A retrospective cohort study (also known as a historic study or longitudinal study) is a study where the participants already have a known disease or outcome. The study looks back into the past to try to determine why the participants have the disease or outcome and when they may have been exposed. In a retrospective cohort study the researcher:
One of the first recognized retrospective cohort studies was Lane-Claypon’s 1926 study of breast cancer risk factors, titled “A Further Report on Cancer of the Breast, With Special Reference to Its Associated Antecedent Conditions.” The study of 500 hospitalized patients and 500 controls led to the identification of most of the risk factors for breast cancer that we know today.
In a retrospective cohort study, the group of interest already has the disease/outcome. In a prospective cohort study, the group does not have the disease/outcome, although some participants usually have high risk factors.
Retrospective example: a group of 100 people with AIDS might be asked about their lifestyle choices and medical history in order to study the origins of the disease. A Second group of 100 people without AIDS are also studied and the two groups are compared.
Prospective example: a group of 100 people with high risk factors for AIDS are followed for 20 years to see if they develop the disease. A control group of 100 people who have low risk factors are also followed for comparison.
A cohort effect is the influence of a group’s life experience on the outcome of an experiment. It’s the effect of being born at the same time (i.e. GenXer vs. Baby Boomer), or in the same region (i.e. born in New Orleans vs. Seattle) or some other factor that makes the group unique. Cohorts in schools are usually defined by age group, while cohorts in organizations are defined by their date of entry into the job.
Lets say you were conducting cross sectional research (a method that compares different age groups at the same point in time) to find out how basic mathematics ability improves with age. You give the same basic math standardized test to groups of students who are 7-years-old, 14-years-old, and 21-years-old. You get the following mean results:
You might conclude that every 7 years that pass makes a difference of 24% in scores. However, what you haven’t accounted for is the cohort effect. The students differ not only in age, but they belong to different cohorts (in this case, groups of people born around the same time), some of which may have grown up when basic mathematics was strongly emphasized in schools. If the 21-year-old cohort in the above study experienced strong emphasis on basic math, it’s a possibility that they could have achieved 72% when they were 14-years old or even 7-years-old.
The problems associated with the cohort effect can be lessened by testing the same cohort over a period of time, a method called longitudinal research. In the above example, you would test a group of 7-year-olds, then test the same group every 7 years. A disadvantage to longitudinal research is that it’s costly, and dropout rates can affect the results.
The new functions are called an arithmetic combination of functions. The domain for the new function is all real number common to the domains of f(x) and g(x), with the exception of the quotient, where x cannot equal zero.
Solution: We aren’t given an x-value here, so in order to combine these functions, substitute every value of x in f(x) = 3x + 4 with g(x) = 2x2 – 1:
If algebra isn’t your forte, you can use your graphing calculator to get a very good approximation for a difference of two functions. For example, let’s say you wanted to find the difference at x = 2 of
Primary composite endpoints are the main measurements for a trial; They answer the most important questions in the trial. For example, if the endpoint of a study is “cure”, then a composite endpoint might be cure or remission.
Secondary composite endpoints are the secondary objectives in the trial. For example, a drug designed to cure/put into remission a disease might also have measures of whether chronic pain and quality of life are improved.
The major risk to studies with composite endpoints is bias. Studies with composite endpoints should be analyzed carefully to avoid bias because of competing risks between endpoints. For example, a study on a particular stroke medication with endpoints of death or hospitalization may see a reduction in hospitalization only because of an increase in mortality. For this reason, death should always be included in a trial that studies non-fatal events (Skali et. al).
When a study has a fairly rare endpoint, it’s common to use a composite endpoint instead. Rare events may require a very large, expensive trial in order to get statistically significant results. Let’s say a study is investigating a new drug for anaphylaxis (a severe allergic reaction which can lead to death). If “death” is the endpoint, a trial could need about a million people to record one death(1). A composite primary endpoint might be “any non-fatal or fatal allergic reaction” — which would require much smaller numbers (thousands, or possibly hundreds).
