Economics of Informed Antibiotic Management and Judicious Use Policies in Animal Agriculture

Abstract

Antibiotic effectiveness can be viewed as a biological commons since one individual's current use may decrease future effectiveness for everyone else. The value of the biological commons declines when the targeted bacteria develop antibiotic resistance. Antibiotic resistance is a global threat to health and development, causing serious economic damage and loss of human lives. The greatest share of antibiotics is used in livestock production, leading to concerns that such use may threaten human health. While various policies are in place to promote judicious use of antibiotics, their effectiveness is unclear. One key challenge in antibiotics management is the uncertainty surrounding various decisions related to antibiotic use, including whether a suspect case has an infection, how likely an infection will spread, and how effective antibiotics can be if used. We develop a disease management model that incorporates linkages among diagnostic testing decisions, antibiotic use decisions, and alternative treatment costs. We show that many unintended consequences may arise from policies designed to promote judicious antibiotic use. Antibiotics and self-tests are complements (substitutes) whenever antibiotic cost is high (low), implying that a self-test subsidy can plausibly increase expected antibiotic use. With regard to a prescription regulation (PR) that switches an antibiotic from over-the-counter to prescription, we show that while PR can reduce therapeutic antibiotic use as intended it may not achieve the social optimum. In a simple real-world application, we find that PR induces excessive veterinary service demand but does not reduce antibiotic use among typical U.S. dairy farms. PR also leads to the substitution of veterinary services for self-tests in obtaining information. We discuss how our analytical framework can be applied to other contexts, including antibiotics for human use.

Appendices

Appendix

A1 Maximization problem in a special case: when veterinary service cost is high, $v > l_{3} - l_{2}$

When facing a veterinary service cost that is sufficiently high (specifically, $v > l_{3} - l_{2}$) to outweigh the loss reduction from veterinary services, the farmer does not prefer veterinary services. As modeled in Fig. 2 in the main text, for this setting all branches related to veterinary services are dominated. Therefore the decision tree can be simplified to be that presented in Fig.7. 

Fig. 7

Decision tree for the test and treatment decisions with high veterinary service cost $v > l_{3} - l_{2}$

Nature plays first and determines the infection types, E or I. Then at information set ① the farmer first decides whether to self-test for infection type (Te). At information set ⑥, ⑦, and ⑨ the farmer makes treatment decisions. When a self-test reveals type E at information set ⑥, the farmer makes antibiotic administration decision. When a self-test reveals type I at information set ⑨, the farmer does not use antibiotics. When no information is purchased at information set ①, then at information set ⑦ the farmer makes antibiotic administration decision.

Backward induction is used to derive optimal strategies. First, at information set ⑥ and ⑦ we solve for optimal antibiotic administration decisions that generate maximum expected payoff. Then at information set ① we solve for optimal self-testing decisions, taking the optimal antibiotic administration decisions as given.

A1.1 Optimal antibiotic decisions

At information set ⑥, a self-test reveals antibiotic to be an effective treatment for the infection at hand. The farmer administers antibiotics whenever,

$$\Phi_{E}^{Te,NC,Tr} > \Phi_{E}^{Te,NC,NTr} ,$$

(A.1)

or

$$b < l_{3} - l_{1} .$$

(A.2)

The farmer administers antibiotics whenever antibiotic cost satisfies inequality (A.2), but not otherwise.⁷

At information set ⑦, the farmer purchases no information about the antibiotic effectiveness in the infection case at hand and then makes the antibiotic administration decision based on the expected value of payoffs across infection types. The farmer administers antibiotics whenever

$$\beta {\kern 1pt} \Phi_{E}^{NTe,NC,Tr} + (1 - \beta )\Phi_{I}^{NTe,NC,Tr} > \beta {\kern 1pt} \Phi_{E}^{NTe,NC,NTr} + (1 - \beta )\Phi_{I}^{NTe,NC,NTr} ,$$

(A.3)

which can be written as

$$b < \beta (l_{3} - l_{1} ).$$

(A.4)

The farmer administers antibiotic whenever inequality (A.4) holds, but not otherwise.⁸

We find two reservation values of antibiotic cost to be important, namely $b_{1} = l_{3} - l_{1}$ and $b_{2} = \beta (l_{3} - l_{1} )$. Reservation values $b_{1}$ and $b_{2}$ are antibiotic costs that make the farmer indifferent between Tr and NTr in scenarios where a self-test reveals type E infection and where no self-test is performed, respectively. The antibiotic cost parameter space is divided into three parts: 1) low antibiotic cost $b < b_{2}$; 2) medium antibiotic cost $b_{2} < b < b_{1}$; 3) high antibiotic cost $b < b_{1}$. The optimal antibiotic administration decisions vary across antibiotic cost levels.

