1. Data Set 8: Hodgkin’s
Disease
Angela Meng and Laura Mockensturm
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2. Background
● Cancer of the lymphatic system
● Body’s ability to fight the disease is weakened
Histological Types:
● Lymphocyte predominance (LP): males younger than 18, great
survival rates
● Nodular sclerosis (NS): affects the colon
● Mixed cellularity lymphoma (MC): affects white blood cells and
plasma cells
● Lymphocyte depletion (LD): adults with immune-deficient viruses,
fewer white blood cells
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4. Odds Ratio and Relative Risk
● Positive: LP
● Partial: NS and MC
● None: LD
Relative Risk of Positive Reaction
● LP is...
o 0.5% higher than the NS patients
o 22.9% higher than the MC patients
o 184.6% higher than the LD patients
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6. Chi-Squared Test for Independence
● The chi-squared test statistic can be calculated by the formula
below with df=(I-1)(J-1)
● X-squared = 75.8901, df = 6, p-value=2.517e-14
● Strong evidence of dependence
● Standard residuals
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10. Goodness of fit test
● Residual deviance=2.7283, df=3,p-value=0.4354
● Indicates our current model is adequate for describing the data
● Pearson’s residuals all fall within the range of ±2
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11. Model 1.1
● Model with no explanatory variable (with intercept term only)
● Residual deviance=68.2955
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12. Likelihood Ratio Test
● Test statistic
65.5672,df=3,p-value=3.793411e-14
● Indicates there is strong association between histological type and
response
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15. Goodness of fit test
● Residual deviance=68.295, df=6,p-value=9.141963e-13
● Indicates our current model is not adequate for describing the data
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17. How to improve our model?
● Only option will be including the interaction between histological
type and response, which gives us the saturated model
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19. Conclusion: Model
● Best Model: Cumulative logit
i) logit[P(Y≤1)] = -1.3181 + 2.2481LP + 1.6389MC + 2.2222NS
ii) logit[P(Y≤2)] = -0.3679 + 2.2481LP + 1.6389MC + 2.2222NS
where LP, MC and NS are dummy variables
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20. Conclusion: Meaning
● Odds Ratio:
o Between LP and LD is 9.4697
o Between MC and LD is 5.1495
o Between NS and LD is 9.2276
● LP is most likely to show positive response
● LD is least likely to show positive response
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21. Citations
"Hodgkin's Lymphoma." Mayo Clinic. Mayo Foundation for Medical
Education and Research, 15 Aug. 2014. Web. 04 Apr. 2015.
"Childhood Hodgkin Lymphoma Treatment (PDQ®)." National Cancer
Institute. National Institute of Healths, 28 Jan. 2015. Web. 04 Apr. 2015.
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Editor's Notes
Before fitting a model to our data, we wanted to see if the the variables are dependent.
Residuals shows our observed values deviates a lot, further evidence to reject the Ho of independence.
All p-values are sig
Outside the range
Talk about perfect fit, we do not want a saturated model. This makes sense because log-linear model does not consider the natural ordering in the response, some information from the original data is lost when using log-linear model, which results in lack of fit in data.
The estimated odds that patients with histological type LP is likely to show a response to the treatment in the direction of positive response (Y≤j) rather than no response (Y>j) is e^2.2481 = 9.4697 times the estimated odds of that of patients with histological type LD. Similarly, the estimated odds that patients with histological type MC is likely to show a response to the treatment in the direction of positive response (Y≤j) rather than no response (Y>j) is e^1.6389 = 5.1495 times the estimated odds of that of patients with histological type LD. And the estimated odds that patients with histological type NS is likely to show a response to the treatment in the direction of positive response (Y≤j) rather than no response (Y>j) is e^2.2222 = 9.2276 times the estimated odds of that of patients with histological type LD.
