# Populations and Risk

Last time we talked about the difference between incidence and prevalence. Today, we will look at how we can use these descriptive measures to understand differences in risk.

Remember from Monday that the population is the group of individuals you would like to learn about. As midwives, we are often interested in specific groups of women. These groups might be defined by age (e.g. reproductive aged women), by condition (e.g. women living with HIV), or any number of other ways we can divide women into groups.

When you divide your population into two or more groups, you can look at the difference in incidence or prevalence of an event to find out if the groups have a different risk. When you look at the groups separately, it is called **stratifying**. Have a look at this article as an example: Maternal age and successful induction of labor in the United States, 2006-2010.

In this study, the researchers were interested in how maternal age related to the odds of cesarean delivery after induction of labor. To find out, they stratified the national vital statistics data for births –in this case each observation (or birth) was placed into the group of nullip or multip. Then each group was stratified again by age. This allowed the research team to calculate the prevalence of cesarean post induction for each group and compare.

You will notice in the abstract they use the term relative risk. Technically this isn’t a correct use of the term risk, they really mean prevalence odds – we’ll talk more about that later. This means they looked at the probability of cesarean in one group compared to the probability of cesarean in another group. To understand this, lets simplify this study to two variables – the age and method of delivery.

With just two variables, we can put each birth into one of the four boxes: Mother <30 years old and cesarean delivery (A); Mother 30 or older and cesarean delivery (B); Mother < 30 years old and vaginal delivery (C); or Mother 30 or older and vaginal delivery (C). We can then have a total count of each group.

Risk |
< 30 |
30 or older |

Cesarean |
A |
B |

Vaginal |
C |
D |

To get the probability of cesarean we would divide the number of cesareans by the total number of births for each group. So the probability of cesarean for <30 is A / A+C and the for 30 or older is B / B+D.

To get the prevalence ratio (called the odds ratio), we would divide the probability of cesarean in the first group by the probability of cesarean in the second group. In the study, they found the odds ratio for nullips in the oldest category was 1.97. This means the odds of cesarean delivery are 97% higher for nullips in the oldest category when compared to nullips in the **reference c****ategory **(generally defined in a study by the lowest incidence or the group believed to be the healthiest).

**Birth Worker Survey**

The Birth Worker Survey allows us to stratify respondents to determine differences in prevalence. A few questions had wide variation in answers. By stratifying the respondents we can identify differences in the way different birth workers think about birth.

### Should you Fire the Midwife?

One question asked respondents if they agreed with the statement: If your midwife/physician will not do what you want, fire her. This bar graph is the distribution of the responses:

We could stratify our response population to determine if any characteristics are associated with belief that you should fire the midwife. For example, in this graph we stratify by whether or not the respondent is a midwife:

When we stratify by midwifery role, the graph starts to get a little complicated — probably because we only had five midwives complete the survey (and only four completed this question). But notice how the midwives were just as likely to answer agree as disagree, but those who are not midwives were much more likely to agree or strongly agree with the statement than disagree? If we had a better sample we might conclude that being a midwife is associated with thinking differently about this statement than birth workers who are not midwives.

### Should Midwives Be Licensed?

Another question with a wide spread was if midwives should be allowed to practice without licensing requirements. Here is the overall distribution.

You can see overall the trend was to disagree with the statement — which indicates belief that midwives should be licensed to practice. So what happens when we stratify these responses?

Once again we see that midwives respond differently than non-midwives. If we did this as a two by two table we may break the responses into agree (including strongly agree and agree) and disagree (including strongly disagree and disagree). We would ignore those with no opinion. If we did that, we would find:

Belief |
Midwife |
Non-Midwife |

Agree |
3 |
4 |

Disagree |
2 |
15 |

Remember the probability is the number who agree divided by the total number responding. Overall 7/24, or 0.29 agreed with the statement. The probability of a midwife agreeing is 3/5 or 0.6; The probability of the non-midwife agreeing is 4/19 or 0.21.

Odds are calculated as the proportion of “success” (what you are measuring) divided by the proportion of “failures” (the opposite of what you are measuring). This makes the equation Odds=proportion / 1-proportion. Since we want to know if the midwife agrees, we ill count agreement as our success. Odds for midwives are then 0.6 / 1-0.6 = 1.5. Odds for non-midwives are 0.21/1-.21 = .27.

To determine the odds ratio of midwives to non-midwives, we compare the odds of the midwives to the odds of the non-midwives. This gives us 1.5 / .27 = 5.56 which means of the birth workers who completed this survey, midwives are more than 5 times as likely to agree that midwives should not need to be licensed to practice. Remember though, this is not a representative sample and only 5 midwives completed the survey.

Notice in this next graph, we also see some distinct differences in trends of answering when we stratify by the location for the respondents last birth experience (the last time the respondent gave birth). What if we did the same thing to compare birth center birthers to hospital birthers. Here is the chart to get you started.

Belief |
Birth Center |
Hospital |

Agree |
3 |
1 |

Disagree |
1 |
10 |

Do the math and see if you find the Odds Ratio for Birth Center vs Hospital Birther is 3.06, meaning a woman reported she last gave birth at a birth center is 3 times more likely to report agreeing that midwives should not need to be licensed to practice. Don’t worry if your number is a little different due to rounding.

Interestingly, we don’t see a visual difference when we stratify working as a childbirth educator:

Stratification helps us understand differences between populations and sub-populations. While these graphs were helpful to visualize differences between groups, by themselves they do not tell us if there are real differences between those who are or are not midwives. For that, we need to do some different statistics. We’ll get to that, but we have a few more preliminary things to cover next week.

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