Determining Sample Size for Studying Sodium Consumption and Hypertension

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Discussion Overview

The discussion revolves around determining the sample size necessary for studying the relationship between sodium consumption and hypertension, specifically focusing on how many participants are needed to ensure a sufficient number of normotensives for the study. The conversation includes considerations of statistical power, significance levels, and the implications of effect size and standard deviation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants propose calculating the total number of individuals needed to identify 1709 normotensives based on the prevalence of hypertension and prehypertension in the population.
  • Others question whether effect size and standard deviation should be considered in the sample size calculation, expressing uncertainty about the relevance of the provided information regarding test reliability.
  • A participant suggests that the approach to determining sample size should start with setting a hypothesis regarding sodium consumption and its effects on hypertension, rather than focusing solely on the statistical parameters given.
  • There is confusion among participants regarding the meaning of "elevation" in the context of the problem, indicating a lack of clarity on how it relates to the study's objectives.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of incorporating effect size and standard deviation into the sample size calculation. There is no consensus on how to approach the problem, and several participants seek clarification on specific terms and methodologies.

Contextual Notes

Participants note limitations in the information provided, particularly the absence of population standard deviations, which may affect the sample size estimation. The discussion remains focused on estimating population sizes without resolving the implications of the statistical parameters mentioned.

Jadan89
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You are interested in studying the relationship between sodium consumption and the development of hypertension. 32% of Americans are hypertensive (systolic blood pressure>140), and a further 29% are prehypertensive (140≥SBP>120). Detecting a 1 mm Hg SBP elevation with 80% power at the 0.05% significance level will require 1709 study participants.

How many total people will you have to identify to have 1709 normotensives (SBP≤120mmhg) for your study? How many will you have to identify if you just exclude hypertensives?

Thank you :)))
 
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Jadan89 said:
You are interested in studying the relationship between sodium consumption and the development of hypertension. 32% of Americans are hypertensive (systolic blood pressure>140), and a further 29% are prehypertensive (140≥SBP>120). Detecting a 1 mm Hg SBP elevation with 80% power at the 0.05% significance level will require 1709 study participants.

How many total people will you have to identify to have 1709 normotensives (SBP≤120mmhg) for your study? How many will you have to identify if you just exclude hypertensives?

Thank you :)))

Hi Jadan89! Welcome to MHB! ;)

Suppose we need $n$ persons to find 1709 normotensives.
Then we can expect that $n\cdot 32\%$ have hypertension and $n\cdot 29\%$ are prehypertensive.
The remainder must be normotensive.
If we have 1709 normotensives, how big must $n$ be? (Wondering)
 
I like Serena said:
Hi Jadan89! Welcome to MHB! ;)

Suppose we need $n$ persons to find 1709 normotensives.
Then we can expect that $n\cdot 32\%$ have hypertension and $n\cdot 29\%$ are prehypertensive.
The remainder must be normotensive.
If we have 1709 normotensives, how big must $n$ be? (Wondering)
Hello! Thank you for welcoming me and the reply!

I should have probaby added this to the original post, but shouldn't the effect size and standard deviation be calculated somehow? or am overthinking this too much?

Thanks again!
 
Last edited:
Jadan89 said:
Hello! Thank you for welcoming me and the reply!

I should have probaby added this to the original post, but shouldn't the effect size and standard deviation be calculated somehow?

Thanks again!

... but we have no information about the population's standard deviations... we only have information about how reliable a test to detect elevation is... :confused:
As long as we're only "estimating population sizes", I think we shouldn't take a test to detect a specific elevation into account.
 
I like Serena said:
... but we have no information about the population's standard deviations... we only have information about how reliable a test to detect elevation is... :confused:
As long as we're only "estimating population sizes", I think we shouldn't take a test to detect a specific elevation into account.

I only assumed we had to use the effect size and standard deviation to calculate the sample size because we were provided with information about the power and significance level. Also, I am not totally sure of what "elevation" means in this problem.

Thanks!
 
Jadan89 said:
I only assumed we had to use the effect size and standard deviation to calculate the sample size because we were provided with information about the power and significance level. Also, I am not totally sure of what "elevation" means in this problem.

Thanks!

To be honest, I don't understand what they mean with the test for elevation either. :o

Still, it's the wrong way around.
First we set a hypothesis, in this case that high sodium consumption results in hypertension.
Then we pick a sample, and measure the effects of sodium on hypertension before and after some treatment or some such.
As I understand the question, we want to know how big the sample should be to contain sufficient normotensitives before applying the treatment and checking the result on hypertension with our test.

Anyway, if you can get clarification about what is meant exactly with that test for elevation, that would help. :)
 
I like Serena said:
To be honest, I don't understand what they mean with the test for elevation either. :o

Still, it's the wrong way around.
First we set a hypothesis, in this case that high sodium consumption results in hypertension.
Then we pick a sample, and measure the effects of sodium on hypertension before and after some treatment or some such.
As I understand the question, we want to know how big the sample should be to contain sufficient normotensitives before applying the treatment and checking the result on hypertension with our test.

Anyway, if you can get clarification about what is meant exactly with that test for elevation, that would help. :)

Thank you, that makes a lot more sense. I was probably confused and overthinking the question because of all the other extra information provided in the problem.

I appreciate the help! :)