Statistical analysis

Statistical analysis

Part A

1. Probability of tumor

Number of test rats

Number of rats with tumors

Rat test dose in mg Kil-EZ per kg rat body weight (mg/kg/day)

Probability of a rat's developing tumors

50

1

0

0.02

50

5

20

0.1

50

10

40

0.2

50

20

80

0.4

50

7

160

0.14

2. The probability is lower at a dose of 160 mg/ kg. day than at a dose of 80 mg/ kg. day

The probability is lower at 160 mg/ kg, day because the number of rats that were suspected with tumor were seven out of fifty rats, that is, less than the rats with tumors that has probability of 0.4. It indicates that the more numbers of rats out of the actual sample size has more probability of tumor. It has been found that the total number of rats with 20 quantity has 0.4 probability that is higher than the number of rats with seven.

3. Graph of probability and dose

The above graph shows the probability of tumor at different level of doses.

4. Cancer potency in kg-day/mg

The formula by which the potency of cancer is calculated is: Probability of tumor = (cancer potency) * dose

Number of test rats

Number of rats with tumors

Rat test dose in mg Kil-EZ per kg rat body weight (mg/kg/day)

Probability of a rat's developing tumors

cancer potency

50

1

0

0.02

0.010

50

5

20

0.1

1.090

50

10

40

0.2

2.170

50

20

80

0.4

4.330

50

7

160

0.14

8.650

The probability at zero doses and at 160 doses should not be included in the chart for calculating the cancer potency, because the cancer potency at the lowest probability will form a outlier and even with the highest probability it will form the outlier too. The cancer potency at these two points deviates from the linear line.

5. Dose that would correspond to cancer probabilities of 1E-6 and 1E-4

Probability of a rat's developing tumors

cancer potency

cancer potency (1E-6)

cancer potency (1E-4)

Dose at cancer probabilities (IE-6) kg-day/mg

Dose at cancer probabilities (IE-4) kg-day/mg

0.02

0.010

0.012

0.028

1.603

0.706

0.1

1.090

1.092

1.108

0.092

0.090

0.2

2.170

2.172

2.188

0.092

0.091

0.4

4.330

4.332

4.348

0.092

0.092

0.14

8.650

8.652

8.668

0.016

0.016

Part B

6. The standard deviation at each dose level

Rat test dose in mg Kil-EZ per kg rat body weight (mg/kg/day)

Standard Deviation

0

0.140

20

0.134

40

0.126

80

0.110

160

0.131

7. 95% confidence intervals for each of the probabilities

Number of test rats

Number of rats with tumors

Rat test dose in mg Kil-EZ per kg rat body weight (mg/kg/day)

Probability of a rat's developing tumors

Standard Deviation

Lower 95% confidence level

Upper 95% confidence level

50

1

0

0.02

0.140

-0.254

0.294

50

5

20

0.1

0.134

-0.163

0.363

50

10

40

0.2

0.126

-0.048

0.448

50

20

80

0.4

0.110

0.185

0.615

50

7*

160

0.14

0.131

-0.117

0.397

8. The upper 95% confidence level for the 20 mg/kg-day dose

The cancer potency at the upper limit is calculated below;

y = 0.045 x + 0.286

y= 0.045 (20) + 0.286

y= 1.186 kg-day/ mg

9. The lower 95% confidence level for the 20 mg/kg-day dose

The cancer potency at lower limit is calculated below;

y= 0.062x - 0.286

y= 0.062(20) - 0.286

y= ...