Interpret results for a proportion end point.

[Learner1]

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?

Please help. Thanks.

 

[jrai]

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]

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]

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]

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]

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.

Please help me with the answers. Thanks.

 

[Learner1]

Thank you so much jrai. This will of immense help to generate a hypothesis and test the significance of a proportion result.

Since my study is the first one using the drug and since I have no experience with efficacy of the drug,

Is it possible to do the study without an hypothesis (as suggested by Dason), and then use the results as the hypothesis for the next controlled trial.