Find a general formula for the MLE for p

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SUMMARY

The discussion centers on finding the Maximum Likelihood Estimator (MLE) for the proportion of patients killed by a risky treatment, denoted as p. The probability distribution of the number of survivors, N, is defined as P(N=n)=((n+1)(1-p)^n)p^2. Observed values of N from eight hospitals are provided: 3, 0, 4, 2, 3, 5, 1, 3. The thread was ultimately closed due to its classification as a homework question, indicating that it should be posted in a designated section for homework and coursework inquiries.

PREREQUISITES
  • Understanding of Maximum Likelihood Estimation (MLE)
  • Familiarity with probability distributions, specifically the binomial distribution
  • Basic knowledge of statistical analysis in clinical experiments
  • Experience with data collection and interpretation in medical research
NEXT STEPS
  • Study the derivation of Maximum Likelihood Estimators in statistical theory
  • Research the properties of binomial distributions and their applications in clinical trials
  • Explore statistical software tools for MLE calculations, such as R or Python's SciPy library
  • Review ethical considerations and guidelines for conducting clinical experiments
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Statisticians, clinical researchers, and students in medical statistics who are involved in analyzing treatment outcomes and estimating probabilities in clinical trials.

ianrice
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An experiment consists of giving a sequences of patients a risky treatment until two have died, and then recording N, the number who survived. If p is the proportion killed by the treatment, then the distribution of N is:

P(N=n)=((n+1)(1-p)^n)p^2


Find a general formula for the MLE for p:


The experiment is done in 8 hospitals, and the observed values of N are 3, 0, 4, 2, 3, 5, 1,3. Compute the estimate for p derived in part (a)
 
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This looks like a homework question or a risky experiment. If it's homework, it should be posted in a different section of the forum along with a statement of your attempts. If this was a risky experiment, please describe all the details.
 
As Stephen said, questions of this nature must be posted in the Homework & Coursework sections, not in the technical math sections. I am closing this thread. You are welcome to repost in the HW & CW sections.
 

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