Consolidation Session 16/5/2022

Social and Population Perspectives

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Deepak Parashar

Student feedback

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• SocPop calculations
• Prevalence with 95%CI
• Incidence rate
• Odds ratio with 95%CI
• Meta-analysis / Forest plots

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This indicates you have a calculation

or interpretation to do

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PRACTICE CALCULATIONS and INTERPRETATIONS

• Any calculations or interpretations would be derived from the ones you have practiced in the ‘group work’ sessions:

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• Incidence rate
• Prevalence with 95% CI
• Odds ratio with 95% CI
• Screening – sensitivity, specificity, Positive Predictive Value (PPV), Negative Predictive Value (NPV) Already covered last week

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Incidence Rate

Incidence is rate at which NEW events occur in a population, over a defined period of time.

Formally: number of new cases per person per year.

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Incidence =

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Number of New cases

Number of People ✕ years observed

Usually expressed number per 1000, or 10,000, or 100,000 person-years

You need to KNOW how to calculate – you will NOT be given the ‘equation’

Practice Q 1: Incidence Rate

In the UK from 2010 to 2012 (i.e. 3 full years of data) there were 26047 cases of tuberculosis. The UK population is 63.2 million.

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Calculate the incidence rate per 100,000 person-years (to 1 decimal place), showing how you calculated

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(Have a go at this calculation – result on next slide)

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Practice Q 1: Incidence Rate

In the UK from 2010 to 2012 there were 26047 cases of tuberculosis. The UK population is 63.2 million. Calculate the incidence rate per 100,000 person-years (to 1 decimal place), showing how you calculated

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26,047 cases

= ----------------------- ✕ 100,000 = 13.7 per 100,000 p-yrs

(63,200,000 ✕ 3 years)

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i.e. 13.7 per 100,000 person-years

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Based on the previous result, how many cases of tuberculosis each year could be expected in a General Practice with 15,000 patients on the list?�

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(Have a go at this calculation – result on next slide)

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How many cases of tuberculosis each year could be expected in a General Practice with 15,000 patients on the list?�

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• 2 patients

• Can be worked out by:

• (13.7 / 100,000) ✕ 15,000 = 2.055 = 2
• (MUST EXPRESS AS A WHOLE NUMBER of PATIENTS)

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Prevalence

• Prevalence is the number of cases (both existing and new) of a disease that are present in a particular population
• at a given time (point prevalence), or
• over a given time period (period prevalence), or
• at any point in their lives (lifetime prevalence)
• Proportion
• Numerator = number of people with condition
• Denominator = number of people in total
• Expressed as % or number per n people

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Calculating Confidence Intervals �for a proportion / prevalence

STEP 1: YOU WILL be GIVEN the EQUATION for the standard error (SE) of a proportion:

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STEP 2: YOU WILL NOT be GIVEN how to then calculate the 95% CI i.e.:

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Lower Bound of 95% CI = p – (1.96 x SE)

Upper Bound of 95% CI = p + (1.96 x SE)

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p is the sample proportion (NOT %)

n is number of observations

Practice Q 2: Prevalence with 95% CI�Results of National Child Measurement Programme - Coventry

Calculate the prevalence (%), and 95% Confidence Intervals, of obesity in both Reception and Year 6 (to one decimal place), using the following formulae:

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(Have a go at this calculation – result on next slide)

Practice Q2: Prevalence with 95% CI�Results of National Child Measurement Programme -Coventry

Calculate the prevalence (%), and 95% Confidence Intervals, of obesity in both Reception and Year 6 .

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Practice Q 2: Worked Example for Reception

1. Calculate the prevalence:

463/4135 = 0.112 (or 11.2%)

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2.

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SE = √ 0.112 (1-0.112) / 4135 = 0.0049

(Note: in this equation you use the proportion, NOT the %)

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3. Use the SE to calculate the 95% Confidence Interval

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Lower 95% CI = p - (1.96 ✕ SE) = 0.112 – (1.96 ✕ 0.0049) = 0.102

Upper 95% CI = p + (1.96 ✕ SE) = 0.112 + (1.96 ✕ 0.0049) = 0.122

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FINAL RESULT: Prevalence is 11.2% (95% CI: 10.2% to 12.2%)

(NOTE: need to ✕ 100 to express prevalence as a %)

Practice Q2: Prevalence with 95% CI�Results of National Child Measurement Programme -Coventry

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Is the prevalence significantly different between Reception and Year 6? State YES or NO, and explain.

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(Have a go at this – result on next slide)

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Practice Q2: Prevalence with 95% CI�Results of National Child Measurement Programme -Coventry

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Is the prevalence significantly different between Reception and Year 6? State YES or NO, and explain.

