Document(s) 9 de 18

Steps in data analysis and report writing

* These steps need not be in the sequence in this diagram. The sequence may be adjusted according to the needs of the research teams.

** These elements are optional and may be omitted if not relevant for research teams

Module 25: MEASURES OF ASSOCIATION BASED ON RISK

1. Introduction
2. Incidence, risk and relative risk
3. Calculating relative risk in different study designs

I. INTRODUCTION

In HSR studies, the objective of many comparative studies (cross-sectional comparative studies, case-control studies, cohort studies, experimental and quasi-experimental studies) is to compare those who develop the problem/condition under study among those with a risk factor (exposed group) and those without this risk factor (non-exposed group). How this is actually done depends on the study design used.

You will remember (Module 9) that in case-control studies and cross-sectional comparative studies, one group of study subjects is selected that has the problem under study (cases) and a control group that does not have the problem. The two groups are then compared with regards to the presence or absence of risk factors. In a cohort study, only study subjects without the problem to be studied are selected. They are then divided into those with the assumed risk factor and those without the risk factor. The two groups are followed up over a longer period and the occurrence of the problem is then measured between those with the assumed risk factor and those without the risk factor. In an experimental study, subjects with a certain problem are selected. One group is then exposed to an intervention by the researcher (epidemiologists call this a ‘beneficial risk factor’), while the other group remains untouched by the intervention. After an appropriate follow-up period, the occurrence of the problem is measured and a comparison made between the two groups, in the hope that the intervention has at least partly solved the problem.

The comparison of a group with a risk factor and a group without, or of cases and controls, allows the researcher to determine whether the potential risk factor influences the problem or not and to what extent the risk factor actually contributes to the problem.

Before one can measure how much a risk factor contributes to a problem, it is important to understand the concept of incidence, risk and relative risk.

II. INCIDENCE, PREVALENCE, RISK AND RELATIVE RISK

Incidence and incidence rate

Note: The population who can develop the condition of interest is known as the population ‘at risk’.

Example 1:

The total number of new tuberculosis cases in District A in the year 2000 was 273. The incidence of tuberculosis in District A in 2000 was therefore 273.

An incidence rate is usually expressed per 1,000 or per 10,000 or per 100,000 (or other factor of 10) inhabitants to make it easier to compare the rates in different communities.

Example 1 (continued):

District A has a population of 200,000. The incidence rate of tuberculosis in the year 2000 in district A was therefore 273/200,000/year or 137/100,000/year. (Divide the numerator and denominator by 2 so the incidence rate is expressed per 100,000 per year, and round off to the nearest whole number, i.e., 136.5 becomes 137.)

The incidence rate estimates the chance (probability or risk) that an individual will develop a disease during a specified period of time.

Example 1 (continued):

If on 31 December 2000, 360 old and new patients would be registered, the prevalence rate would be 360/200,000 or 180/100,000 per year.

Like incidence rates, prevalence rates can be expressed per 1,000, 10,000 or 100,000 inhabitants.

Risk and relative risk

Example 1 (continued):

The risk of getting tuberculosis in district A in 2000 was 137/100,000/year.

The risk may not be the same for various subgroups in the population. Whereas the risk of getting tuberculosis in farmers might be 100/100,000/year, it may be 200/100,000/year in mine workers. In this example, mine workers were twice as likely to get tuberculosis as farmer.

It may therefore be concluded that being a mine worker is a risk factor for contracting tuberculosis and carries a relative risk of 2.

When determining relative risk we have to consider two subgroups in the study population: the subgroup in which the risk factor is present (exposed) and the one in which the risk factor is absent (unexposed).

It is important to note that the identification of a risk factor does not imply that there is a causal relationship between the factor and the condition. However, the higher a relative risk is, the more likely it becomes that the risk factor is causal and not due to chance or confounding.

III. CALCULATING RELATIVE RISK IN DIFFERENT STUDY DESIGNS

1. Calculating relative risk in cohort and intervention studies

In cohort and intervention studies, it is possible to calculate the incidence rate (risk) directly. This is because the outcomes or diseases/problems under study occur during the study.

In these studies, the incidence rates in the exposed and non-exposed groups are calculated, which are then used to calculate the relative risk using the formula presented in section II of this Module.

In a cohort study, the data needs to be put in the table format given in Table 25.1.