A1.2 Optimal self-testing decisions

When solving for optimal self-testing decisions, we take optimal antibiotic decisions at subsequent information set settings as given. Therefore we need to consider the self-testing decision at three antibiotic cost levels. At the time point when self-testing decisions are made, the farmer is uncertain about infection types. She therefore compares the expected payoffs associated with self-tests and no tests. The expected payoffs are weighted averages of payoffs in different infection cases.

A1.2.1 Low antibiotic cost $b < b_{2}$

The farmer chooses Tr at information sets ⑥ and ⑦. Then she makes self-testing decisions by comparing expected payoffs from self-testing and no test. Thus, the farmer performs a self-test whenever.

$$\beta \Phi_{E}^{Te,NC,Tr} + (1 - \beta )\Phi_{I}^{Te,NC,NTr} > \beta \Phi_{E}^{NTe,NC,Tr} + (1 - \beta )\Phi_{I}^{NTe,NC,Tr} ,$$

(A.5)

which can be written as

$$d < b(1 - \beta ).$$

(A.6)

The farmer performs a self-test whenever inequality (A.6) holds but not otherwise.⁹

A1.2.2 Medium antibiotic cost $b_{2} < b < b_{1}$.

The farmer chooses Tr at information set ⑥ and NTr at information set ⑦. Then she makes self-testing decisions by comparing expected payoffs from self-testing and no test. Thus, the farmer performs a self-test whenever

$$\beta \Phi_{E}^{Te,NC,Tr} + (1 - \beta )\Phi_{I}^{Te,NC,NTr} > \beta \Phi_{E}^{NTe,NC,NTr} + (1 - \beta )\Phi_{I}^{NTe,NC,NTr} ,$$

(A.7)

which can be written as

$$d < \beta (l_{3} - l_{1} - b).$$

(A.8)

The farmer performs a self-test if and only if this inequality holds. ¹⁰

A1.2.3 High antibiotic cost $b > b_{1}$.

The farmer chooses NTr at information sets ⑥ and ⑦. Then she makes self-testing decisions by comparing expected payoffs from self-testing and no test. Thus, the farmer performs a self-test whenever.

$$\beta \Phi_{E}^{Te,NC,NTr} + (1 - \beta )\Phi_{I}^{Te,NC,NTr} > \Phi_{I}^{NTe,NC,NTr} .$$

(A.9)

As antibiotic cost has a positive value, inequality (A.9) does not hold. Therefore the farmer chooses not to perform a self-test.¹¹

Three optimal strategies can arise under high veterinary service cost, $v > l_{3} - l_{2}$. They are:

S1 Do not perform a self-test at information set ①, and treat with antibiotics at information set ⑦.

S2 Perform a self-test at information set ①. In type E infection cases treat with antibiotics (at information set ⑥) while in type I infection cases do not treat with antibiotics (at information set ⑨)

S3 Do not perform a self-test at information set ①, and do not treat with antibiotics at information set ⑦.

We summarize and organize the conditions on cost parameters under which each strategy is optimal. The respective conditions under which S1-S3 are optimal are

$$(S1) \, \left\{ {\begin{array}{*{20}l} {b < \beta (l_{3} - l_{1} )} \hfill \\ {d > b(1 - \beta )} \hfill \\ \end{array} } \right. \,$$

(A.10)

$$(S2) \, \left\{ {\begin{array}{*{20}l} {b < \beta (l_{3} - l_{1} )} \hfill \\ {d < b(1 - \beta )} \hfill \\ \end{array} } \right.{\text{ or}}\left\{ {\begin{array}{*{20}l} {b > \beta (l_{3} - l_{1} )} \hfill \\ {b < l_{3} - l_{1} } \hfill \\ {d < \beta (l_{3} - l_{1} - b)} \hfill \\ \end{array} } \right. \,$$

(A.11)

$$S3 \, \left\{ {\begin{array}{*{20}l} {b > \beta (l_{3} - l_{1} )} \hfill \\ {b < l_{3} - l_{1} } \hfill \\ {d > \beta (l_{3} - l_{1} - b)} \hfill \\ \end{array} } \right.{\text{ or }}b > l_{3} - l_{1}$$