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ANS: YES - we know this because the 95% CI for Reception and Year 6 do not overlap with each other

Odds Ratio (OR) with 95% CI (case-control study)� �

OR = a/b or ad or a/c

c/d bc b/d

You will NOT be given this ‘equation’

You WILL be given this equation

You will NOT be given this

Recap: interpreting OR with 95% CI

1. OR estimate – our best estimate of the odds of the outcome in the population
• OR = 0.8: ((1-0.8)*100%=) 20% decrease in the odds of the outcome compared to baseline category
• OR = 2: two-fold ((2-1)*100%=) 100% increase in the odds of the outcome compared to baseline category
2. 95% CI – we are 95% confident that the odds ratio lies between these two limits.
3. Is the null (OR=1) included in the 95% CI?
4. Hence is it statistically (non-)significant at the (100-95%=) 5% level?

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Recap: interpreting OR with 95% CI

1. OR estimate – our best estimate of the odds of the outcome in the population
• OR = 0.8: ((1-0.8)*100%=) 20% decrease in the odds of the outcome compared to baseline category
• OR = 2: two-fold ((2-1)*100%=) 100% increase in the odds of the outcome compared to baseline category
2. 95% CI – we are 95% confident that the odds ratio lies between these two limits.
3. Is the null (OR=1) included in the 95% CI?
4. Hence is it statistically (non-)significant at the (100-95%=) 5% level?

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Recap: interpreting OR with 95% CI

1. OR estimate – our best estimate of the odds of the outcome in the population
• OR = 0.8: ((1-0.8)*100%=) 20% decrease in the odds of the outcome compared to baseline category
• OR = 2: two-fold ((2-1)*100%=) 100% increase in the odds of the outcome compared to baseline category
2. 95% CI – there is 95% probability that the true population odds ratio lies between these two limits.
3. Is the null (OR=1) included in the 95% CI?
4. Hence is it statistically (non-)significant at the (100-95%=) 5% level?

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Odds Ratio = a/b = odds of being a case if exposed

c/d odds of being a case if not exposed

If 95% CI includes 1 = NO ASSOCIATION

If 95% CI >1 = POSITIVE Signif ASSOCIATION (increased odds)

If 95% CI < 1 = INVERSE Signif ASSOCIATION (decreased odds)

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To check your understanding, are these OR with their 95% CI statistically significant?: (result on next page)

OR = 2 (95% CI 1.5 to 2.5)

OR = 2 (95% CI 0.9 to 2.9)

OR = 0.8 (95% CI 0.7 to 0.9)

OR = 0.8 (95% CI 0.4 to 1.2)

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Odds Ratio = a/b = odds of being a case if exposed

c/d odds of being a case if not exposed

If 95% CI includes 1 = NO ASSOCIATION

If 95% CI >1 = POSITIVE Signif ASSOCIATION (increased odds)

If 95% CI < 1 = INVERSE Signif ASSOCIATION (decreased odds)

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To check your understanding, are these OR with their 95% CI statistically significant?: (result on next page)

OR = 2 (95% CI 1.5 to 2.5) - Yes

OR = 2 (95% CI 0.9 to 2.9) - No

OR = 0.8 (95% CI 0.7 to 0.9) - Yes

OR = 0.8 (95% CI 0.4 to 1.2) - No

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Practice Q 3: Odds Ratio & 95% CI

• Researchers interviewed 134 wedding guests out of the 550 who attended. Of these 93 were cases and 41 were controls. They were asked about the food they had eaten.
• 27 of the 93 cases and 16 of the 41 controls had eaten samosas. The 2 x 2 table was drawn up:

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• Calculate the odds ratio and 95% confidence interval (to 2 decimal places), using this equation for the error factor:

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(Have a go at this calculation – result on next slide)

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= 27 ✕ 25 / 66 ✕ 16 = 0.64

Error Factor: 2.16

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Lower 95% CI = 0.64 / 2.16 = 0.30

Upper 95% CI = 0.64 ✕ 2.16 = 1.38

Note that this is the standard way to set out a 2x2 table

Practice Q 3: �Are the Samosas implicated?�OR=0.64, 95% CI 0.30 to 1.38

• INTERPRET YOUR RESULT

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(Have a go at this interpretation – result on next slides)

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Practice Q 3:�Are the Samosas implicated?�OR=0.64, 95% CI 0.30 to 1.38

• An Odds Ratio of 0.64 is our best estimate and suggests those who ate the samosas at the wedding had a 36% decreased odds of contracting food poisoning (compared with those who did not eat the samosas).

• The 95% confidence interval indicates that with 95% probability the true OR would be between 0.30 to 1.38.

• The result is not statistically significant at the p<0.05 level because the 95% confidence interval range contains the null hypothesis value i.e. odds ratio =1 (need to state this null value).

