Cancer is the leading cause of death in Australia. It is estimated that more than 130,000 cases will be diagnosed with cancer in 2017 and further, that the estimated number of deaths will be around 50,000. If we look at the time series data of cancer incidence and cancer mortality it seems there is a very high significant correlation between these variables. This may be spurious and misinterpreted which is quite often the case in epidemiological studies. In this paper we have introduced the concept of co-integration and shown that although cancer incidences are increasing very fast, cancer mortality is not increasing that fast. This paper demonstrated that there is no long term relationship or co-integration between these two variables. However, there exists a short-run causal relationship from cancer to mortality for the cases of lung and prostate cancers. The impulse response function reveals that the mortality peaks at second year and the effect gradually disappear after 8 years.