LF103 Quantitative skills for biology Assessment 1
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LF103 Quantitative skills for biology
Assessment 1
Instructions
Submit via Moodle.
Your answers should be saved as a PDF. It is your own responsibility to ensure that all text and images are present and correct when saving. Check your file before submitting it. Ensure your answers are labelled with the question number so they can be efficiently marked.
Do not include software output (Excel or SPSS) other than graphs and charts where asked for. You should report the relevant output from the software. Your Excel spreadsheets and SPSS output will not be collected or marked.
When any graphical output is asked for, ensure axes are labelled, and the chart given a title and/or caption. Use captions/legends where appropriate.
Carry forward exact results in your analysis but give numerical answers to a sensible level of accuracy (decimal places). Beware illusory accuracy.
Problem 1 (29 Marks)
A recently developed antibiotic (with unknown kinetics) was given to a group of patients (a total of 10 men aged between 25 and 35 years) by IV bolus injection (100 mg of drug injected directly into the systemic circulation – a loading dose). To measure how the antibiotic concentration changed with time, blood samples were taken at regular intervals. The spreadsheet marked ‘drug decay’ shows the mean concentration of the antibiotic in the blood, and the standard deviation of these measurements.
a) What are standard deviations a measure of?
(1 mark)
b) Create a scatter plot for the concentration of antibiotic in the blood samples against time, with the standard deviations in concentration set as error bars. Why do you think the concentration of the antibiotic falls with time? Find the Pearson correlation coefficient; determine how correlated drug concentration is with time.
(6 marks)
c) What is the difference between zero order and first order decay?
(2 marks)
d) By visual examination of your graph and the data, estimate the half-life of the drug.
(1 mark)
e) Despite drugs usually exhibiting first order decay, these data appear to follow zero order decay. Use the ‘add trendline’ function (including equation display) to fit a straight-line trendline to the scatter plot. The negative of the slope of the line is equal to the rate constant of elimination
(Kel). What is the value of Kel and what are its units?
(2 marks)
f) Zero order decay can be described using equation 1.
Ct = C0 − Kel × t (1)
Where C0 is the starting concentration, t is time, Ct is the concentration at time t, and Kel is the elimination rate constant. Using equation 1, calculate the theoretical blood sample concentrations for each time point. Add this theoretical model to your graph. How well does it describe the experimental data? What reasons are there for the theoretical fit to not
exactly match the data?
(3 marks)
g) On the spreadsheet named ‘drug decay 2’, you will find more concentrations taken at later time points. Add this data to the dataset in the first spreadsheet. Create a new scatter plot including these extra results; use the standard deviations as error bars. Describe the rate of antibiotic decay with this data included. Why might the decay at later time points differ from that at earlier time points?
(4 marks)
h) Take natural logs of the concentrations (of all of the data, not the model fit); this should produce a straight line. Create a new plot of these transformed data. Add a straight-line trendline, including the equation of the line. From this report the new elimination rate constant. What are its units and explain why.
(5 marks)
i) Taking blood samples can be annoying to the patient and requires clinical skill, time and sterile equipment. Some data on drug kinetics can be obtained by analysing patient urine (which is cheap, easy and convenient to collect). However, measuring the concentration of the drug in the urine is unhelpful as the concentration depends on the volume of urine, which can vary widely over a day. Instead the absolute amount of drug in the urine must be measured. The spreadsheet ‘drug decay’ also includes the measurements of drug concentration in urine after administration of 100mg of a different antibiotic. Calculate the total amount of drug excreted in the urine in mg. What proportion of the drug is excreted in the urine? What could have happened to the missing drug? If 100% of the drug had been excreted what might this tell you about the efficacy ofthe antibiotic?
(5 marks)
Problem 2 (31 Marks)
As part of research into elephants in Cameroon a conservation team create morphological records of tranquilised elephants and use these to infer general health. As it is practically impossible to weigh an elephant in the wild, the measurements taken are the elephant’s girth around their thorax at heart level (‘heart girth’), the length of the elephants and their foot pad circumference. These data are matched with the elephant ID number given at birth. The data can be found in the spreadsheet named ‘elephants’ .
a) These measurements can be used to infer the mass of the elephants. A formula has been developed which gives a reasonable approximation of mass in kilograms, given in equation 2.
Est mass = (11.5 x heart girth) + (7.55 x length) + (12.5 x pad circum) – 4016 (2)
Calculate the estimated mass of each elephant. Report on the mass of elephant 10. What reasons might there be for the mass of elephant 19 being negative?
(3 marks)
b) Examine the length data. Are there any anomalies? If so, what are they? What is likely responsible for this? If any anomalies are present, what would be reasonable assumptions to correct them? Correct any ofthese in your dataset, so they give similar values to other elephants of the same age.
(3 marks)
c) The estimated masses of elephants are normally distributed. Calculate the
mean and standard deviation of the mass of the elephants; do not include elephant 19, as this individual is so much smaller than the rest of the elephants. Using these values calculate the normal probability distribution using the values in column I as the input. Create a ‘Smoothed
Lined Scatter’ plot of the distribution.
(3 marks)
d) Having defined the distribution that the masses of elephants form, it can be used to make inferences about the size of all wild elephants. Use this distribution and the appropriate function to determine the percentage of
elephants that weigh more than 6000kg (very large elephants!).
(3 marks)
Open the SPSS file named ‘elephants’ .
e) Calculate and compare summary statistics for the pad circumference of males and females. What do these values suggest about the differences in
pad circumference for males and females?
(3 marks)
f) Create a histogram of pad circumferences to compare male and females. Analyse your histograms. What conclusions can you draw about the pad circumference of male and female elephants? How good is this comparison? What formal test could you conduct to compare the pad circumferences of male and female elephants?
(7 marks)
g) Given the scientific question of whether male elephants have larger footpads than female elephants, conduct suitable hypothesis test(s), always stating your hypotheses, and draw conclusions from the
hypothesis testing output.
(6 marks)
h) Consider the sample: does anything about it make the tests in (g) unfair?
(3 marks)
Problem 3 (20 Marks)
During the winter months, GP surgeries report an increase in the number of cases of influenza they see. 147 GPs across a range of surgeries recorded how many cases of influenza they saw in a single day, ranging from 0 to 8. The data are shown in the spreadsheet named ‘influenza’ . The health authority collects these data and analyses them to search for patterns in reporting.
a) Calculate the mean number of cases seen per GP.
(1 mark)
b) Which distribution may be appropriate to describe this data?
(1 mark)
c) Given the mean number of cases and the appropriate distribution from (b), calculate all of the expected frequencies of 147 visits. Report these
frequencies to a suitable level of accuracy in your answers.
(3 marks)
d) Create a suitable chart to compare the observed and expected frequencies of influenza cases. Do the observed data match the expected values from
the distribution?
(4 marks)
e) Use a significance test to determine if the observed data fit the
distribution data that you have calculated. State your hypotheses.
(5 marks)
f) Of the 147 cases, the age and sex were also recorded. Determine with
suitable hypothesis testing whether age and sex are associated. State your hypotheses. If there is evidence for some association between age and sex, identify the particular combinations that are contributing to this conclusion (which combinations contribute to a high test statistic?). (6 marks)
Total Marks available: 80
2023-02-15