(A.12)

Figure 3 in the main text presents the optimal strategies in cost parameter b-d plane, by holding veterinary service cost $v$ fixed at a high level (i.e., $v > l_{3} - l_{2}$). Boundary condition $d = b(1 - \beta )$ is depicted as the upward sloping line, boundary condition $d = \beta (l_{3} - l_{1} - b)$ is depicted as the downward sloping line, and boundary condition $b = \beta (l_{3} - l_{1} )$ is depicted as the vertical line. Note that the three boundary lines intersect at the same point $(\beta (l_{3} - l_{2} ),\beta (1 - \beta )(l_{3} - l_{2} ))$ in the b-d plane. In the main text we give a more detailed explanation of Fig. 3.

A2 Dairy survey data statistics

During the summer of 2017, a stratified design survey was circulated to dairy producers. Feng et al. (2018) provide some details on survey design. The response rate was 17% and a total of 660 useable surveys were received, accounting for about 4% of all registered dairy herds in these states. The survey consisted of three parts. Parts I and II of the survey inquired about farm resources, farmer demographics, overall views on the milk production business environment, and farmer expansion/contraction plans for the next three years. Antibiotic use and management behaviors, as well as perceived advantages and costs, were all investigated in Part III. Table

Table 4 Descriptive statistics of costs to producers’ herds for a mastitis case in the survey data

4 summarizes producer-level data on costs due to a mastitis case.

A3 Empirically parameterized model

We extrapolate possible values for parameters in our model from the survey data and the available literature. Table

Table 5 Description of assumed costs (baseline) as well as an increase/decrease of 20% scenarios

5 summarizes parameter values in a baseline scenario and scenarios where an increase or a decrease of 20% in parameters occurs.

For self-test cost, we use the median diagnosis cost in our dataset as the baseline level, i.e., $d = \$ 5$. This is also a reasonable value compared with estimates in the literature ($6 in Pinzón-Sánchez et al. (2011); $10 in Cha et al. (2011)). We asked about therapeutics cost in the dairy survey where therapeutics cost can include antibiotic cost but also some other veterinary drugs as well. The median therapeutics cost in our dataset is $30 and is higher than the antibiotic cost estimated in literature ($7–$25 in Ruegg (2020); $4–$8 in Cha et al. (2011); $6.75 in Pinzón-Sánchez et al. (2011)). Therefore we infer from the survey dataset and literature that $b = \$ 10$ is a reasonable antibiotic cost. To be consistent with our assumptions, the veterinary service cost estimate should include hourly rates paid for veterinarians and costs associated with alternative treatment. The median veterinary service cost is $12 in the dataset. This is viewed as a reasonable number given that U.S. Department of Agriculture (2016) estimates veterinary service cost associated with a mastitis case on dairy farms to be in the $1.45–$9.21 range. Cha et al. (2011) estimate the cost of treatment other than antibiotics to be $15.5. We combine veterinary service cost ($12) and other treatment costs ($15.5) and assume veterinary service cost parameter d to be $27.5. This estimate is comparable to the numbers provided ($19.16 ± 15.27) in Liang et al. (2017).

Parameter $\beta$ indicates the probability that mastitis occurs for which antibiotic treatment is effective. For most cases, antibiotics should be used to treat mastitis caused by gram-positive pathogens, while farmers should avoid antibiotic use for mastitis caused by gram-negative pathogens or when no pathogens are recovered. The incidence of mastitis caused by gram-positive pathogens is assumed to be 35% (Pinzón-Sánchez et al. 2011).

Labor and non-saleable milk costs are inevitable for a mastitis case even when antibiotics cure the mastitis case, while other losses such as death loss, loss from future milk production, loss from premature culling and loss from future reproduction are more likely to occur when the mastitis case is not treated effectively. Therefore we use the sum of median labor cost ($15) and median non-saleable milk cost ($80) to parameterize $l_{1}$ while we add all costs and losses incurred in a mastitis case to parameterize $l_{3}$. Median total cost is $630. Logic requires that $l_{2}$ be greater than $l_{1}$ but less than $l_{3}$. When we parameterize $l_{2}$, we should ensure it satisfies the assumption we made in Sect. 3.1 in the main manuscript, i.e., $l_{2} - l_{1} < \beta (l_{3} - l_{1} )$. Thus, $l_{2} \in (\$ 95,{\kern 1pt} \,{\kern 1pt} \$ 282.25)$. We assume $l_{2} = \$ 150$ as a baseline level. Economic losses assumed are comparable to estimates in the literature (Cha et al. 2011; Liang et al. 2017; Ruegg 2020).

