Provided that the model conditions described earlier hold true, the results shown here (particularly, the percentile and sales data in Table 2) can be applied to other generic markets by scaling up or down from US$100 million. Put differently, revenue probabilities in a US$50 million market would be half the levels shown in Table 2 or twice these levels in a US$200 million market.

This analysis demonstrates that, at least from the manufacturer’s perspective, sales of generic drugs in the United States are determined by a relatively small number of wholesaler contracts that are either won or lost in totality. Furthermore, while the number of total contracts is limited, commercial success or failure will likely be dictated by the outcome of a much smaller number of large-scale contracts. As a result, the shape of the revenue distribution curve is substantially different than would be the case for a continuous variable market. Although situations with multiple binary variables are difficult to model using standard spreadsheet techniques, probability-based approaches such as MCA are well-suited for these tasks. Applied to a hypothetical generic drug market, MCA reveals the four-cluster nature of revenue distribution and the impact of competition on the probabilities associated with achieving various sales levels.

Given that the category now accounts for more than 80% of all dispensed prescriptions, generics are the pharmaceutical industry’s most widespread example of a binary market. However, the technique discussed here has application for other types of drug marketing as well. Examples include hospital pharmaceuticals, particularly in cases where a small number of trauma or children’s hospitals make up the majority of the market and sectors where group purchasing organizations play a major role in controlling access.