5.11 Consider the survival times of 48 patients with hypernephroma, who received

Question

5.11 Consider the survival times of 48 patients with hypernephroma, who received either combined chemotherapy and immunotherapy (treatment 1) or others (treatment 2). The investigators wish to compare the effective- ness of the two treatments but suspect that age may be a confounder. The survival data in Exercise Table 5.2 are stratified by age. Are the two treat- ments equally effective after adjusting for age? Survival Times of Patients with Exercise Table 5.2 Hypernephroma Treatment 1 Age (Years) Treatment 2 Age (Years) 65 65 77+ 68 35 84 52 56 18 17 18 9 36 10 9 12 21 14 52 48 15 9 25+ 28+ 25+ 26 26 108+ 72 38 108 36 20 14 20 181+ 40 16 12 26

Explanation / Answer

Chegg=read.csv("Chegg_CSV.csv", sep=",", header=T)
> Model=aov(Survival_time~ factor(Treatment)+factor(Age), data=Chegg)
> summary(Model)
Df Sum Sq Mean Sq F value Pr(>F)
factor(Treatment) 1 1334 1334 1.371 0.24795
factor(Age) 2 10985 5492 5.646 0.00657 **
Residuals 44 42799 973
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
426 observations deleted due to missingness

Conclusion: The estimated p-value of treatment is  0.24795. Hence, we know that the mean of the survival time between the two treatment is same after adjusting the age at 0.05 level of significance.

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