Plausible values and Plausibility Range

1

Prevalence of FSWs in some west African Countries

0.1% 4.3% 2

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?

3

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?

4

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 5

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 … 6

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 8

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 9

Different Names for Range

• Statistical terminology – Confidence Interval – Uncertainty Limit – Credibility Interval • Non-statistical terminology (in this course) – Plausibility Range 10

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 11

Application of available formulas

• To estimate number of IDUs, capture-recapture study has been implemented: 12

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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 17

Other Countries Experience

• Indonesia applied the following formula: (

X i



X n

 1 __ ) 2 – –

X

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 18

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) 19

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 20