13 Statistics

VVK13-001
Answer the following.

a. Define median, 1st quartile and 3rd quartile.
b. What is the difference between rate and ratio?
c. What is the basic difference between a 'case control' and 'cohort' study design?
d. What is the difference between incidence and prevalence?

Answer

a. If the observations are arranged in ascending or descending order: Median: 50% observations are below and 50% are above this value. 1st Quartile: 25% observations are below and 75% are above this value. 3rd Quartile: 75% observations are below and 25% are above this value.
b. Rate: Numerator is part of denominator Ratio: Numerator is not part of denominator.
c. Case control study is retrospective and cohort study is prospective.
d. Incidence: The number of new cases occurring in defined population during a specified period of time. Prevalence: Number of all cases old and new at a given point of time or over a period of time in a given population.

VVK13-002
Interpret the following statement.
In a RCT, the 'odds' of developing HMD were 0.55 (95% CI 0.3–2.1) in infants whose mothers were given 'antenatal steroids'.

Answer

In infants of mothers who had received antenatal steroids the chances of developing HMD are 45% less as compared to those whose mother had not received antenatal steroids. However, the 95% confidence intervals are not significant.

VVK13-003
In a small government hospital, 60% of early neonatal deaths have low-birth-weight. It is also seen that nearly 5% births in this hospital die within a week and about 30% births have low-birth-weight. Calculate the probability that a low-birth-weight baby would die in early neonatal period.

Answer

10%

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A 4: First arrange all values in ascending or descending order

98, 98, 98, 99, 100, 101, 101, 101, 101, 102

a. Mean = Sum of all/total no = 1000/10 = 100
b. Median = Middle value in ascending or descending order

(100 + 101)/2 = 100.5

c. Mode = That value which is the most frequent (comes for most times) =101

A 5:

a. Specificity = True negative = $d / (b + d) \times 100$
b. Sensitivity = True positive = $a / (a + c) \times 100$
c. Positive predictive value = True positive/all positive =

$a / (a + b) \times 100$

d. Negative predictive value = True negative/All negatives =

$d / (c + d) \times 100$

A 6:

Stillbirth rate =
$\frac{No of fetal deaths (with weight > 1000 g)}{Total live + stillbirths (with weight > 1000 g)} \times 1000 g$

$\frac{5}{40 + 5} \times 1000 = \frac{1000}{9} = 111.1$

Neonatal mortality rate =
$\frac{No of deaths in first month}{Total live births} \times 1000$

$\frac{5}{40}$
× 1000 = 125

b. Perinatal mortality rate is total number of late fetal deaths (> 28 weeks of gestation or fetus > 1000 grams) +

neonatal deaths in the first seven days of life

A 7:

a. Prevalence rate:

No of existing + new cases
Population at risk
$\frac{(500 + 100) \times 100}{5000} = \frac{600 \times 100}{5000} = 12$

b. Incidence rate:

No of new cases of specific disease

during a given period of time
$\frac{100 \times 1000}{Population at risk} \times 1000 = \frac{100 \times 1000}{5000} = 20$

c. Case fatality rate:

Total no of deaths due to a particular disease
$\frac{20}{Total no of cases due to the same disease} \times 100 = \frac{(500 + 100)}{(500 + 100)} \times 100$

$= \frac{20 \times 100}{600} = 3.33$

d. Advantage:
- i. To estimate magnitude of health disease problem in country.
- ii. To identify potential risk population.
- iii. For administrative and planning purposes.

VVK13-004
The height of 10 children of the same age group is given: (all in cm).
101, 98, 98, 99, 102, 101,100, 98, 101, 101

Calculate:

a. Mean
b. Mode
c. Median.

Answer

No model answer in source material.

VVK13-005
At a camp, a new model of mass miniature radiography was used to screen for tuberculosis. Subsequently, the subjects were also subjected to CT scan of the chest to confirm whether the results were reliable or not. The results were as follows.

Screening test	Diseased	Not diseased
Positive	a (TP)	b (FP)
Negative	c (FN)	d (TN)

Calculate (give formulae)

a. Specificity
b. Sensitivity
c. Positive predictive value
d. Negative predictive value.

Answer

No model answer in source material.

VVK13-006
Out of 50 babies delivered in a hospital, 10 were stillbirths. Out of this, 5 were less than 1000 g. Out of the survivors, 5 died in first month of life.

a. Calculate:
b. Define perinatal mortality rate.