While many agree that antibiotic use in agriculture is a critical contributor to antibiotic resistance (Ma et al. 2021), the magnitude of its threat to human health has been insufficiently investigated (Chang et al. 2015; Dadgostar 2019; He et al. 2020). Lacking conclusive estimates in previous literature, we develop informed speculative estimates of the resistance cost that may be attributed to agricultural antibiotic use.

The estimation proceeds in steps. First we estimate total cost of antibiotic resistance in the United States, where such cost measurements are widely viewed as being both country-specific and difficult to arrive at (Murray et al. 2022; Pulingam et al. 2022; Tillotson and Zinner 2017). Our estimate consists of three parts: death due to antibiotic resistance, losses of extra health care cost incurred, and economic losses due to lost productivity. Antibiotic resistance causes 35,900 deaths, $20 billion (in 2008 dollars) in extra health care costs and $35 billion economic losses due to lost productivity annually (US CDC 2013). To place a monetary value on death caused by antibiotic resistance, we multiply the number of deaths, 35,900, by the value of a statistical life estimate $11.1 million (in 2015 dollars) (Kniesner and Viscusi 2019; US CDC 2019). Before summing up the three components of antibiotic resistance cost, we need to use an inflation factor to adjust the values of economic losses from 2008 to 2015. In 2009–2015, the U.S. inflation rate was − 0.36%, 1.64%, 3.16%, 2.07%, 1.46%, 1.62%, 0.12% respectively. We convert the inflation rate into a factor by adding 1 to each rate and then multiply these factors to get the cumulative inflation factor which is calculated to be 1.1. Then the values of economic losses in 2008 dollars multiplied by this cumulative inflation factor are the values of economic losses in 2015 dollars. Therefore, total cost is (20 + 35)*1.1 (inflation factor) + 11.1*35.9 = $459 billion (in 2015 dollars). Our total cost estimate is very likely to be downward biased because we do not include secondary external social cost¹² induced by resistance (Dadgostar 2019; Tillotson and Zinner 2017).

The next step is to estimate how much agricultural antibiotic use contributes to resistance cost. Since previous quantitative research findings provide no reliable estimates of resistance cost attributable to agriculture (Chang et al. 2015), we tentatively assume that 5% of the total cost can be attributed to antibiotic use in livestock production. This number is arrived at by considering the following statements that are generally valid for the United States. The livestock farming community is not spatially well connected with major population bases. Also large livestock farms follow biosecurity protocols intent on preventing the spread of bacteria into and out of farms. Lastly, waste and runoff from livestock farms is generally contained and filtered by soils. Therefore we assume a relatively low antibiotic resistance cost as a result of on-farm antibiotic use. Total sales of antibiotics in livestock production in 2020 was 10,449,476 kg where MI antibiotics account for 57% of total sales in that year (US FDA 2021b). Assuming that the impact of MI antibiotics and N-MI antibiotics on resistance development are homogenous, we estimate the antibiotic resistance cost associated with 1 kg MI antibiotic use in animals to be $2,196. This figure is calculated as 459*10⁹*5%/10,449,476. Assuming that antibiotic resistance arising from N-MI antibiotic use can be ignored, we estimate the antibiotic resistance cost associated with 1 kg MI antibiotic use in animals to be $3,853. This figure is calculated as 459*10⁹*5%/(10,449,476*57%). We infer that the amount of antibiotic use in a mastitis case is about 1 g (Ruegg 2020). Therefore antibiotic resistance cost associated with antibiotic use in one mastitis case is estimated to be in the $2.2–$3.9 range.

Using these parameter values, we can indicate which scenario is most likely relevant to practices on U.S. dairy farms. We find that it is optimal for an unregulated farmer to self-test to obtain information. For revealed type E infection farmers administer OTC antibiotics while for revealed type I infection they call a veterinarian but do not use antibiotics. PR does not decrease antibiotic use but instead substitutes veterinary services for self-tests in obtaining information. Dairy farmers’ optimal strategy without regulations attains the social optimum. Therefore, PR causes excessive demand for veterinary services but does not decrease antibiotic use among typical dairy farmers.

In order to perform robustness checks, we also examine how an increase or decrease of 20% in each of these parameters affects the impact of PR. Table 5 presents the values of parameters used for robustness checks. The findings are robust when we increase or decrease parameter values by 20%.