# Interpret results for a proportion end point.

#### Learner1

##### New Member
I am doing a study to determine the efficacy of a drug. The efficacy of the drug is measured as the proportion of patients with HbA1c (diabetes control level)<7%. With the help from Talks Stats, I was able to determine a sample size of 73, where p = 95%, t (CI) = 1.96 (95%) and m =5% (using formula n=t^2 x p(1-p)/m^2).

If 51/73 (70%) patients meet the criteria of HbA1c<7%, How do I interpret the result? How do I determine the statistical significance of this result? Is the drug efficacious?

#### jrai

##### New Member
What is your initial hypothesis about the proportion? You must be testing some hypothesis about this group. For establishing the efficacy of the drug there must be a control group.

#### Learner1

##### New Member
Thanks. I agree with you.

This is a small exploratory study with no control group. This will be the first study to quantify the efficacy of the drug (a herbal preparation). How do I frame the hypothesis?

#### jrai

##### New Member
The hypothesis has to be formed before you conduct the experiment. Say you formed the hypothesis that 85% of people in the group meet the criteria. The observed proportion is 0.7 & hypothesized proportion is 0.85. The test statistic z=(observed-hypothesized)/sqrt(hypothesized/n*(1-hypothesized))=(0.7-0.85)/sqrt(0.85*0.15/73)= -3.58. This is less than the cutoff of -1.64(for 95% confidence. Use excel function =normsinv(0.05)). Therefore, you conclude that either some rare event has happened or the hypothesis was incorrect.

This is a 2-tailed test. You can even do the single tailed tests(involving inequality). For further reading: http://stattrek.com/lesson5/proportion.aspx

#### Dason

You don't necessarily need a hypothesis. The goal could just be to create a confidence interval.

#### Learner1

##### New Member
You don't necessarily need a hypothesis. The goal could just be to create a confidence interval.

Thank you Dason. Will the confidence interval (t) used to calculate the sample size suffice? Please explain.

#### Learner1

##### New Member
You don't necessarily need a hypothesis. The goal could just be to create a confidence interval.
I did a little homework. Please let me know if I am correct.

I do not have an hypothesis for the study because this is the first study for the drug.

If 51/73 subject achieve the endpoint (HbA1c<7%), then using the formula (Reference: http://davidmlane.com/hyperstat/B21574.html)

p ± z σp

where σp is √p (1-p)/N

for a 95% CI the lower and upper limit is calculated as 0.602 and 0.798 (without correction for continuity)

Now, Can I say with 95% CI that the success rate of the drug falls between 60 and 79%? If yes, Can I use this value to generate a hypothesis for my next study.