The effects of detailing on prescribing decisions under quality uncertainty

Abstract

Motivated by recent empirical findings on the relationship between new clinical evidence and the effectiveness of detailing, this paper develops a new structural model of detailing and prescribing decisions under the environment where both manufacturers and physicians are uncertain about drug qualities. Our model assumes (1) a representative opinion leader is responsible for updating the prior belief about the quality of drugs via consumption experiences and clinical trial outcomes, and (2) manufacturers use detailing as a means to build/maintain the measure of physicians who are informed of the current information sets. Unlike previous learning models with informative detailing, our model directly links the effectiveness of detailing to the current information sets and the measures of well-informed physicians. To illustrate the empirical implications of the new model, we estimate our model using a product level panel data on sales volume, prices, detailing minutes, and clinical trial outcomes for ACE-inhibitors with diuretics in Canada. Using our estimates, we demonstrate how the effectiveness of detailing depends on the information sets and the measures of well-informed physicians. Furthermore, we conduct a policy experiment to examine how a public awareness campaign, which encourages physicians/patients to report their drug experiences, would affect managerial incentives to detail. The results demonstrate that the empirical and managerial implications of our model can be very different from those of previous models. We argue that our results point out the importance of developing a structural model that captures the mechanism of how detailing/advertising conveys information in the market under study.

Appendices

Appendix A: Identification

1.1 A.1 Learning parameters

In this appendix, we show how learning parameters are identified in our model. Given our functional form assumption on the utility function, the subutility associated with the expected quality and perceived variance for informed physicians is written as

$$ - \exp(-r E[q_j|I(t)] + \frac{1}{2}r^2(\sigma_j^2(t)+\sigma_\delta^2)). $$

At time t, the expected quality and perceived variance given the past consumption and clinical trial signals are expressed as

$$\begin{array}{lll} E[q_j|I(t)] &=& \frac{\sigma_\delta^2\sigma_\eta^2 \underline{q}_j + \sigma_\eta^2\underline{\sigma}_j^2\sum_{s=1}^{N_{jt-1}} \mu_{js}^e + \underline{\sigma}_j^2 \sigma_\delta^2 \sum_{s=1}^{N_{jt-1}^c} \mu_{js}^c} {\sigma_\delta^2\sigma_\eta^2 + \sigma_\eta^2\underline{\sigma}_j^2 N_{jt-1} + \underline{\sigma}_j^2\sigma_\delta^2 N_{jt-1}^c}\\ \sigma_j^2(t) &=& \frac{\underline{\sigma}_j^2\sigma_\delta^2\sigma_\eta^2}{\sigma_\delta^2\sigma_\eta^2 + \sigma_\eta^2\underline{\sigma}_j^2 N_{jt-1} + \underline{\sigma}_j^2\sigma_\delta^2 N_{jt-1}^c}, \end{array}$$

where $\sigma_\delta^2$ is the signal variance for consumption signals, $\sigma_\eta^2$ is the signal variance for clinical trial signals, $\underline{q}_j$ is the initial mean quality for drug j, $\underline{\sigma}_j^2$ is the initial perceived variance for drug j,¹⁹ N _jt is the cumulative number of consumption signals for drug j at time t, $N_{jt}^c$ is the cumulative number of clinical trial signals for drug j at time t, and $\mu_{js}^e$ and $\mu_{js}^c$ are the sth consumption and clinical trial signals for drug j, respectively. Note that $\mu_{js}^e=q_j+\sigma_\delta\delta_{js}$ and $\mu_{js}^c = q_j+\sigma_\eta\eta_{js}$ where q _j is the true mean quality for drug j, and δ _js and η _js are signal noises. Thus, for the subutility function, the terms inside the exponential function above can be rewritten as

$$\begin{array}{lll} \lefteqn{r E[q_j|I(t)] - \frac{1}{2}r^2(\sigma_j^2(t)+\sigma_\delta^2) }\\ &=& \frac{r(\sigma_\delta^2\sigma_\eta^2 \underline{q}_j + \sigma_\eta^2\underline{\sigma}_j^2\sum_{s=1}^{N_{jt-1}} (q_j+\sigma_\delta\delta_{js}) + \underline{\sigma}_j^2 \sigma_\delta^2 \sum_{s=1}^{N_{jt-1}^c} (q_j+\sigma_\eta\eta_{js}))}{\sigma_\delta^2\sigma_\eta^2 + \sigma_\eta^2\underline{\sigma}_j^2 N_{jt-1} + \underline{\sigma}_j^2\sigma_\delta^2 N_{jt-1}^c}\\ &&-\frac{\frac{1}{2}r^2(\underline{\sigma}_j^2\sigma_\delta^2\sigma_\eta^2+\sigma_\delta^2(\sigma_\delta^2\sigma_\eta^2 + \sigma_\eta^2\underline{\sigma}_j^2 N_{jt-1} + \underline{\sigma}_j^2\sigma_\delta^2 N_{jt-1}^c))}{\sigma_\delta^2\sigma_\eta^2 + \sigma_\eta^2\underline{\sigma}_j^2 N_{jt-1} + \underline{\sigma}_j^2\sigma_\delta^2 N_{jt-1}^c}\\ &=& \frac{\sigma_\delta^2\sigma_\eta^2(r\underline{q}_j - \frac{1}{2}r^2(\underline{\sigma}_j^2+\sigma_\delta^2))}{\sigma_\delta^2\sigma_\eta^2 +\sigma_\eta^2\underline{\sigma}_j^2 N_{jt-1} + \underline{\sigma}_j^2\sigma_\delta^2 N_{jt-1}^c} + \frac{\sigma_\eta^2\underline{\sigma}_j^2(rq_j-\frac{1}{2}r^2\sigma_\delta^2)}{\sigma_\delta^2\sigma_\eta^2 + \sigma_\eta^2\underline{\sigma}_j^2 N_{jt-1} + \underline{\sigma}_j^2\sigma_\delta^2 N_{jt-1}^c}N_{jt-1}\\ &&+ \frac{\underline{\sigma}_j^2\sigma_\delta^2(rq_j-\frac{1}{2}r^2\sigma_\delta^2)}{\sigma_\delta^2\sigma_\eta^2 + \sigma_\eta^2\underline{\sigma}_j^2 N_{jt-1} + \underline{\sigma}_j^2\sigma_\delta^2 N_{jt-1}^c}N_{jt-1}^c \\&&+ \frac{r\underline{\sigma}_j^2\sigma_\delta\sigma_\eta \left(\sigma_\eta\sum_{s=1}^{N_{jt-1}}\delta_{js}+\sigma_\delta\sum_{s=1}^{N_{jt-1}^c}\eta_{js}\right)}{\sigma_\delta^2\sigma_\eta^2 + \sigma_\eta^2\underline{\sigma}_j^2 N_{jt-1} + \underline{\sigma}_j^2\sigma_\delta^2 N_{jt-1}^c} \end{array}$$