Answer

No model answer in source material.

VVK13-007
Out of a population of 5000 children in a village, 500 cases of malnutrition already exist. There are 100 newly diagnosed cases in a year. 20 children died of malnutrition. Calculate.

a. Prevalence rate.
b. Incidence rate.
c. Case fatality rate.
d. What is advantage of calculating prevalence rate?

Answer

No model answer in source material.

VVK13-008
Answer the following questions.

a. Define p-value.
b. In a study of 30 patients of liver cirrhosis, enzyme level was evaluated before and after treatment. What statistical test would you apply in this case?
c. When do you apply non-parametric test?

Answer

a. It is the probability of type 1 error, i.e. the chance that a difference or association is concluded when actually there is none.
b. Paired 't' test.
c. Non-parametric test is applied when distribution is non-Gaussian and sample size is small.

VVK13-009
a. Calculate the odd's ratio in the given case control study design:

Exposure (risk factor)	Disease present	Disease absent
Yes	a	b
No	c	d
Total	a + c	b + d
b. What is the significance of the term odds ratio in statistical terms?

Answer

a. For case control studies, ratio of odds

$= \frac{a / c}{b / d} = a d / b c$

b. Odds ratio is a measure of strength of association between outcome and antecedent

OR = 1 means that the risk factor has no association with the disease

OR>1 suggests risk factor associated with increased disease

OR<1 suggests risk factor protective against disease.

VVK13-010

images/VVK-P-Osce 13. Statistics_page_2_Figure_3.jpeg

a. What is this plot known as? And where are they primarily used?
b. What is the arrowed figure known as?
c. In this plot which study has the best association regarding the outcome?

Answer

a.Forest plot are used in meta-analysis.

b.Diamond.

c.Study done by Kay.

VVK13-011
You are doing a study "Is zinc better than racecadotril for diarrhea" and the results are like this.

Zinc	Racecadotril
Improvement	Nil	Improvement	Nil
12	27	6	20

a. Calculate the relative risk.
b. What does it signify?

Answer

a. RR (Treatment) is =
$\frac{n (Exposed)}{n (Non exposed)}$

$= \frac{12 / 39}{6 / 26} = 1.52$

b. Outcome variable is 1.52 times more in the zinc group than in the racecadotril group.

A 12.

1000 - under 5 mortality

a. Child survival index = ________________________________________________ 10 = 1000-5/10 = 99.5

b. Student 't' test
c. Chi-square test

VVK13-012

a. In an area the under 5 mortality is 5/1000 live births. Calculate the child survival index in that area.
b. What is the appropriate statistical test to compare two means?
c. What is the appropriate statistical test to compare two proportions?

Answer

No model answer in source material.

VVK13-013

images/VVK-P-Osce 13. Statistics_page_3_Figure_3.jpeg

a. What is this plot known as?
b. What is this used for?
c. Describe the plot.

Answer

a. Box-and-whisker plot.
b. They display a statistical summary of a variables : median, quartiles, range and extreme values.
c. The central box represents the values from the lower to upper quartile (25 to 75 percentile).

The middle line represents the median.

The horizontal line extends from the minimum to the maximum value, excluding outside and far out values which are displayed as separate points.

VVK13-014
In an international clinical trial, two chemotherapy treatments are being compared (Choose the correct answer for each of the following questions).

a. How are systematic differences between treatment groups best minimized?
i. Analyze results by country separately.
v. Randomization.
b. What is the rationale for conducting a clinical trial in a double blind manner?
i. It effectively increases the size of the trial by using each patient as their own control.
v. It reduces the effects of sampling variations.
c. In a normal distribution the mean of the data will be similar to the:
i. Maximum.
v. Standard error.
d. The table below shows the number of adverse effects reported in a randomized trial comparing two treatments—A and B.
i. 4/16
v. 4/60

Answer

a. v (Randomisation).
b. iv (Reduces systematic bias between the treatment and control groups).
c. ii (Median).
d. iii (4/28).

VVK13-015
Calculate sensitivity, specificity, positive and negative predictive value of ECG test for myocardial infarction (MI) from the data given below.

ECG		M I	Total
	Present	Absent
Positive	300	100	400
Negative	25	75	100
Total	325	175	500

Answer

Sensitivity = 300/325 = 92.3%
Specificity = 75/175 = 42.9%
PPV = 300/400 = 75%
NPV= 75/100 = 75%

VVK13-016
Consider the following reterospective data on the parity of mothers of 210 normal and 140 IUGR babies.

