Data Set 8: Hodgkin’s DiseaseAngela Meng and Laura Mockensturm

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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 cells2

The Present Study

● 538 patients● Followed for 3 months during treatment

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Odds Ratio and Relative Risk

● Positive: LP● Partial: NS and MC● None: LDRelative Risk of Positive Reaction● LP is...

o 0.5% higher than the NS patientso 22.9% higher than the MC patientso 184.6% higher than the LD patients

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Cumulative Proportions

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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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Cumulative Logit Model

Model:

Model Assumptions:● Separate intercept, αj, for each cumulative logit● Same slope, β

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Model 1

● Explainatory variable (X) - histological type with 4 categories

● Response variable (Y) - response with 3 categories with natural ordering (positive - partial - none)

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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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Model 1.1

● Model with no explanatory variable (with intercept term only)● Residual deviance=68.2955

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Likelihood Ratio Test

● Test statistic65.5672,df=3,p-value=3.793411e-14

● Indicates there is strong association between histological type and response

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Log-linear Model

Treats X and Y symmetrically

DF = (I-1)(J-1)

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Model 2 -log-linear model with homogeneous association

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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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Examine the standard residuals

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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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Model 2.1

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Conclusion: Model

● Best Model: Cumulative logit

i) logit[P(Y≤1)] = -1.3181 + 2.2481LP + 1.6389MC + 2.2222NSii) logit[P(Y≤2)] = -0.3679 + 2.2481LP + 1.6389MC + 2.2222NS

where LP, MC and NS are dummy variables

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Conclusion: Meaning

● Odds Ratio:o Between LP and LD is 9.4697o Between MC and LD is 5.1495o 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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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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