The nonlinear expression above implies that the variations in N _jt and $N_{jt}^c$ across periods identify $\underline{\sigma}_j^2\sigma_\delta^2$, $\sigma_\delta^2\sigma_\eta^2$, $\sigma_\eta^2\underline{\sigma}_j^2$, and the following three parts:

$$ \sigma_\delta^2\sigma_\eta^2(r\underline{q}_j - \frac{1}{2}r^2(\underline{\sigma}_j^2+\sigma_\delta^2)), \;\;\;\; \sigma_\eta^2\underline{\sigma}_j^2(rq_j-\frac{1}{2}r^2\sigma_\delta^2), \;\;\;\; \underline{\sigma}_j^2\sigma_\delta^2(rq_j-\frac{1}{2}r^2\sigma_\delta^2). $$

We can thus pin down $\underline{\sigma}_j^2$, $\sigma_\delta^2$, and $\sigma_\eta^2$. It is clear that we cannot separately identify r, $\underline{q}_j$, and q _j . In our application, we normalize q ₁ = 1. This allows us to pin down r and $\underline{q}_j$. Note that since r is common across drugs, we only need to fix the true mean quality for one of the drugs.

Coscelli and Shum (2004) argue that under their functional form assumption on the utility function, $\underline{\sigma}_j$ and r cannot be separately identified. Thus, they consider two alternative normalizations: (1) assume consumers are risk neutral, (2) assume the initial prior mean quality is equal to the true mean quality for all drugs (rational expectation assumption). Our identification requirements are slightly different from Coscelli and Shum (2004) because they assume utility is linear in the expected quality and perceived variance whereas we assume a CARA specification.

1.2 A.2 β ₀, β ₁ and φ _G

It is worth discussing the identification of β ₁ and φ _G (the parameters that determine M). It may first appear that it is hard to separately identify them, because intuitively the effect on M due to an increase in β ₁ (which captures the role of building up M) could be canceled by increasing φ _G (which captures the depreciation rate of M) appropriately. However, a more careful examination of Eqs. (7) and (8) reveals that there are subtle differences in terms of how M is generated by β ₁ and φ _G . Notice that for each M _jt , there is a unique (β ₀ + β ₁ G _jt ) which can be written as

$$ \beta_0 + \beta_1\left(\sum\limits_{\tau=1}^{t-1}(1-\phi_G)^{t-\tau}D_{j\tau}\right) + \beta_1D_{jt}. $$

It should be clear that the variation in D _jt across time and drugs would be sufficient to identify β ₀, β ₁ and φ _G . Intuitively, as long as we have more than three observations, there will be overidentifying restrictions that allow us to estimate these three parameters.

Appendix B: Incorporating the outcome of clinical trials in Bayesian updating

In this appendix, we show how to draw a quality signal from a direct comparison clinical trial. Each clinical trial tells us: (1) which drug does better in the trial, (2) the number of participants who take each drug (i.e., $n_j^c$, for j = 1,2). How do we simulate a draw of $\bar{q}^c_j$, for j = 1,2? Let’s first define $\Delta \bar{q}^c\equiv \bar{q}^c_1-\bar{q}^c_2$. Given the distribution of $\bar{q}^c_j$, $\Delta \bar{q}\sim N\left(q_1-q_2,\sigma_\eta^2\left(\frac{1}{n_1^c}+\frac{1}{n_2^c}\right)\right)$. The outcome of clinical trials belongs to one of the three cases: (1) $\Delta \bar{q}^{c>0}$, (2) $\Delta \bar{q}^{c<0}$, and (3) $\Delta \bar{q}^{c=0}$. In case (1), we make a draw for $\Delta \bar{q}^{c*}$ from $N\left(q_1-q_2,\sigma_\eta^2\left(\frac{1}{n_1^c}+\frac{1}{n_2^c}\right)\right)$ truncated below at zero. Case (2) is similar. In case (3), we simply set $\Delta \bar{q}^{c*} = 0$. Then, we make a draw for drug 1, $\bar{q}_1^{c*}$, from $N(q_1,\frac{\sigma_\eta^2}{n_1^c})$, and set $\bar{q}_2^{c*}$ by $\bar{q}_2^{c*} = \bar{q}_1^{c*} - \Delta \bar{q}^{c*}$. With these simulated draws, we can update prior using the Bayesian updating rule.