# Antimalarial Drug Efficacy: Statistical Analysis Research Paper

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Updated: Jul 23rd, 2020

## Introduction

Besides its use in the analysis of designs that have one independent variable (IV), factorial analysis of variance (ANOVA) can also be used to analyze designs that involve many independent variable (IV) using factorial designs. This statistical test gives unbiased estimates of the effects and interaction among design variables (Jackson, 2012). The effects in experimental variables are determined by estimating the variability at different levels that is not caused by the independent variables themselves. In this context, the independent variables are known as factors. In social sciences, factorial designs are usually preferred because they have more benefits compared to single variable designs. They give specific information regarding the interaction among variables as well as their combined effect on the dependent variable (DV). The proposed study, using a concrete example, examines the specific factorial design issues and describes the unique information provided by the factorial design. The example in the proposed research involves the efficacy of an antimalarial drug, XYZ, on students.

Literature shows that a highly potent drug, unlike a drug with low efficacy, is given in small concentrations to evoke a response. Highly potent drugs also seem to have fewer side effects in at-risk groups. However, it is often difficult to interpret literature regarding the inherent dosage-efficacy relationships. Thus, the research question for the proposed research will be: What are the efficacy levels of different dosages (100mg, 150mg and 200mg) of antimalarial drug XYZ on high school and university students? Factorial ANOVA applies to this research question because it incorporates three (more than two independent) variables and one dependent variable. In this study, the dependent variable will be the drug efficacy levels, which will be based on the study participant’s parasitemia. The three independent variables will include the different drug dosages (100mg, 150mg and 200mg). The test statistic will not only measure the effect of the dosages on efficacy (DV) but will also test the interaction among the three variables (Polit & Lake, 2010). The study’s annotated null hypothesis is as stated below:

H0: µhigh school= µuniversity; H0: µ100mg = µ150mg = µ200mg

For the null hypotheses, it is hypothesized that the independent variable will have no effect on parasitemia levels of both high school and university participants. It is also hypothesized that the potency for the three drug dosages will be the same. The annotated alternative hypothesis for this study will be as stated below:

H1: high school ≠ µuniversity

It implies that the efficacy levels of the drug will be different between the two treatment groups (high school and university participants). For factorial ANOVA, assignment errors associated with the independent variable is a major source of errors (Jackson, 2012). Incorrect assignment of the three dosages to the study participants will give incorrect results; hence, valid conclusions cannot be made.

## Methods

The purpose of the proposed study will be to determine the efficacy of the three dosages of the antimalarial drug. Therefore, there will be three independent variables or factors with each having two levels (high school and university students). A sample of 36 students (18 males and 18 females infected with malaria) will be selected, using purposive sampling, to participate in the proposed study. Half of the participants will be selected from a high school and the other half from a university. It is expected that the participants’ ages will range from 14 to 18 for high school students and 18 to 25 for university students. Students diagnosed with malaria at the respective institution’s hospitals will be selected for this study. Thus, the study will use the purposive sampling technique to select the participants. The design of the proposed study (a 3 x 3 factorial design) is shown in the table below:

 Students High school University (undergraduates) Dosage Level 100mg n=6 n=6 150 mg n=6 n=6 200mg n=6 n=6

The factorial design will have 6 cells each with 6 subjects.

## Procedures

The three drug dosages, 100mg, 150mg and 200mg will be randomly assigned to the study participants. The researcher will then assess the efficacy of three dosages of the test drug based on the participants’ parasitemia. The malaria parasite load will be determined through microscopy of a blood smear. Thus, low parasitemia in a participant will imply that the particular drug dosage has cleared much of the parasites. On the other hand, high parasitemia will imply that the drug dosage did not clear the parasites.

The dependent variable for the proposed study will be the efficacy levels. This variable is a categorical variable and will be measured on a nominal scale with three main categories based on parasitemia levels: High efficacy (low parasitemia); medium efficacy (less change in parasitemia); and low efficacy (no change in parasitemia). On the other hand, the independent variables will include the drug dosages of 100mg, 150mg and 200mg. They are also categorical variables and will be measured on a nominal scale (Polit & Lake, 2010). The results obtained from the experiment will help to assess the effects and interaction among the different variables.

## Results

The factorial design used in this study will yield three types of information (factors). The first factor will assess whether the dosage level affects parasitemia in the participants while the second factor will determine whether age (high school or university) is related to parasitemia. The third factor will assess whether the effects of dosage levels rely on the participant’s age. The treatment effect will be measured in two ways; for the main effect, a difference in means for each factor compared to the remaining factors while the interaction effect will be the difference in effect between two factors or levels.

Thus, the three way factorial design will provide information about the interaction and the effects of the IVs. There are several possible results from the proposed design. First, the results might be insignificant implying that there are no differences between the cell means. Another possibility is that the effect of the dosage level (IVs) is significant. Thus, the participants receiving the three dosage levels had lower parasitemia than controls.

## Discussion

In the proposed study, four assumptions will be made; first, it will be assumed that the dependent variable follows a normal distribution. It will also be assumed that the three dosage levels (treatment groups) are independent in order to use the factorial design. The research will also assume homogeneity of the population. It will also be assumed that the factors are constant, that is, the researcher will determine the levels of each independent variable. Based on the research question, three conclusions will be made from the study, with the Ho rejected in each case. First, if the 200mg dosage level has the highest effect, then, it will be concluded that the efficacy of XYZ increases with dosage. Second, if the dosage levels evoke higher responses in the university students than high school students, it will be concluded that age has an effect on dosage levels. Third, if the experimenter observes an interaction among the IVs, it will be concluded that XYZ dosage level has an effect on participant’s parasitemia, which increases as the individual matures. This design’s result can be applied in determining the effects of a drug, e.g. cannabis, on the user’s memory. The factorial design will give more information about the correlation between cannabis use and memory performance.

## References

Jackson, S. L. (2012). Research methods and statistics: A critical thinking approach (4thEd.). Belmont, CA: Wadsworth.

Polit, D. F., & Lake, E. (2010). Statistics and data analysis for nursing research. NewYork, NY: Pearson.

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