IUGR	Parity < 3	Parity > 3	Total
Present	98	112	210
Absent	92	48	140

a. What are the odds for mothers with parity < 3 giving birth to IUGR baby as compared to mother with parity > 3?
b. What is the difference between odds ratio and relative risk?

Answer

a. Ods ratio = ad/bc
- = 98 × 48/92 × 112 = 0.45
b. Relative risk is applicable only to prospective studies while odds ratio is used only in retrospective studies.

VVK13-017
Which of the following statements are true regarding power of a study?

a. Power is the probability of rightly rejecting a null hypothesis when it is false.
b. Power is directly related to the magnitude of the difference to be detected.
c. Power increases as the sample size increases.
d. An increase in the level of significance is a negative feature whereas an increase in power is a positive feature of a statistical test. These should be balanced.
e. Power increases if a higher probability of type I error can be tolerated.

Answer

All the given statements are correct.

VVK13-018
State true/false regarding case control study design.

a. A case control study is done to generate a hypothesis.
b. A case control study requires a large number of subjects and large number of controls.
c. A case control study cannot be retrospective.
d. A case control study is an analytical study.
e. A case control study is an observational study.

Answer

a. False: It tests already set up hypothesis.
b. False: It can be done on relatively small number of cases and controls because status of disease in the subjects is already known.
c. False: It is always retrospective.

adolescent, adult

d. True: Involves comparison of presence of an antecedent in cases and controls.
e. True: It does not involve any human interventions. Only natural occurrence is observed.

VVK13-019
Match the items with appropriate scale of measurement.

a.	Number of cigarettes smoked	i.	Ordinal
b.	Body temperature	ii.	Ratio
c.	Age in completed years	iii.	Interval
d.	Age in categories, e.g. child,	iv.	Metric
	adolescent, adult
e. Stage of a cancer v. Continous variable f. Blood sugar levels vi. Discrete variable

Answer

a. Number of cigarettes smoked - Ratio b. Body temperature - Interval c. Age in completed years - Metric d. Age in categories, e.g. child, - Ordinal

e. Stage of a cancer - Discrete variable f. Blood sugar levels - Continous variable

A 20:

a. Positive predictive value is the chance of presence of the disease when the test is positive. If this is 90%, there is still a chance of 10% that the disease is not present. Thus PPV can be used to reassure the patient that there is still some chance of absence of disease despite positive test.
b. Test with high negative predictive value (NPV).
c. Test with high positive predictive value (PPV).

A 21:

a. Attack rate of measles = $\frac{No. of cases/spells in a year}{No. at risk for measles}$

$= 10 / (1300 - 800) = 10 / 500 = 2 %$

secondary cases

b. Secondary attack rate = $\frac{1}{No. of susceptible children coming in contact}$ = $\frac{8}{15} = \frac{53}{8}$

VVK13-020

a. You use a histological test for cancer that has sensitivity, specificity, positive predictivity and negative predictivity in excess of 90%. Which of the four indicators would you use to reassure a patient that the positive test could still be an error?
b. Which test would you use for ruling out a disease in a patient?
c. Which test would you use for confirming a disease in a patient?

Answer

No model answer in source material.

VVK13-021
Consider the following data.

•	Total population of children in an area	-	1300
•	Protected against measles by vaccination	-	800
•	Total cases of measles in one year	-	10
•	Primary cases	-	2
•	Number of susceptible children coming in contact	-	15
	of primary cases
•	Secondary cases that received infection from primary	-	8
	cases within the infective period

a. Calculate attack rate of measles. b. Calculate secondary attack rate of measles.

Answer

No model answer in source material.

VVK13-022
In a hospital data, fetal deaths during the late gestation period (> 28 weeks) was found to be only 2%. Out of all the remaining live births, 3% died within 1 week. What is the perinatal mortality rate in this hospital?

Answer

• 49/1000.

Fetal deaths = 2%
So live births out of 100 pregnancies (≥ 28 weeks gestation) = 98
So death within first week = 3% of 98 = 2.94

$P M R = \frac{S t i l l b i r t h + d e a t h w i t h i n o n e w e e k}{S t i l l b i r t h + l i v e b i r t h} = \frac{2 + 2.94}{2 + 98}$

= 4.94% = 49/1000 (as it is a rate and not ratio)