by Ritu Narayan
Sampling is a critical issue in any research study design. Most of us have grappled with balancing costs, time and of course, statistical power when deciding our sampling strategies.
How do we know when to go for a simple random sample or to go for stratification or for clustering? Let’s talk about stratified sampling here and one research scenario when it is useful.
One Scenario for Stratified Sampling
Suppose you are studying minority groups and their behavior, say Yiddish speakers in the U.S. and their voting. Yiddish speakers are a small subset of the US population, just .6%. (more…)
by Annette Gerritsen, Ph.D.
In an earlier article I discussed how to do a cross-tabulation in SPSS. But what if you do not have a data set with the values of the two variables of interest?
For example, if you do a critical appraisal of a published study and only have proportions and denominators.
In this article it will be demonstrated how SPSS can come up with a cross table and do a Chi-square test in both situations. And you will see that the results are exactly the same.
‘Normal’ dataset
If you want to test if there is an association between two nominal variables, you do a Chi-square test.
In SPSS you just indicate that one variable (the independent one) should come in the row, (more…)
Censored data are inherent in any analysis, like Event History or Survival Analysis, in which the outcome measures the Time to Event TTE. Censoring occurs when the event doesn’t occur for an observed individual during the time we observe them.
Despite the name, the event of “survival” could be any categorical event that you would like to describe the mean or median TTE. To take the censoring into account, though, you need to make sure your data are set up correctly.
Here is a simple example, for a data set that measures days after surgery until an (more…)
Time to event analyses (aka, Survival Analysis and Event History Analysis) are used often within medical, sales and epidemiological research. Some examples of time-to-event analysis are measuring the median time to death after being diagnosed with a heart condition, comparing male and female time to purchase after being given a coupon and estimating time to infection after exposure to a disease.
Survival time has two components that must be clearly defined: a beginning point and an endpoint that is reached either when the event occurs or when the follow-up time has ended.
One basic concept needed to understand time-to-event (TTE) analysis is censoring.
In simple TTE, you should have two types of observations:
1. The event occurred, and we are able to measure when it occurred OR
2. The event did NOT occur during the time we observed the individual, and we only know the total number of days in which it didn’t occur. (CENSORED).
Again you have two groups, one where the time-to-event is known exactly and one where it is not. The latter group is only known to have a certain amount of time where the event of interest did not occur. We don’t know if it would have occurred had we observed the individual longer. But knowing that it didn’t occur for so long tells us something about the risk of the envent for that person.
For example, let the time-to-event be a person’s age at onset of cancer. If you stop following someone after age 65, you may know that the person did NOT have cancer at age 65, but you do not have any information after that age.
You know that their age of getting cancer is greater than 65. But you do not know if they will never get cancer or if they’ll get it at age 66, only that they have a “survival” time greater than 65 years. They are censored because we did not gather information on that subject after age 65.
So one cause of censoring is merely that we can’t follow people forever. At some point you have to end your study, and not all people will have experienced the event.
But another common cause is that people are lost to follow-up during a study. This is called random censoring. It occurs when follow-up ends for reasons that are not under control of the investigator.
In survival analysis, censored observations contribute to the total number at risk up to the time that they ceased to be followed. One advantage here is that the length of time that an individual is followed does not have to be equal for everyone. All observations could have different amounts of follow-up time, and the analysis can take that into account.
Allison, P. D. (1995). Survival Analysis Using SAS. Cary, NC: SAS Institute Inc.
Hosmer, D. W. (2008). Applied Survival Analysis (2nd ed.). Hoboken, NJ: John Wiley & Sons, Inc.
by Annette Gerritsen, Ph.D.
Cross-tabulation in cohort studies
Assume you have just done a cohort study. How do you actually do the cross-tabulation to calculate the cumulative incidence in both groups?
Best is to always put the outcome variable (disease yes/no) in the columns and the exposure variable in the rows. In other words, put the dependent variable–the one that describes the problem under study–in the columns. And put the independent variable–the factor assumed to cause the problem–in the rows.
Let’s take as example a cohort study used to see whether there is a causal relationship between the use of a certain water source and the incidence of diarrhea among children under five in a village with different water sources. In this case, the variable diarrhea (yes/no) should be in the columns. The variable water source (suspected/other) should be in the rows.
SPSS will put the lowest value of the variable in the first column or row. So in order to get those with diarrhea in the first column you should label ‘diarrhea’ as 1 and ‘no diarrhea’ as 2. The same is true for the exposure variable: label the ‘suspected water source’ as 1 and the ‘other water source’ as 2.
You will then be able to calculate the cumulative incidence (risk of developing the disease) among those with the exposure: a / (a + b) and among those without the exposure: c / (c + d).
In the case of the diarrhea study (Table 1), you could calculate the cumulative incidence of diarrhea among those exposed to the suspected water source, which would be (78 / 1,500 =) 5.2%.
You can also do this for those exposed to other water sources, which would be (50 / 1,000 =) 5.0%.
SPSS can give you these percentages immediately (in cell ‘a’ and ‘c’ respectively), when you ask to display row percentages in the Cells option (Table 2).
Cross-tabulation in Case-Control Studies
When you have used a case-control design for the diarrhea study, the actual cross-tabulation is quite similar, only “presence of diarrhea yes/no”, is now changed into “cases” and “controls.
Label the cases as 1, and the controls as 2. Be aware that row percentages have no meaning in terms of occurrence of disease in case-control studies. This is because in case-control studies the researcher determines how many patients and how many controls are included.
The ratio between the number of patients and controls (e.g. 2 : 1 or 4 : 1) influences the row percentages. So in a case-control study, the cumulative incidence cannot be calculated.
When having conducted a case-control study, you can ask to display column percentages. That gives you the proportion of those exposed to the suspected water source among the cases (in cell ‘a’) and among the controls (in cell ‘b’).
Table 3 gives the SPSS output for the same diarrhea study assuming that it had a case-control design. Using the data provided, (78 / 128 =) 60.9% of the cases were exposed to the suspected water source, while this was (1,422 / 2,372 =) 59.9% of the controls (asked for column percentages).
Another article will be devoted to measures of association: How do you actually compare cumulative incidence rates in cohort studies? And what measure of association can be used in case-control studies?
About the Author: With expertise in epidemiology, biostatistics and quantitative research projects, Annette Gerritsen, Ph.D. provides services to her clients focussing on the methodological soundness of each phase of an epidemiological study to ensure getting valid answers to the proposed research questions. She is the founder of Epi Result.
Two designs commonly used in epidemiology are the cohort and case-control studies. Both study causal relationships between a risk factor and a disease. What is the difference between these two designs? And when should you opt for the one or the other?
Cohort studies
Cohort studies begin with a group of people (a cohort) free of disease. The people in the cohort are grouped by whether or not they are exposed to a potential cause of disease. The whole cohort is followed over time to see if (more…)
