In estimating statistics and conducting tests you may use appropriate computer applications but include computer outputs that contain the values that you use to answer the questions. Graphics or figures required should be produced using a computer.
Where hand drawn graphics are to be submitted, to facilitate electronic submission these should be scanned and appended to your work.
Answer BOTH of the following questions:
(a) As part of a study of a new computer-aided system to assist GPs in their consultation practices, 300 patients seeing the same GP were asked to complete a questionnaire to assess their satisfaction with the consultation process after consultations that either used the new system or not according to a random allocation.
Of the 150 patients who were randomised to a consultation using the new system, 103 indicated that they were satisfied and 39 indicated that they were not satisfied. For the 150 patients who were randomised to a standard consultation, the numbers of satisfied and not satisfied patients were respectively 93 and 47. The remaining patients in each group declined the opportunity to complete the questionnaire.
(i) Express the results of this study in the form of a table, including totals and percentages that you consider to be helpful in the interpretation of the data. (1 mark)
(ii) Obtain an estimate of a measure of the difference in proportions of satisfied patients for the two consultation types on an intention to treat basis. Also obtain a 95% confidence interval for this difference, and explain the meaning of this interval. (6 marks)
(iii) Use a chi-squared test to determine whether the proportions of satisfied patients for the two consultation types are statistically significantly different and give your conclusion from this test. State a condition for the chi-squared test to be a valid test for the comparison of two proportions, and explain whether or not you think this is reasonable for this dataset. (5 marks)
(b) An alternative design for this study described in (a) might have been to survey 50 patients from each of six GPs with three of the GPs randomly chosen to give telephone consultations and the remaining three GPs giving video consultations. Discuss the advantages and disadvantages of the two different approaches. (3 marks)
(c) As part of the study described in (a) above, the GP rated her level of satisfaction with the 144 video consultations using the new system, giving a score from 0 (completely dissatisfied) to 100 (completely satisfied). The length (in minutes) of the consultations were also recorded, and a linear regression analysis was conducted to investigate whether the satisfaction score was related to the consultation length.
Some of the results from a linear regression analysis of the data are given in the Table 1 below.
Table 1 Analysis summary
|
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
||
|
B |
Std. Error |
Beta |
||||
|
1 |
(Constant) |
61.167 |
1.602 |
0.028 |
38.190 |
.000 |
|
|
consultation.length |
0.102 |
.309 |
0.3304 |
.742 |
|
a Dependent Variable: satisfaction.score
(i) Explain what model is being fitted in this analysis. (1 mark)
(ii) Describe the assumptions underlying the analysis. How would you verify these assumptions if you had access to the complete dataset? (6 marks)
(ii) The t-value of 38.190 in the upper line of the table is highly significant. Explain why this does not mean that there is a significant relationship between consultation length and satisfaction score. How should this significant t-value be interpreted? (2 marks)
(iii) What can be concluded about the relationship between consultation length and satisfaction score from the analysis given? (1 mark)
Question B 25 marks (“The full paper is available in the assignment folder saved as “assignment paper.pdf” or by following the link below)
A study was performed on routinely collected data to assess the association between air pollution and infant deaths [1]. You have access to this open access study and may read the full paper. However this is not essential to complete the assignment with results that you need to consider identified below.
Table 1 describes the baseline characteristics of the study population (live births in the study period) and for each of the outcomes of interest – infant deaths, neonatal deaths and post-neonatal deaths. Table 2 and Figure 2 give the main results. More detailed results in other tables are not part of this assignment.
1. Kotecha SJ, Watkins WJ, Lowe J, Grigg J, Kotecha S (2020) Differential association of air pollution exposure with neonatal and postneonatal mortality in England and Wales: A cohort study. PLOS Medicine 17(10): e1003400. https://doi.org/10.1371/journal.pmed.1003400
Use examples from the tabulated data to illustrate your answers to the following questions
1. Table 1 considers a range of factors that are not the main exposures being considered, for example maternal age, and socioeconomic deprivation. These are presented overall (live births) and according to outcomes (infant deaths, neonatal deaths, and postneonatal deaths).
Describe the findings presented in this table. Give an overview supported by specific examples. [4 marks in total]
2. Looking at Table 1 can you suggest any risk of confounding that may have affected an analysis comparing exposure to environmental pollutants and the outcomes of this study? If you suspect a risk for confounding describe the basis for this opinion, and what analysis could be used to address this risk. [4 marks in total]
3. Table 2 shows the results for crude analysis and adjusted analysis. The lowest quintile of exposure to each pollutant is used as the baseline. Adjusted models consider adjustment for the “Index of multiple deprivation” (IMD) and a “Fully adjusted” model that also includes birth weight, maternal age, sex, and multiple birth. Looking at the results look at the results
a. Is there evidence for confounding in the unadjusted analysis? If you identify evidence for confounding, is this consistent across analyses for different exposures and outcomes?
b. Considering the results assessing the association between SO2 and postneonatal deaths, can you say whether the IMD was associated with exposure to SO2?
c. What do you understand by the estimated odds ratio of 1.147 (95% confidence interval 1.076 – 1.224) comparing the risk of postneonatal death, in the “fully adjusted” model comparing the fifth quintile (highest) of exposure to SO2 with the first quintile? Specifically - describe in words what this result means including explaining the confidence interval. [10 marks in total]
4. Describe and interpret the evidence that the risk of postneonatal deaths associated each pollutant is consistent, or that it differs. [4 marks in total]
5. In the interpretation of the results the authors move from association to considering that their results likely represent pollutants as causing infant mortality.
a. Is there any reason to expect that “residual confounding” might be important? Is this likely to explain the associations even if there is no real effect?
b. Might information bias have affected the estimates in this study? Give a possible example if answering yes, and a rationale if answering no [3 marks in total]
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