in the same way as用的不合适, as 应改为that .
因为后面是一个同位语从句, as不能引导同位语从句, 而that 可以.
改正后的句子:
Crimes vary in degree in the same way that disease range from the common cold to fatal form of cancer.
that引导的是一个同位语从句对way作进一步的说明.
in the same way意思是“以同样的方式”.
range from ...to...(范围)从...到..
句意: 从普通的感冒到各种致命的癌症,疾病有轻有重,违法犯罪也同样有轻重之分.