About this Problem Solving Task
On completion of this problem solving task you should be able to:
• display numerical and graphical summaries of key features of a data set
• analyse a first-order differential equation used to model a physical system.
Here is a checklist of the steps you need to go through before submitting this online.
• Individualise your data by subsetting to keep only the row with your student number in it.
• Answer the questions in the relevant areas in this document.
– For all steps that require you to show your working, give enough detail (and explanatory text where needed) that anyone reading can follow the logic of your solution.
– Correct answers with no working will not attract full marks.
– Provide any R code used to solve the problem in your R script file.
• Interpret the analysis in the space provided in the Interpretation section
– Ensure all plots are included at a resolution that makes them readable and that they have either a caption or a title
• Provide your completed document by uploading it to Blackboard as either a Microsoft Word file of format .doc or .docx or a PDF file of format .pdf. Pages files will be awarded a mark of 0
• Provide your R script file
– PSTs with no script files will be considered incomplete and awarded a mark of 0.
– The script file should
• have file extension .R
• contain all code required to read in the downloaded data, and
• perform all the steps of the analysis that require the use of R
Submit your PST and R script file on Blackboard by the due date. Ensure you have attached both files.
This is an individual piece of assessment. You should not work with others to complete the task, share your work, or ask other students for their work. Please ensure you are familiar with QUT’s policy on Academic Integrity
Theophylline is an anti-asthmatic drug which was distributed in tablet form (American Society of Health-System Pharmacists Inc. 2018). In the last few decades, research has led to the development of inhalers and nebulizers for delivery of a range of different anti-asthmatic drugs (Shahidi and Fitzgerald 2010). Nonetheless, the investigation of theophylline allows us to understand the uptake of a drug from the stomach into the bloodstream and its clearance via the kidneys.
This problem solving task contains two main objectives. The first is to examine, describe, and visualise experimental data that comes from a study of the pharmokinetics of theophylline in patients’ bloodstreams following an oral administration of the drug. The second is to consider a mathematical model of the system to describe the dynamics (how it changes with time) of theophylline within the bloodstream. You will then use the information you have synthesized from both the experimental data and the mathematical model to answer questions about the behavior of theophylline and the accuracy of the mathematical model.
c_0 value =200 k_a value = 0.062 k_c value = 1.296
Section A. Experimental Data [30% Total]
In this section of the problem solving task, you will be investigating the Theoph data set in R. Note that this is a built-in data set, and to store it in your environment you simply need to run data(Theoph).
Exercise: How many observations are in your data set?
Answer:
Exercise: How many variables are in your data set?
Answer:
In this section, you must collect information about the variables in the Theoph data set and use it to build a data dictionary.
A data dictionary typically displays crucial information and summary statistics about the variables in your data set. This includes the name and type of each variable, its units, and its range. Since Theoph is a built-in data set, you can find out the variable names and units by running ?datasets::Theoph
As for the range, this is something you need to compute by yourself. In terms of presenting the range in the data dictionary table, please observe the following guidance:
• For continuous or count variables, the range is two numbers, the minimum and the maximum values. If a is the minimum and b the maximum, then you might write the range as (a, b) or a-b. It is not the difference between the minimum and maximum values.
• For ordinal categorical variables, give the range as usual.
• For nominal categorical variables, simply list the categories.
Exercise: Complete the table below by adding a new row for each variable in the Theoph data set. Use descriptive titles for variables rather than the column name in the data set.
Answer:
Exercise: Which variable in our data frame represents our outcome/response/dependent variable?
Answer:
Exercise: Which variables in our data frame represents potential explanatory/independent variables?
Answer:
In this section, you will need to calculate summary statistics for the Theoph data set. Where necessary, round to two decimal places and ensure the units are described appropriately.
Ensure your tables have an appropriate number of columns and rows, have horizontal borders in appropriate places and have captions above the table.
Do not simply present screenshots of R output. You are expected to format your responses in Word.
Exercise: Generate a table that shows the min, mean, median, max and standard deviation of the variables weight and dose. Show all results in one table, rounded to two decimal places. (You may need to stitch several tables together.)
Answer:
Exercise: Generate a table that shows the minimum, median and maximum concentration for each subject.
Answer:
In this section, use Tufte’s principles of graphical excellence to guide the creation of ggplot2 figures that help the reader understand the variability in the data. Ensure all code is included in the R script file you upload. All plots are to be labelled appropriately and included at a size and resolution such that the plot is legible. There are many different ways to visualise the data, so don’t feel restricted to one particular type of plot. Ensure your plots have meaningful captions (below the figure) and/or titles.
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