• Null hypothesis cannot be rejected. The results indicate that eating the samosas was not associated with contracting food poisoning.

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Practice interpretation�Is jeera chicken implicated in the outbreak of food poisoning?

• OR = 9.87, 95% CI = 3.26 to 29.91

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Practice interpretation�Is jeera chicken implicated in the outbreak of food poisoning?

• OR = 9.87, 95% CI = 3.26 to 29.91

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• An Odds Ratio of 9.87 is our best estimate and suggests those that ate the jeera chicken at the wedding had a 10-fold increased odds of contracting food poisoning.

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• The 95% confidence interval indicates that with 95% probability the true OR would be between 3.26 to 29.91.

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• The result is statistically significant at the p<0.05 level because the 95% confidence interval range does not include 1 (null hypothesis value, odds ratio =1).

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• Null hypothesis can be rejected. The results indicate that eating the jeera chicken was significantly associated with contracting food poisoning.

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Forest Plots��Meta-analysis (Smith et al. 2015): risk of recurrent dislocation

“Pooled data from five trials […] showed a smaller incidence of recurrent dislocation at two to five years follow-up in the surgical group (21/162 versus NS 32/132; risk ratio (RR) 0.53 favouring surgery, 95% confidence interval (CI) 0.33 to 0.87; five studies, 294 participants…”

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Interpreting a meta-analysis (or forest plot) �(dislocation Smith et al. 2015)

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Size of square = weight in meta-analysis

P value = test of overall effect

I² = statistics indicating the level of heterogeneity

P value = test for presence of heterogeneity

Diamond = pooled effect/weighted average

Vertical line at 1 = no effect of treatment vs comparator

Square = point estimate

horizontal line =95% confidence interval

Heterogeneity in systematic reviews

• Variability among studies in a systematic review may be termed heterogeneity

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• Clinical heterogeneity - variability in the participants, interventions and outcomes

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• Methodological heterogeneity - variability in study design and risk of bias

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• Statistical heterogeneity - a consequence of clinical or methodological diversity, or both, among the studies.

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• Exploring statistical heterogeneity in a meta-analysis aims to tease out factors contributing to differences.
• Sources of heterogeneity should be accounted for and taken into consideration when interpreting results and drawing conclusions.

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Assessing statistical heterogeneity

• The I² statistic describes the percentage of variability in the effect estimates that can be attributed to heterogeneity beyond what is expected by chance alone

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• No hard and fast rules on what level of inconsistency is reasonable in a meta-analysis – but as a rough guide the Cochrane Handbook suggests:

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• I² values of:
• 0% to 40% - might not be important
• 30% to 60% - may represent moderate heterogeneity
• 50% to 90% - may represent substantial heterogeneity
• 75% to 100% - considerable heterogeneity

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The findings

• Differences between the intervention and control group:
• smaller incidence of recurrent dislocation (21/162 versus 32/132; risk ratio (RR) 0.53 favouring surgery, 95% (CI) 0.33 to 0.87

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Does physical activity promotion in primary care lead to increased physical activity or fitness in people aged over 16? �

• Systematic review with meta-analysis by Orrow (2012).
• Review searched for RCTs in sedentary adults recruited in primary care, with a minimum follow up of 12 months, with physical activity or fitness as outcomes.
• Process was robust. Identified 15 trials (a total of 8745 pooled patients).

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• 11 trials had self reported physical activity as the outcome, with a small to medium positive intervention effect at 12 months (OR 1.42, 95% CI 1.17 to 1.73). NB. Self Reported physical activity is prone to social desirability bias.

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• Objective measures such as cardiorespiratory fitness – reported in only 4 trials – did not demonstrate any statistically significant findings.

• More evidence is needed to fully support these health promotion interventions. Must be considered in context of cost-effectiveness (not assessed). Results should be interpreted with caution, due to the limitations of self-reported outcome measures.

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• Other systematic reviews and meta-analyses – support or alter this conclusion?

Forest Plot

Describe

a. Vertical line at 1

b. The squares, and why are some bigger?

c. Horizontal lines sticking out from squares. Why are some longer?

d. The diamond, and if it crosses 1 or not?

e. Column marked weight

Describe:

a. Vertical line at 1

b. The squares, and why are some bigger?

c. Horizontal lines sticking out from squares. Why are some longer?

d. The diamond, and if it crosses 1 or not?

e. Column marked weight

Line of no difference

Weight each study is given in meta-analysis

95% Confidence Intervals of individual studies

Pooled analysis – point estimate and 95%CI

% that study contributes to pooled result

Consolidation Lecture�+�SocPop Revision guide�+�Incidence Prevalence Revision Questions��available on Block 5 moodle pages