Drug resistant pathogens pose one of the major public health challenges of this century. Conventional wisdom is that aggressive treatment should be used to kill pathogens rapidly, before they have a chance to acquire resistance. However, if drug pathogens are already present, this strategy may actually backfire by intensifying the natural selection placed on drug-resistant pathogens. A study took mice and infected them with a mixture of drug-resistant and drug-susceptible malaria parasites, then randomized mice to one of four different treatments of an antimalarial drug (with 18 mice in each group): untreated (no drug), light (4 mg/kg for 1 day), moderate \((8 \mathrm{mg} / \mathrm{kg}\) for 1 day), or aggressive ( 8 \(\mathrm{mg} / \mathrm{kg}\) for 5 or 7 days). Data are available in DrugResistance.

(a) For each mouse, response variables included measures of drug resistance, such as - Density of drug-resistant parasites (ResistanceDensity per \(\mu \mathrm{l}\) )
- Number of days (out of the 50-day experiment) each mouse had infectious drugresistant parasites present (DaysInfectious)
and measures of health such as - Body mass (Weight in grams)
- Red blood cell density ( \(R B C\) in million/ \(\mu\) l)
The different response variables are displayed in Figure 8.8 by treatment group, with measures of drug resistance in the top row and measures of health outcomes in the bottom row. Higher values correspond to more drug resistance (which is bad) in the drug-resistance response variables and to healthier outcomes (which are good) in the health response variables. Does there appear to be an association between treatment level and the response variables measuring drug resistance? If so, describe the association.

Does there appear to be an association between treatment level and the response variables measuring health? If so, describe the association.

(b) Because we are interested in dose here, exclude the untreated category, and only compare the different actual treatments (Light, Moderate, and Aggressive). Conduct the ANOVA test and give the \(p\)-value for each of the four response variables by treatment level. Which variables are significantly associated with treatment level? Which variables are not significantly associated with treatment level?

(c) What have you learned about treatment level and drug resistance? How does this compare with the conventional wisdom that aggressive treatments are more effective at preventing drug resistance?

(d) For the response variables measuring drug resistance, do the conditions for ANOVA appear to be satisfied? If not, which condition is most obviously violated? For the response variables measuring health, do the conditions for ANOVA appear to be satisfied? If not, which condition is most obviously violated? If the conditions do appear to be violated, keep in mind that the p-values calculated in part (b) will not be entirely accurate.

Transcribed Image Text:

Resistant Parasite Density (#/l) Body Mass (g) 150000 100000 50000 20 15 10 10 5 0 T Untreated Light Moderate Aggressive Untreated Light Moderate Aggressive Red Blood Cell Density (x10%/l) Days Infectious with Resistant Parasites 8 12 10 8 Untreated Light Moderate Aggressive Untreated Light Moderate Aggressive Figure 8.8 Measures of drug resistance (top row) and health outcomes (bottom row)