# Exercise: Analyses for qualitative data

## Providencia alcalifaciens

The table below is taken from a study investigating the cause of diarrhoea in patients with gastroenteritis and shows the relationship between foreign travel and a positive result for the organism Providencia alcalifaciens (Haynes and Hawkey 1989).

Recent travel abroad? P. alcalifaciens Total
positive
(no.)
negative
(no.)
yes 25 229 254
no 5 368 373
Total 28 597 627
Chi-squared = 23.98, P<0.001

1. What is meant by ‘chi-squared = 23.98, P<0.001?’

2. What conditions do the data have to meet for the test to be valid?

3. What conclusions can be drawn from these data?

## Oxygen pulse and stroke volume

In each of six patients, a series of measurements of oxygen pulse and stroke volume was made to ask whether there was any relationship between these (S Jones, unpublished). The oxygen pulse/oxygen uptake graphs could be classified as rising or plateau and the stroke volume/oxygen uptake graphs as rising or falling. The oxygen pulse assessment was tabulated by the stroke volume assessment:
Oxygen
Pulse
Stroke Volume
Rising Falling
Rising 2 0
Plateau 0 4

### Question about oxygen pulse and stroke volume

1. What method could we use to test the null hypothesis that the two classifications are unrelated, and why?

## Helicobacter pylori

Blood from 471 male volunteers aged 18 to 65 years was tested for antibodies to Helicobacter pylori (Webb et al., 1994). Seroprevalence of H pylori increased with age as shown in the following table:

Age group
<30 30-34   35-39   40-44   45-49   50-54   55-65
Seropositive 22 26 14 30 32 23 29
Seronegative 52 55 59 53 41 28 17
% seropositive   30% 32% 19% 36% 44% 45% 63%
For trend, chi-squared = 20.6, P<0.001.

1. What is a trend test and how would you interpret the one presented here?

2. What would be the advantages and disadvantages compared to a chi-squared test for association in a contingency table?

3. Suggest an alternative way of testing the difference in age in the two seropositivity groups, assuming that the raw data were available.

## Asthma

The following is the abstract of a paper (Illi et al., 2001):

Objective: To investigate the association between early childhood infections and subsequent development of asthma.

Design: Longitudinal birth cohort study.

Setting: Five children's hospitals in five German cities.

Participants: 1314 children born in 1990 followed from birth to the age of 7 years.

Main outcome measures: Asthma and asthmatic symptoms assessed longitudinally by parental questionnaires; atopic sensitisation assessed longitudinally by determination of IgE concentrations to various allergens; bronchial hyperreactivity assessed by bronchial histamine challenge at age 7 years. Results: Compared with children with 1 episode of runny nose before the age of 1 year, those with 2 episodes were less likely to have a doctor's diagnosis of asthma at 7 years old (odds ratio 0.52 (95% confidence interval 0.29 to 0.92)) or to have wheeze at 7 years old (0.60 (0.38 to 0.94)), and were less likely to be atopic before the age of 5 years. Similarly, having 1 viral infection of the herpes type in the first 3 years of life was inversely associated with asthma at age 7 (odds ratio 0.48 (0.26 to 0.89)). Repeated lower respiratory tract infections in the first 3 years of life showed a positive association with wheeze up to the age of 7 years (odds ratio 3.37 (1.92 to 5.92) for 4 infections v 3 infections).

Conclusion: Repeated viral infections other than lower respiratory tract infections early in life may reduce the risk of developing asthma up to school age.

1. What is meant by odds ratio 0.52 for runny nose and asthma and what does it tell us?

2. What is meant by 95% confidence interval 0.29 to 0.92 and what further information does this provide?

3. What is meant by odds ratio 3.37 (1.92 to 5.92) for lower respiratory tract infections and wheeze?

4. On a less statistical point, what is wrong with the way the conclusion is phrased?

## References

Haynes, J. and Hawkey, P.M. (1989) Providencia alcalifaciens and travellers’ diarrhoea British Medical Journal 299, 94-5.

Illi S, von Mutius E, Lau S, Bergmann R, Niggemann B, Sommerfeld C, Wahn U. (2001) Early childhood infectious diseases and the development of asthma up to school age: a birth cohort study. British Medical Journal 322, 390-395.

Webb, P.M., Knight, T., Greaves, S., Wilson, A., Newell, D.G., Elder, J., Forman, D. (1994) Relation between infection with Helicobacter pylori and living conditions in childhood: evidence for person to person transmission in early life. British Medical Journal 308, 750-3.

(Questions 1 and 3 taken from Martin Bland and Janet Peacock: Statistical Questions in Evidence-based Medicine, Oxford University Press, Oxford, 2000.)