The standard treatment of cancer by a standard chemical substantially shrinks or

Question

The standard treatment of cancer by a standard chemical substantially shrinks or eliminates tumors in about 60% of patients, i.e., the response rate is 60%. To verify the improvement of a newly developed chemical, a clinical trial is conducted to randomly assign patients to the standard chemical and to the newly developed chemical. The objective of this c trial is to identify a 15% higher response rate for the new chemical (i.e., 75%), at 95% confidence level. (a) If the patients are assigned with equal numbers in each group. How many patients in each group would be needed? (b) What if the patients are assigned with a 2 to 1 ratio to the standard group and to the new chemical group?

Explanation / Answer

Here we don't know population size . so for instance population size is the total no. of cancer patients in a country. confidence interval is called as margin of error, no sample is perfect so sample results are just estimated but not accurate. Confidence interval determines how much higher or lower than the population mean we are willing to let our sample mean to fall. ( +/- 5%) Confidence level given to be 95% , ie we are confident that actual mean falls within the confidence interval Standerd deviation : is how much variance we expect in our responses. As we have not administered the survey yet , therefore most safe value for standerd deviation is 0.5 , most forgiving number... 95% - Z score = 1.96 Sample size = ( Z score)2 *(standerd deviation) *(1 - standerd deviation) / ( margin of error)2 = (1.96)2 *(0.5)*(0.5) / (0.05)2 = (3.8416 *0.25) / 0.0025 = 384.16 = 385 a) Thus 385 patients in each group are needed. b) Now if the patients are assigned to 2 :1 ratio to the standerd & new chemical group then, obviously our objective will not be fulfilled to identify additional 15% success ratio. As sample size should be kept same for various groups to make analysis as ther may be som non respondents . In short , all the events ahould be equally likely, EXPERIMENT SHOULD BE RANDOM TO GET MORE ACCURATE RESULTS. Again as the sample size decreases , precision of the results also will get decreased. so comparison will not be possible. In the selected sample, some patients may have initial stage which is curable , some may have reached to the final stage , as a result they may not respond to the medicine , such unavoidable erros may happen . so sample size should be kept equal / uniform to get more accurate results by comparison reducing margin of error.

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