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Plausible values and Plausibility Range

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Prevalence of FSWs in some west African Countries

0.1%

4.3%

3

Plausible values • In west African countries, prevalence of FSWs ranged 0.1% to

4.3%.

• Suppose you implement a study in another country in this region, and get a prevalence of 10%.

• How plausible this figure is?

• Did you implement the study in high risk locations?

• What are the potential biases in your study (selection of respondents, data collection, …)?

• What are the main cultural and socioeconomic differences between this country and others?

4

Comparison of prevalence across risk zones

• Suppose, we have stratified the country into low, intermediate and high risk zones.

• We have selected one province from each zone.

• The prevalence in low zone was higher than that of high zone.

• How plausible it is?

• Have you implemented standard approach in all provinces?

• Have you trained the interviewers of the study?

• Have you used the right criteria to define the risk zones?

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Point Estimate vs. plausible range

• One of the aims of statistics is estimating population

parameters from sample statistics

• For example, in a randomly selected sample of prisoners, 25

out of 200 ones reports sharing of injection equipment

• Thus in the sample, 12.5% of the prisoners share injection

equipments

• This value of 12.5% is called a point estimate of the

population proportion

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Sampling Variation• Point estimate is a value derived from one randomly selected

sample

• We use it as the best guess for the population parameter

• What would happen if we select another random sample?

• If you repeat the mapping or the NSU survey, do you expect to

get the same estimates?

• What is the impact of respondents, locations, and time …

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Construction of a Range• It is preferred to report a range of possible values, instead of a

single point estimate

• It is conventional to create 95% range which means that 95% of

the time constructed range contains the true value of the

parameter of interest

• The width of the range provides some idea about uncertainty of

the unknown parameter

• A very wide interval may indicate that more data should be

collected before anything very definite can be said about the

parameter.

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Advantages of Reporting a Range

• A smaller confidence interval is always more desirable than a

larger one because it shows that the population parameter

can be estimated more accurately

• Point estimation gives us a particular value as an estimate of

the population parameter

• Interval estimation gives us a range of values which is likely to

contain the population parameter

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Interpretation of Range

• The upper and lower bounds of the interval give us

information on how big or small the true parameter might be

• Wide range indicates great uncertainty in the true value of the

parameter

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Different Names for Range

• Statistical terminology

– Confidence Interval

– Uncertainty Limit

– Credibility Interval

• Non-statistical terminology (in this course)

– Plausibility Range

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How to Construct Statistical Ranges?

• Standard Formulas Based on Normal approximation

• Monte Carlo

• Bootstrapping

– Works based on resampling with replacement from the original

sample

– Estimation of parameter of interest in each sample

– Use of 2.5 and 97.5 percentiles at lower and upper bounds

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Application of available formulas• To estimate number of IDUs, capture-recapture study has

been implemented:

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15

16

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How to Construct Non-Statistical Ranges?

• In the following slides we introduce some approaches

followed by other researchers

• In addition, we introduce some other approaches based on

common sense

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Other Countries Experience• Indonesia applied the following formula:

– x(i) = estimated size in district (i)

– = mean of district sizes

– n = number of districts

• Probably they used this statistics as SE and applied normal

approximation theory

__

X

1

)(__2

n

XX i

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Ad Hoc Methods (1)

• In other study, time-varying parameters were assigned

uncertainty bounds in the model up to ± 50% of the

best parameter estimates.

• Parameter estimates:50000

• 20%*50000=10000

• uncertainty bounds: 50000 ± 10000

• (40000, 60000)

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Ad Hoc Methods (2)

• Ask respondents to provide a range, instead of a single value

• For example, in NSU, ask respondents to count minimum and

maximum of FSWs they know

• Analysis lower bound data should provide the lower bound of

the plausibility range

• Analyzing the upper bound data should provide the upper

bound of the plausibility range