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Question 1: Identify each of the variables in the above table either as nominal, ordinal, discrete or continuous.

Question 2: Fill up the following table using appropriate summary statistics for each of the listed variables. Discuss whether dyslipidaemia is related to HbA1c, diastolic BP, insulin status and patients’ age.

Question 3: Graphically determine the relationship between dyslipidaemia and each of the following variables: duration of diabetes group, BMI group and occupation type. Present each of the above variables on an appropriate graph and discuss.

Question 4: For the following questions show the detailed calculations, most marks will be allocated for correct calculations.

(a) The lifetime of a battery is normally distributed with a mean life of 40 hours and a standard deviation of 1.2 hours. Find the probability that a randomly selected battery lasts longer than 42 hours.

(b) At a hospital, the ages of all new employees hired during the last 5 years are normally distributed. Within this curve, 95% of the ages, centered about the mean, are between 24.6 and 37.4 years. Find the mean age and the standard deviation of the data.

(c) Given that the scores on a medical test follow a normal distribution with a mean of 460 and a standard deviation of 100. If all students in a class of 41 attend the test what is the probability that the given class will obtain a mean score of above 589.93?

Question 5: Consider that the distribution of systolic blood pressure in the population is positively skewed. What will be the shape of the sampling distribution of the sample mean of systolic blood pressure in large samples?

Question 6: Briefly discuss the difference between:

1. Randomized clinical trial (RCT) and prospective cohort study,
2. Case-control study and historical (retrospective) cohort study,
3. Prospective cohort study and historical cohort study

## Identifying Variables in the Cohort Study

 Variables Classification Value labels ID Number Ordinal NA Age (in years) Discrete NA Age Group Nominal 1: < 40 years, 2: 40 - 49 years, 3: 50 – 59 years and 4: >= 60 years Gender Nominal 1: Male; 2: Female Occupation Type Nominal 1: Sedentary worker; 2: Moderate worker; 3: Heavy physical worker Physical Activity Level Nominal 0: Sufficient PA; 1: Insufficient PA Weight (in Kg) Continuous NA Height (in meter) Continuous NA BMI (in Kg/m2) Continuous NA BMI Group Nominal 0: Normal; 1: Overweight; 2: Obese Diastolic BP Discrete NA Systolic BP Discrete NA Hypertension Nominal 0: Normotensive; 1: Hypertensive Duration of Diabetes Discrete NA Duration of Diabetes Group Nominal 1: < 5 years; 2: 5 -< 10 years; 3: >= 10 years HbA1c Continuous NA HbA1c Group Nominal 0: <7 years; 1: >= 7 years Takes insulin Nominal 0: No; 1: Yes Duration of Insulin (years) Discrete NA Total Cholesterol Discrete NA Total Cholesterol Group Nominal 0: <200; 1: >= 200 Triglyceride Discrete NA Triglyceride Group Nominal 0: <150; 1: >= 150 HDL Cholesterol Discrete NA HDL Cholesterol Group Nominal 0: Normal; 1: Low LDL Cholesterol Discrete NA LDL Cholesterol Group Nominal 0: <100; 1: >= 100 Serum Creatinine Continuous NA Serum Creatinine Group Nominal 0: < 100; 1: >= 100 TC_HDL ratio Continuous NA LDL_HDL ratio Continuous NA Dyslipidemia Nominal 0: No Dyslipidemia; 1: Yes Dyslipidemia
 Variable Dyslipidemia (% or median & IQR or mean & SD) Yes No Hb1Ac 84.43 15.57 BP diastolic 84.43 15.57 Insulin status: Yes 31.97 5.74 No 52.46 9.84 Age group: < 40 years 12.84 3.01 40 – 49 years 30.33 4.37 50 – 59 years 34.15 7.38 ≥ 60 years 7.10 0.82

The relationship between two categorical variables can be shown only with the help of clustered bar charts. This is the most appropriate chart to show the relationship between categorical variables. From figure 3.1, it is clear that dyslipdaemia is maximum in normal people and minimum in obese people.