Table 25.1. General cohort study table format for risk calculation

The risk of developing the problem among those with the risk factor = a/(a+b)

Risk of developing the problem in those without the risk factor = c/(c+d)

Example 2:

A study was carried out in country X to find out whether the risk of diarrhoea in under-five children was different between two nearby wards (each made up of a number of villages). It was suspected that Ward B had a higher risk because the community used unprotected wells while Ward A used borehole water. Ward A had a population of 10,000, while Ward B included 15,000 people. The respective under-five populations were 1,000 and 1,500. The records kept by village health workers (VHWs) responsible for the wards in the previous four weeks were checked. Ward B had had 78 cases of diarrhea while Ward A had had 50 cases.

Is the risk of diarrhea different between the two wards?

Because Ward B had the potential risk factor (unprotected water sources), the population of this area is expected to be at higher risk of developing diarrhoea. This data can now be put in a cross-tabulation using the format of table 25.1, and the risk and relative risk can then be calculated using the formulae already discussed.

Table 25.2. Relationship between exposure to unsafe water and diarrhea in under-5 children

The 95% confidence intervals (CI) for this RR are calculated for you, and are 0.74 to 1.47.

Interpretation:

Under-five children in Ward B have < 1.04 times more risk of developing diarrhea than those in Ward A, but this risk is not significantly different as the 95% CI includes 1. (This significance will be further evaluated using statistical significance tests in Modules 28-30.)

2. Estimating relative risk in a case-control study

In a case-control study, it is usually not possible to calculate relative risk directly as in the incident studies discussed earlier.* In most situations, the odds ratio (OR) is used, which estimates the relative risk.

To compute the OR, the data has to be presented in the table format given in table 25.3.

Table 25.3: Case-control study table format

The OR is sometimes called the cross-products ratio. It is the product of the left upper cell (a) and the right lower cell (d) or a times d, divided by the product of the right upper cell (b) and the left lower cell (c), or b times d.

After calculating the odds ratio (OR), we usually call it the relative risk (RR) as that is what it is estimating.

* In ‘incident studies’ the incidence of a certain problem or outcome and the risk or contributing factor can both be observed; therefore the relative risk can be calculated directly.

Example 3:

An HSR case-control study was conducted in Namibia to identify factors contributing to early neonatal mortality (first seven days of life) in the maternity hospital in the capital Windhoek (Muharukua et al. 1998). For each case, 5 controls were selected. The final sample size was 290, 49 of whom were neonates who died between birth and day seven of life (cases) and 241 neonates who survived the first seven days of life (controls). Among the potential risk factors evaluated was low birth weight (less than 2,500 g).

Of the 281 neonates about whom information was available on low birth weight (LBW), 44 were cases and 237 controls. 28 of the 44 cases were LBW, while 29 of the 237 controls had a low weight.

This data, put in the cross-tabulation format given in table 25.3, is shown in Table 25.4.

Table 25.4: Relationship between prematurely and neonatal death in a case-control study in Namibia

Where     a = 28;     b = 29;     c = 16;     d = 208

The 95% CI, (calculated using Epitable in Epi Info 6.04c as shown in the Computer Companion, Vol II Part 3 of the HSR Training Series, WHO/AFRO, Harare, l996) is 5.69 - 28.00 (see Module 27 for formulae for calculating 95% CI).

Interpretation:

The risk of a neonate born with a low birth weight in the maternity hospital in Windhoek dying in the first seven days of life is 12.55 times that of normal weight neonates. Low birth weight is therefore a very strong risk factor for neonatal death.

3. Calculating relative risk in a cross-sectional comparative study (prevalence survey)

As in a case-control study, incidence will usually not be directly calculated in a cross-sectional comparative prevalence study. The measure of association in these studies is called a prevalence odds ratio (POR). The POR is calculated in exactly the same way as the odds ratio in a case-control study.

Example 4:

In Botswana, a cross-sectional comparative study was conducted to determine the magnitude of the problem of teenage pregnancy and to identify contributing factors. The researchers sampled 400 teenagers at random and found that 23% of the teenagers had been pregnant. Among other things, they wanted to evaluate whether teenagers who had received organisational support (i.e., peer education) would be less likely to become pregnant than those who had not received support.

From the collected data, only 14 of the 90 teenagers who had experienced a pregnancy had received organisational support while 86 of the 310 never pregnant teenagers had received support. This data is shown in Table 25.5.

Table 25.5: Relationship between organisational support and teenage pregnancy in Botswana

Where     a = 76;     b = 224;     c = 14;     d = 86

The 95% CI is 1.07 to 4.11 (calculated from Epitable in Epi Info version 6.04 c, Computer Companion, Vol II Part 3 of HSR Training Series).

Interpretation:

Teenagers who received no organisational support were 2 times more likely to become pregnant than those who received support. Please note that this finding is both practically and statistically significant.

