Seychelles Cancer Awareness Survey Planning

.title[
# Seychelles Cancer Awareness Survey Planning
]
.author[
### L’Escale, Mahe, Seychelles
]
.date[
### 27-29 May 2024
]

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## Technical Notes and Discussions

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# Outline

* General sample size considerations for surveys

* Specific sample size considerations for specific types of surveys

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# General sample size considerations for surveys

* Sample size will depend on which indicator/s need to be measured

* Sample size will depend on survey design

* Sample size will depend on amount of resources available

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# Sample size equation for prevalence surveys

* Basic formula:

$$ n ~ = ~ \frac{z ^ 2 ~ \times ~ p(1 - p)}{d ^ 2}  $$

where:

\$n ~ = ~ \text{sample size}\$

\$z ~ = ~ \text{z-score (standard deviation) for confidence interval required}\$

\$p ~ = ~ \text{known proportion of the indicator being measured}\$

\$d ~ = ~ \text{precision required}\$

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# Sample size considerations for prevalence surveys

* To calculate this adequate sample size there is a simple formula

* However it needs some practical issues in selecting values for the assumptions required in the formula

* In some situations, the decision to select the appropriate values for these assumptions are not simple

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# Sample size considerations for prevalence surveys - z statisic

* `$z$` statistic is usually a choice between these values:

| z statistic| p-value|confidence intervals |
|-----------:|-------:|:--------------------|
|        1.65|    0.10|90%                  |
|        1.96|    0.05|95%                  |
|        2.58|    0.01|99%                  |

* For most prevalence surveys (and most studies), a **95% confidence interval** is what we want to aim for

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# Sample size considerations for prevalence surveys - true prevalence

* Need to use a known value of true prevalence (\$p\$) of the indicator being measured

* This can usually be found from a literature review to find similar studies/surveys that measured similar indicators

* If proposed/planned study is so unique and measures indicators not measured before, then a best guess of true prevalence can be used; or,

* Use a true prevalence value that gives the highest possible sample size requirement - this value is **0.50 (50%)**

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# Sample size considerations for prevalence surveys - precision

* Precision, in general terms, is the amount of "swing" below and above the estimated prevalence within which the true prevalence lies

* Selecting a value for precision (\$d\$) to aim for should take into account the assumed or known true prevalence (\$p\$).

* Some authors recommended to select a precision of 5% if the prevalence of the disease is going to be between 10% and 90%

* However, when the assumed prevalence is too small (going to be below 10%) or too high (going to be greater than 90%), the precision of 5% seems to be inappropriate

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# Effect of varying true prevalence

| z-statistic| true prevalence| precision| sample size|
|-----------:|---------------:|---------:|-----------:|
|        1.96|            0.05|      0.05|          73|
|        1.96|            0.10|      0.05|         139|
|        1.96|            0.20|      0.05|         246|
|        1.96|            0.30|      0.05|         323|
|        1.96|            0.40|      0.05|         369|
|        1.96|            0.50|      0.05|         385|
|        1.96|            0.60|      0.05|         369|
|        1.96|            0.70|      0.05|         323|
|        1.96|            0.90|      0.05|         139|
|        1.96|            0.95|      0.05|          73|

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# Effect of varying precision

| z-statistic| true prevalence| precision| sample size|
|-----------:|---------------:|---------:|-----------:|
|        1.96|            0.05|      0.03|         203|
|        1.96|            0.05|      0.05|          73|
|        1.96|            0.05|      0.08|          29|
|        1.96|            0.20|      0.03|         683|
|        1.96|            0.20|      0.05|         246|
|        1.96|            0.20|      0.08|          97|
|        1.96|            0.50|      0.03|        1068|
|        1.96|            0.50|      0.05|         385|
|        1.96|            0.50|      0.08|         151|

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# Effect of varying precision - continued

| z-statistic| true prevalence| precision| sample size|
|-----------:|---------------:|---------:|-----------:|
|        1.96|            0.70|      0.03|         897|
|        1.96|            0.70|      0.05|         323|
|        1.96|            0.70|      0.08|         127|
|        1.96|            0.95|      0.03|         203|
|        1.96|            0.95|      0.05|          73|
|        1.96|            0.95|      0.08|          29|

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# Sample size considerations for prevalence surveys - finite population

* The size of the universe/total population from which sampling is to be done impacts sample size

* A finite population correction can be applied to sample size calculations to make it more appropriate/applicable to a known population size

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# Finite population correction for sample size

$$ n_{adjusted} ~ = ~ \frac{n}{1 + \frac{n}{pop}} $$
where:

\$n_{adjusted} ~ = ~ \text{Adjusted sample size}\$

\$n ~ = ~ \text{calculated sample size}\$

\$pop ~ = ~ \text{population}\$

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# Adjusted sample sizes accounting for finite population

| z-statistic| true prevalence| precision| sample size| adjusted|
|-----------:|---------------:|---------:|-----------:|--------:|
|        1.96|            0.05|      0.05|          73|       73|
|        1.96|            0.10|      0.05|         139|      139|
|        1.96|            0.20|      0.05|         246|      246|
|        1.96|            0.30|      0.05|         323|      322|
|        1.96|            0.40|      0.05|         369|      368|
|        1.96|            0.50|      0.05|         385|      384|
|        1.96|            0.60|      0.05|         369|      368|
|        1.96|            0.70|      0.05|         323|      322|
|        1.96|            0.90|      0.05|         139|      139|
|        1.96|            0.95|      0.05|          73|       73|

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# Questions?

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# Thank you!