Calculate separate Odds ratios and confidence intervals

Assignment Help Applied Statistics

Reference no: EM132356335

Statistics Questions -

Q1. Table 1: Results from the ViraPap test used in a sample of 681 'healthy women' who visited their GP.

		Southern hybridization		Total
		Positive	Negative	Total
ViraPap (new test)	Positive	35	42	77
ViraPap (new test)	Negative	4	600	604
Total		39	642	681

1(a) Using the Southern hybridization as the 'gold standard' results calculate the sensitivity and the specificity of the ViraPap test.

1(b) Calculate the 95% Confidence Interval for both the Sensitivity and the Specificity calculated in part 1(a).

1(c) Calculate the difference in the proportion of positive tests from the ViraPap and Southern hybridization tests. Present the 95% Confidence Interval and associated p-value for this difference.

1(d) Briefly interpret your results from parts la to lc.

Q2. Table 2 presents results from a hypothetical case-control study designed to assess the association between smoking and ovarian cancer.

Ever-users of oral contraceptives
	Smoking
	Yes	No	Total
Ovarian cancer cases	50	12	62
Controls	148	35	183
Total	198	47	245

Never users of oral contraceptives
	Smoking
	Yes	No
Ovarian cancer cases	20	70	90
Controls	15	60	75
Total	35	130	165

2(a) Explain why we would use an Odds Ratio as opposed to a Relative Risk to estimate the association between Smoking and Ovarian cancer in this study.

2(b) Ignoring oral contraceptive use in the data provided, calculate by hand the odds ratio which assesses the association between smoking and ovarian cancer. Also calculate by hand the corresponding confidence interval and p-value. Specify the formulas you used to produce your answer. Briefly interpret your results.

2(c) Now calculate separate Odds ratios and confidence intervals (by hand or using software) to assess the association between smoking and ovarian cancer within each group of oral contraceptive users. Interpret the results with reflection on the differences between the results from 2b and 2c.

Q3. Table 3: Association between background characteristics, sexual behaviours and HIV among Female Sex Workers.

Duration of sex-work (years)	Total	HIV cases
< 1	2225	32
1 - 3	2215	27
> 3	1605	38

Undertake parts 3a) to 3d) by hand, providing details of your working and the formulas used.

3(a) Undertake a standard chi-squared test to assess whether there is an association between Duration of sex-work and cases of HIV.

Briefly interpret your results. What is a drawback of using the standard chi-squared test on this data?

3(b) Use a test for trend to assess the association between number of sexual partners and HIV cases. Carefully interpret your results in simple terms.

3(c) Perform a sensitivity analysis to assess whether your results change if you assign different values to the sexual partners variable. How does this change your result?

3(d) Using <1 years as the baseline category, calculate the Risk Ratio of HIV for 1-3 years and >3 years. Present the confidence intervals and p-values for each Risk Ratio.

Q4. The Geometric Distribution has the following Probability Density Function.

f (y; θ) = θ (1 - θ)^y

4(a) Show that this distribution belongs to the exponential family. Determine whether this distribution is of the canonical form. Specify the 'natural parameter' of this distribution.

4(b) Using the properties of the exponential family of distributions or another method calculate the formula for E[Y] and Var[Y] of the distribution.

References - Selected Scenarios and Datasets adapted and modified from: dos Santos Silva. (1999) Cancer Epidemiology Principles and Methods. IARC. 1999. And Kiviat et al. (1990) Comparison of Southern transfer hybridization and dot filter hybridization for detection of human papillomavirus infection with types 6, 11, 16, 18, 31, 33 and 35. Am. J. Clin. Pathol. 94, 561-565.

Note - Please make sure you address all the 4 questions and reply to these accurately. It is a Master's degree level assignment.

Reference no: EM132356335

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