Warning

When you find an association between a potential risk factor and the problem, this may not be an actual relationship. There may be a number of reasons for this finding, one of which is that there could be other risk factors (confounders) that provide the actual explanation. These other risk factors therefore need to be taken into account. Module 26 deals with the issue of confounding, including how to evaluate and control for it.

Annex 25.1: Relative risk calculations for quasi-experimental and experimental study designs, and for cross-sectional comparative studies using incidence data.

The cohort study on the association between exposure to unsafe water and diarrhoea in under-5 children shown in example 2, was actually done as the first part of a quasi-experimental intervention study. The study showed that the occurrence of diarrhoea was the same for Ward A and Ward B.

Example 2 (continued):

The researchers then developed a health education intervention package and proceeded to carry out an intervention study to evaluate the effectiveness of the package. The health education intervention was implemented in Ward A over a period of 2 months, while the usual health services were available in Ward B. The researchers were confident that any difference in risk of diarrhea after the intervention could be attributed to it, as the incidence in wards A and B was the same before the intervention. After the 2 months, VHWs again recorded the incidence of diarrhea over a period of 4 weeks in the two wards. Ward A recorded 16 cases while Ward B recorded 55 cases.

The study design used here is a quasi-experimental study, because there is comparison but no randomisation (see Module 9, intervention studies).

The question driving the study was: Does the intervention work; does it result in a significant decrease in diarrhoea?

Table 25.6: Relationship between exposure to unsafe water and diarrhoea in under-5 children after the intervention

From table 25.6,     a = 55;     b = 1445;     c = 16;     d = 984

The 95% confidence interval (CI) for this RR is calculated for you, and is 1.64 to 3.98 (using Epitable of Epi Info version 6.04c, see Computer Companion, Vol. II Part 3 of the HSR Training Series).

Interpretation:

The health education package does work. The risk of diarrhea in under-fives after the intervention is now much higher (2.29 times) in Ward B than in ward A. The finding is both practically important (the risk of diarrhoea is twice as high in the non-intervention group) and statistically significant (95% confidence levels do not include 1). Formal statistical testing will be covered in Modules 29 and 30. Remember that the risks of diarrhea were not significantly different before the intervention (Table 25.2).

Calculating relative risk in a cross-sectional comparative study (incidence study)

The incidence rate can also be calculated directly in a cross-sectional comparative study where incident cases (problems) are identified. This can then be used to calculate the relative risk as already shown (Table 25.2).

The data however has to be put in a table format as given in table 25.7.

Table 25.7: Cross-sectional study table format (incident outcomes)

The formula given for calculating relative risk can then be applied.

Example 5

In a study carried out on factors that contribute to delayed perinatal care in Machinga District, Malawi in 1997 (Tamaona et al, 1997), 88% of the 97 ANC mothers interviewed delayed seeking perinatal care (until after 3 months of pregnancy). To find out whether distance from health facilities was a risk factor for this delay in perinatal care, the mothers were separated into those living 10 km or less from health facility (near) and those living more than 10 km away (far). 60 of the 62 mothers living far from the health facility delayed using perinatal care compared to 28 of 35 mothers living near.

The data is shown in Table 25.8 using the format given in Table 25.7. The incidence (problem) is delay in seeking perinatal care while the risk factor is living far (>10 km).

Table 25.8: Relationship between distance and delay in seeking perinatal care in Machinga District, Malawi

The 95% CI for this RR is 1.02 - 1.44 (worked out using Epitable in Epi Info Version 6.04c, refer to Computer Companion, Volume II Part 3 of the HSR Training Series.)

Interpretation:

Women using ANC who live beyond 10 km from a health facility in Machinga District, Malawi, are therefore 1.21 times more likely to delay presenting for perinatal care than those living 10 km or less from the nearest health facility. The difference is statistically significant, but it is not a very important one (only 1.2 times more likely to delay). Improving access here may not change delay in perinatal care that much. There must be other factors, overriding the distance, which make mothers stay away.

Trainer’s Notes

Module 25: MEASURES OF RISK AND ASSOCIATION

Introduction and discussion

It is important that the participants understand the concept of risk. Try to ensure that they also have a good idea of how to apply this concept in all study designs. Let them calculate some odd ratio’s in plenary on their own data.

Impress on them the importance of quasi-experimental study designs and how these can be used to evaluate programmes in a scientific manner.

The team of facilitators should provide computer support to improve on depth of analysis as manual data analysis may result in inadequate analysis of the contribution of the risk factors to the problem under study.

Document(s) 9 de 18