Figure 3.1: Relationship between BMI group and dyslipdaemia

Again, from figure 3.2, it is clear that dyslipdaemia increases with the increase in age. Figure 3.3 shows the relationship between dyslipdaemia. It shows that dyslipdaemia is maximum in sedentary workers and is almost negligible in heavy physical workers.

Figure 3.2: Relationship between diabetes group and dyslipdaemia

Figure 3.3: Relationship between occupation type and dyslipdaemia

Let X be the lifetime of a battery. The lifetime of a battery is normally distributed. The mean life is given by 40 hours and the standard deviation is given by 1.2 hours. Therefore, the probability that a randomly selected bulb will last longer than 42 hours is P (X > 42) =

Let X be ages of all new employees hired during the last 5 years in a hospital. The ages are said to be distributed normally. The 95% confidence interval of the ages are given by (24.6, 37.4). Since the data is normally distributed, it can be said that the difference between the confidence interval can be distributed into four equal parts to determine the standard deviation. Thus the standard deviation can be given by ((37.4 – 24.6) / 4) = 3.2. By approaching two standard deviations towards the left of the distribution, the mean can be obtained. Thus, the mean is given by ((37.4 – (2 * 3.2)) = 31.

Let X be the scores of a medical test. The scores of a medical test is normally distributed. The mean score is given by 460 and the standard deviation is given by 100. Therefore, the probability that the given class will obtain a score higher than 589.93 is P (X > 589.93) =

The distribution of systolic blood pressure in the population is positively skewed. Thus, the shape of the sampling distribution will also be distributed normally. This can be said from the central limit theorem. The theorem states that when innumerable random samples are drawn from a population, then, the sample means of each of the samples will be equal to the population mean µ and the population standard deviation σ. The sample will also be normally distributed as the population. The sample will always follow a normal distribution if the sample size becomes large, whatever the size of the population may be.

## Summary Statistics and Dyslipidaemia Relationships

In this case, it is known that the population is distributed normally. Thus, from the theorem, it can be clearly said that the sampling distribution of the blood pressure of the population is also normally distributed as the sampling distribution contains innumerable number of random samples from the population.

1.A randomized clinical trial is the type of study where the participants are assigned randomly to different groups which compare different treatments. The participants or the researchers are not allowed to choose in which group which participant is going to be in. It will always be selected randomly. This procedure will be able to make the different groups similar to each other and the treatments received by the participants can be compared in each of the groups objectively. The when the trial starts, the best treatment is not known. The patient gets full freedom to decide whether he wants to participate in the random trial. This is randomized clinical trial.

When a research is conducted over a long period of time on the group of some individuals possessing a lot of similar characteristics and differing in one certain characteristic (eg, smoker and non-smoker female nurses) for comparison of them for a particular outcome (eg., lung cancer) is known as prospective cohort study

2.Case Control study is a study of comparison of two types of patients. One group possesses a particular disease of interest and the other group does not possess the disease. It also indicates the frequency of exposure to the disease or risk and determine the relationship between them.

Retrospective cohort study on the other hand, is the type of research study where, the records of medical history of the participants similar in many ways and different in a particular characteristic are compared for the outcome of interest. In this case, the data is always available and is not based on experiments.

3.In both prospective and retrospective and retrospective cohort study, the participants of interest are the same. They all possess similar characteristic and differ in one characteristic. The difference between the two types of study is that prospective cohort study is done on the basis of the samples selected and monitoring them over a period of time. Thus, the collection of data is time consuming. On the other hand, the retrospective study is done on the basis of medical history data of the individuals on the characteristic of interest. Thus, in prospective study, the sample is selected and then the data is collected by monitoring them, but in retrospective study, the data is obtained at first and then the sample is selected on the basis of the accepted data.

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