Sample Size Calculation, Power Calculation, Random Allocation, Chi Square Test, Correlation and Regression, ANOVA, Wilcoxon test

Group Work on Sample Size Calculation

1.      The mean birth weight (SD) of newborn is observed to be 2.25(0.4) kg in pregnant women belonging to low socioeconomic group. A study is to be carried out to determine whether nutritional supplementation would increase the birth weight of newborn. It is planned to include two groups of pregnant woman - one without supplementation (control group) and the other with supplementation (test group). Calculate the size of each group.

2.      The cure rate of a drug in a disease is 20%. It is claimed yoga is better than the drug and a trial is to be conducted find out the truth. It is decided that a even 10% increase in cure rate would be clinically important. The alpha and beta were set at 0.1 and 0.1. The results will be analysed using Chi Square test. How many patients would be required for the trial?

3.      The mean(SD) hospital stay of patients after a conventional surgical procedure (CP) is 12.3(4.8) days. A modified procedure(MP) is to be tried to reduce the stay. Two groups of patients will be undergoing either CP or MP. Their hospital stay will be compared using unpaired t test at p<0.05 with power of 90%. The minimum important difference is expected to be 3.Calculate the sample size for each group.

4.      An analgesic is to be compared to a placebo. The placebo effect in analgesic studies is reported to be up to 30%. It was decided to detect a minimum difference of 20% at 5% significance level with 80% power. The results will be analysed using Chi Square test.

Group Work on Power Calculation

1.        A study on the diuretic effect of a plant product concluded that the plant product was not effective. The study was conducted on two groups of 5 volunteers each. One group was given the plant product and the other placebo. The difference obtained was 0.5 litres/24 h. The SDs were 0.29 and 0.33 for the groups which were analysed using unpaired t test with a pre-set alpha level of 0.05 and the difference was not significant (P>0.05).  Find out whether the study had enough power to detect the difference?     (Solve the problem with 10 volunteers in each group)

2.      The protective effect of a vaccine was tested and when the results were analysed using the Chi Square test (alpha = 0.05), it was found that vaccine was not effective (P>0.05). 28/100 in vaccine group and 17/100 placebo group were protected by the vaccine while others developed the disease. Find out whether the study had enough power to detect the difference?  (Solve the problem with 250 patients in each group)

Group work on Random Allocation

1.      Allocate a total of 20 subjects to 2 groups namely 1 & 2.

2.      Three groups of 8 mice each are to be used in an experiment. Generate random numbers to allocate animals to different groups.

Group Work on Choosing a Statistical Test

Task : Choose a statistical test to be used in the following situations

1. In an experiment, 2 groups of 6 rats were injected with amphetamine and saline  respectively and food intake (weight of pellets consumed in grams) was measured for 2 hours.

2. The effects of atropine (1.0 %  solution) on the pupil size was studied in 8 rabbits. The pupil size was measured (in mm) before and after administration of saline in one eye and atropine in the other.

3. The analgesic effect of morphine (3 mg/kg; sc) and aspirin (10 mg/kg; sc) were compared using 0.6% acetic acid writhing in three groups of mice. Saline group was used as control.

4. A new drug was tested to see whether its concentration in the body alters with time. 10 mg of the drug was given iv and plasma concentration was measured at 4, 8, 12, 24, 48 & 72 hr.

5. The wound healing effect of a traditional drug was tested in rats. Two groups of rats (6 each) were administered either saline or test drug and the effect was measured in scores(0-5; 0 -No healing; 5- Complete healing)

6. The antihypertensive effect of a drug was measured in 10 rats. Baseline mean BP was measured on day 0. The drug was given on day 1,2,3….10. BP was recorded  on days 1,2,3….10.

7. Does the blood pressure vary with bodyweight? To find out this, mean BP and weight of 100 rats were measured.

8. To evaluate an adverse effect, two groups 1000 subjects were administered either a drug or placebo. The proportion of subjects affected were 78.54% and 21.63%.

9. The effect of physostigmine on salivary secretion was tested in dogs. Before and after giving the drug, the secretion was quantified as no secretion(0), small(1), medium(2) and large(3) and compared.   

Worked Example – Task no.1 Aim - To see whether amphetamine alters food intake. Analysis type - Comparison of means Parameter to be analysed - food intake No. & Name of the groups / data sets to be analysed - 2;   saline & amphetamine Distribution of data  (Normal or Non-normal)  -  Normal Design (Paired or Unpaired) -    Unpaired                                                    STATISTICAL TEST TO BE USED -  Unpaired t (to be chosen from the table provided)

Group Work on ‘t’ test

t test – unpaired

1. In an experiment, 2 groups of 6 rats were injected with amphetamine and saline  respectively and food intake was measured for 2 hrs.  The initial weight of rat food was 10 g for each rat. At the end of 2 hrs, the remaining food was weighed and the following data were obtained:

Group I  - Amphetamine   - 8.21, 5.3, 6.4, 7.5, 6.1, 7.2 g

Group II - Saline   - 9.5, 9.4, 9.2, 8.9, 9.9, 9.2 g

2. The analgesic effect of morphine (3 mg/kg; sc) and aspirin (10 mg/kg; sc) were compared using 0.6% acetic acid writhing. The data are as follows.

