Resistance and Empiric Substitution

Before computing Equation 4, we validated the model by comparing predicted and actual market shares. Figure 5-2 displays actual market shares (the bars) and predicted market shares, D(R, pj, xj, 8), as well as the 95% confidence intervals based on 100 bootstrap runs.

A single simulation run entails (a) drawing the bk's and sk's from their respective distributions, (b) drawing |ar's from triangle distributions, (c) drawing e^'s from independent logistic distributions, (d) computing utility levels for Equation 1, and (e) computing Equation 2 and then Equation 3 to calculate market shares. Considering that we have 18 different market shares to predict, the model does a tolerably good job. The confidence intervals around the means of the predicted market shares are quite wide because of the random parameter specification. Some of the means are off by quite a bit too, but others are very close to actual market shares (for example, for trimethoprim-sulfamethoxazole).

We calculated that the average spending per prescription for antibiotics to treat new cases of otitis media during 1997 and 1998 was $18.41. Our predicted per-prescription cost is $19.20 (95% confidence interval: $17.08, $21.39). We estimated by restricting the coefficients on the year-attribute interactions to be zero that in the absence of resistance, the per-prescription cost would be only $15.05 (95% confidence interval: $13.66, $17.03).

TMP/SMX Sulfisox. Eryth/Sulf. Erythro. Clarithro. Azithro. Loracarbef Cephalexin Cef. Axetil Cefprozil Cef. Proxetil Cefixime Cefadroxil Cefaclor Penicillin Ampicillin Amox/Clav Amoxicillin

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Market Share

Figure 5-2. Actual and Predicted Market Share

Notes: The bars represent actual market shares. TMP/SMX = trimethoprim/sulfamethoxa-zole, Sulfisox. = sulfisoxazole, Eryth/Sulf. = erythromycin/sulfisoxazole, Erythro. = erythromycin, Clarithro. = clarithromycin, Azithro. = azithromycin, Cef. Axetil = cefuroxime axetil, Cef. Protexil = cefpodoxime protexil, and Amox/Clav = amoxicillin clavulanate.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Market Share

Figure 5-2. Actual and Predicted Market Share

Notes: The bars represent actual market shares. TMP/SMX = trimethoprim/sulfamethoxa-zole, Sulfisox. = sulfisoxazole, Eryth/Sulf. = erythromycin/sulfisoxazole, Erythro. = erythromycin, Clarithro. = clarithromycin, Azithro. = azithromycin, Cef. Axetil = cefuroxime axetil, Cef. Protexil = cefpodoxime protexil, and Amox/Clav = amoxicillin clavulanate.

Multiplying the difference between the actual per prescription cost and the simulated per-prescription cost by the total number of prescriptions for otitis media per year—about 12 million—yields an estimate of the impact of resistance on antibiotic costs: ($18.01 - $15.09) x 12,000,000 = $40,000,000. Thus we concluded that resistance increases total spending on antibiotics to treat new episodes of ear infection (about $216 million) by about 20%.

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