A Question Of Confidence? From Sample To Population

9.11.05

Peak expiratory flow rate
• Measured in litres per minutes.
• Based on greatest flow in 2 milliseconds of forced expiration starting from a full lung of air.
• Used to monitor reversible airflow limitation.
• Best of three attempts.

Why do they vary?
• Random/chance variable
-Between subject/samples
-Biological variation
-Height
-Sex
-Age.
-Within subjects/samples.
• Systematic errors (leading to bias)
-Instrumental error.
-Observer error.

Reliability
• Degree to which results can be repeated to give the same value.
• Precision/reproducibility/stability of measurement.

Accuracy/validity
• Degree to which measurement/estimate based on measurements represents TRUE VALUE of attribute being measured.
• Degree to which value represents truth.

Peak expiratory flow rate used to monitor changes in asthma.
• How do we know that (new) treatment for asthma 'works'?

Estimating population figures from a sample
• Most statistical analysis is based on that fact that the sample was used to estimate the population parameters.
• Usually, the best estimate of the population 'average' is the sample mean.
• However, different samples give difference means eg. student height.
• How do we know what the true population is?

Multiple samples
• Each sample will have different means.
• To improve the estimate, look at the "mean of means" - measure distribution by means of standard error.

Improving the reliability of the estimate
• Increasing the size and number of samples.
• The reliability of the estimate is the STANDARD ERROR OF THE MEAN.
• It is not practical to repeat samples in "real life."
• SEM calculated statistically.
• THIS IS NOT THE STANDARD DEVIATION!
-Measure of dispersal in SINGLE sample.

From sample to population
• Based on sample mean and SE, CONFIDENCE INTERVALS can be constructed.

Confidence interval
• Value within which we can be 95% confident that the true value lies.
• General formula = Population +/- 1.96*SE.
• Can be calculatd about most population estimates
-Population point estimates.
-Because confidence intervals don't overlap.

Applicability
• If we want to know whether treatment is improving peak flow, we can compare mean (and confidence interval) of peak expiratory flow rate in the group that has treatment with the mean (and confidence interval) of the peak expiratory flow rate of the group without treatment.
• Despite sample means being difference, if confidence intervals overlap, we cannot exclude the possibility that the two population means are the same ie. the treatment has had no effect.

YOU CAN BE 95% CONFIDENT THAT THE TRUE POPULATION VALUE LIES BETWEEN THE LOWER AND UPPER CONFIDENCE INTERVAL.

Is the estimate valid?
• Recall validity (accuracy) is the degree to which the value represents the truth.

Bias
• Systematic error in the study.
• May relate to sample selection (selection bias) ie. the sample is not representative of the population.
• May relate to systematic measurement errors (measurement bias) eg. systematic error in the measurement tool or its use.

Confounding
• The third factor related to both independent (exposure) and dependent (outcome) variable.
• Eg. age
-Older people may be less likely to try new treatment and may have les severe illness, so they may have a difference response wrt peak expiratory flow rate.
• There are techniques available to allow for this IF YOU KNOW ABOUT IT!

So…
• Opportunities for bias can exist in
-selection
-measurement
-analysis stages of study.

Inferential statistics
• Means, proportion, percentages or any other summary measure.

Assumptions
• Sample REPRESENTATIVE.
• Measure in samples is BEST ESTIMATE.

Another way of expressing association:
• Population of asthma prevalence in 16-24 year olds.
-Male = 70.7 per 1000.
-Female = 81.7 per 1000.
• RELATIVE RISK of asthma in females of 16-24 years compare with males is [ratio]
1.08 (95% confidence interval 1.06-1.10)

Relative risk
• Ratio of risk of death/disease among those exposed to risk to those among unexposed.
Relative risk of 1 means no excess risk.