Aspirin     (n=7)   :  15, 18, 18, 20, 22, 17, 16 writhings (in 15 min)

Morphine (n=6)   :  5, 8,11, 2, 10, 4 writhings (in 15 min)

t test - Paired

1. The effects of atropine (1.0 %  solution) on the pupil size was studied in 6 rabbits. The pupil size was measured before and after administration of saline in one eye and atropine in the other. The data obtained were as follows:

Right eye

Saline(1drop)before 5, 6, 3, 4, 7, 5 mm                 

                     after    6, 5, 4, 4, 6, 6 mm       Difference :  1, -1, 1,  0, -1, 1

Left eye

Atropine(1 drop)  before   6, 4, 7, 3,  5, 6 mm

                            After     7, 8, 9,  6, 8,  9, mm   Difference :  1, 4, 2,  3, 3, 3

2. The cardiostimulant activity of a plant extract (2 µg) was tested on 6 isolated frog heart preparations and the following data were obtained :

Basal heart rate-  75, 70, 61, 52, 73, 75 bpm

Plant extract      -  91, 89, 83, 59, 81, 87 bpm

Group Work on Wilcoxon test

Wilcoxon – paired

1.        The severity of pain was scored using a 10 point scale (0 – no pain, 10-intolerable pain) before and after giving an analgesic in 6 subjects :

Before – 8, 6, 8, 9, 7, 8, 7, 8, 7, 9          After – 1, 5, 2, 3, 5, 5, 0, 2, 3, 4

2.        The number of stools passed per day in 10 children suffering from  acute gastroenteritis is given as follows :

Before treatment – 6, 4, 5, 6, 6, 8, 7, 5, 9, 9     

After treatment – 6, 8, 5, 2, 2, 3, 4, 4, 5, 6

Wilcoxon – unpaired

1. The wound healing effect of a traditional drug was tested in rats. Two groups of rats (6 each) were administered either saline or test drug and the effect was measured in scores (0-5; 0 -No healing; 5- Complete healing)

Saline – 0, 1, 3, 2, 1, 0                Drug – 2, 1, 3, 4, 5, 2

2.     The effect of atropine on physostigmine induced salivary secretion was studied in 2 groups of dogs. Salivation was scored (0 - no salivation; 1- mild; 2- moderate; 3-high; 4-frothing) after physostigmine administration. One group was pretreated with atropine :

Saline pretreatment – 4, 3, 4, 2, 4, 4, 3, 4, 3, 4        

Atropine pretreatment – 1, 0, 0, 2, 2, 1, 1, 2, 2, 1

Group work on Chi Squared Test

Task : Compute a 2X2 contingency table for the following and answer the questions.

1. Out of 25 women who had uterine cancer, 20 claimed to have used estrogens. Out of 30 women without uterine cancer 5 claimed to have used estrogens. Is there an association between uterine cancer and estrogen use?

2. In a clinical trial of a new antiepileptic drug “epistil”, 1540 patients received the test drug and 1603 received the control drug (phenytoin). 152 patients in the test group and 214 in the control group developed nystagmus.

      Is there an association between nystagmus and epistil?

Group work on Correlation and Regression

1. In a pharmacokinetic study the plasma drug levels at different time points were estimated in a volunteer. Carry out the regression analysis:

Time :   4         8          12        16        24        48        h

Conc.   121      65        30        17        4          0.1       mg/ml

2. In diabetic rats the blood sugar and endogenous insulin levels were estimated. Find out if there a correlation between these two parameters:

Rat no             1          2          3          4          5          6          7          8

Blood sugar     156      102      134      184      198      203      123      176   mg%

Insulin             16        21        18        11        10        8          20        11      IU

3. The blood levels of a drug were measured by two different methods using the HPLC. One method is the gold standard used routinely. The other one is newly developed. Find out whether the new one “agrees” with the standard?

Sample no.      1          2          3          4          5          6          7          8

GS                   12        23        43        14        15        17        16        19  mcg/ml

New                14        22        48        17        16        19        16        24  mcg/ml     

 

Group work on ANOVA

1. The  % change in blood sugar level after administration of three doses of a plant product was compared with that in vehicle treated (control) animals (n=6 in each group). The data are given below :

Groups	% change in blood sugar (mean ± SEM)
Control	12.21 ± 2.81
Plant (10 mg/kg)	18.43 ± 3.12
Plant (30 mg/kg)	26.33 ± 2.96
Plant (100 mg/kg)	28.78 ± 3.02

           

Find out whether the plant product exhibits a dose dependent effect.

2. Tail flick latency observed for three different plant based drugs are given below:

Groups	n	Latency in sec (mean ± SEM)
Control	8	13.2 ± 0.8
Plant 1	8	18.43 ± 1.2
Plant 2	8	20.33 ± 1.3
Plant 3	8	19.78 ± 0.9

Analyse whether the plants exhibit analgesic action or not.

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