Question

Drug Resistance and Dosing Exercise 8.39 on page 561 explores the topic of drug dosing and drug resistance by randomizing mice to four different drug treatment levels: untreated (no drug), light ( \(4 \mathrm{mg} / \mathrm{kg}\) for 1 day), moderate \((8 \mathrm{mg} / \mathrm{kg}\) for 1 day), or aggressive ( \(8 \mathrm{mg} / \mathrm{kg}\) for 5 or 7 days). Exercise 8.39 found that, contrary to conventional wisdom, higher doses can actually promote drug resistance, rather than prevent it. Here, we further tease apart two different aspects of drug dosing: duration (how many days the drug is given for) and amount per day. Recall that four different response variables were measured; two measuring drug resistance (density of resistant parasites and number of days infectious with resistant parasites) and two measuring health (body mass and red blood cell density). In Exercise 8.39 we don't find any significant differences in the health responses (Weight and \(R B C)\) so we concentrate on the drug resistance measures (ResistanceDensity and DaysInfectious) in this exercise. The data are available in DrugResistance and we are not including the untreated group. (a) Investigate duration by comparing the moderate treatment with the aggressive treatment (both of which gave the same amount of drug per day, but for differing number of days). Which of the two resistance response variables (ResistanceDensity and DaysInfectious) have means significantly different between these two treatment groups? For significant differences, indicate which group has the higher mean. (b) Investigate amount per day by comparing the light treatment with the moderate treatment (both of which lasted only 1 day, but at differing amounts). Which of the two resistance response variables have means significantly different between these two treatment groups? For significant differences, indicate which group has the higher mean. (c) Does duration or amount seem to be more influential (at least within the context of this study)? Why?

Short answer

The results will vary based on the actual data values. However, the influence of duration and amount can be determined by comparing the significance of the differences in means for the variable ResistanceDensity and DaysInfectious across different treatment groups.

Step-by-step solution

Investigate Duration

First, compare the resistance response variables (ResistanceDensity and DaysInfectious) means for the moderate treatment and the aggressive treatment group. For this, you may use the method of Independent samples t-test which is used to compare the means of two independent groups in order to determine whether there is statistical evidence that the associated population means are significantly different.

Analyze Difference and Determine Higher Mean

If there is a significant difference in means of ResistanceDensity and DaysInfectious between moderate and aggressive treatment groups, indicate the group which has the higher mean. You can use a statistical software to calculate the means for the two groups and determine which one is higher.

Investigate Amount Per Day

Next, compare the resistance response variables (ResistanceDensity and DaysInfectious) means for the light treatment and the moderate treatment group, which lasted only 1 day, but at differing amounts. Again, using the Independent samples t-test would be beneficial here to compare the means of the two independent groups.

Analyze Difference and Determine Higher Mean

If there is a significant difference in means of ResistanceDensity and DaysInfectious between light and moderate treatment groups, indicate the group which has the higher mean. You can use a statistical software to calculate the means for the two groups and determine which one is higher.

Evaluate Influence of Duration and Amount

Finally, evaluate whether duration or amount seems to be more influential within the context of this study. You can do this by looking at the significance of the differences calculated in previous steps. This will involve a level of interpretation based on your analysis.