Composite endpoints should only be used when each endpoint in the composite is meaningful, both to the trial purpose and to the patient. Each endpoint should be analyzed separately to gauge if the clinical trial has meaningful results for all members of the composite, or just some (ICOH, CPMP). For example, glycoprotein IIb/IIIa inhibitors show a statistically significant reduction for the composite endpoints of death, myocardial infarction, or refractory angina. However, death — the most important endpoint — showed no change (Freemantle et. al).
N. Freemantle, M. Calvert, J. Wood, J. Eastaugh, C. Griffin, “Composite Outcomes in Randomized Trials. Greater Precision but with Greater Uncertainty?” Journal of the American Medical Association, 289, 2554–2559 (2003).
Concordant pairs and discordant pairs refer to comparing two pairs of data points to see if they “match.” The meaning is slightly different depending on if you are finding these pairs from various coefficients (like Kendall’s Tau) or if you are performing experimental studies and clinical trials.
Excellent StatisticsConcordant pairs and discordant pairs are used in Kendall’s Tau, for Goodman and Kruskal’s Gamma and in Logistic Regression. They are calculated for ordinal (ordered) variables and tell you if there is agreement (or disagreement) between scores. To calculate concordance or discordance, your data must be ordered and placed into pairs.
Note that in the first column, interviewer 1’s choices have been ordered from smallest to greatest. That way, a comparison can be made between the choices for interviewer 1 and 2. With concordant or discordant pairs, you’re basically answering the question: did the judges/raters rank the pairs in the same order? You aren’t necessarily looking for the exact same rank, but rather if one job seeker was consistently ranked higher by both interviewers.
Concordant pairs: both interviewers rank both applicants in the same order — that is, they both move in the same direction. While they aren’t the same rank (i.e. both 1st or both 2nd), each pair is ordered equally higher or equally lower. Interviewer 1 ranked F as 6th and G as 7th, while interviewer 2 ranked F as 5th and G as 8th. F and G are concordant because F was consistently ranked higher than G.
Discordant pairs: Candidates E and F are discordant because the interviewers ranked in opposite directions (one said E had a higher rank than F, while the other said F ranked higher than 6).
The term “concordant pair” is sometimes used (i.e. in case control studies) to mean a pair who are both exposed (or both not exposed) to some factor. In other words, it is based on exposure status. In a matched pairs design, a concordant pair means that the exposure status of one case is the same as a control case.
A medication’s indication can act as a confounder in observational studies, especially when the drug’s effectiveness is being assessed (Ahrens & Pigeot, 2007). Indication refers to how a particular drug is used for treatment of a certain disease. For example, aspirin is an indication for cardiovascular disease.
Confounding by indication is likely to happen when a particular medicine is linked to the outcome of interest in a study. For example, let’s say you’re observational study is looking into the effects of a new drug A on outcomes for patients with cardiovascular disease (CVD). As the study is observational, there’s no control group or experimental group, and you’re merely observing what happens. In this particular example, patients with more severe cases of CVD are more likely to be prescribed drug A, but they are also more likely to have adverse events (e.g. a stroke). Therefore, your study might conclude that drug A isn’t very effective, because it appears patients have more severe events. These misleading effects (or lack of effects) are what confounding by indication is all about.
Confounding by contraindication is, despite the similar sounding name, completely different from confounding by indication. O. Miettinen, in Epidemiological Research: Terms and Concepts, notes that it’s very rare to find confounding by contraindication in a study, while confounding by indication is quite common.
Confounding by indication is difficult to control for. One of the reasons is that the specific reason why the drug was prescribed usually isn’t recorded (Ahrens & Pigeot, 2007). The solution would be a controlled clinical trial, but they can be expensive and challenging to implement.
Confounding by indication is often confused as a type of selection bias, but it’s actually a type of confounding bias. Confounding isn’t actually a true “bias”, because bias is usually a result of data collection errors or measurement errors. Confounding by indication isn’t (despite the allusion) actually a bias; It’s just something that might result in confounding bias. On the other hand, selection bias is a specific type of bias that affects the types of people who are in your study; It removes the randomness you’re hoping to achieve. For example, the healthy worker effect results in healthier workers in your study, because people who are working are healthier than people who are unemployed or out of work due to a job-related disability.
A consistent estimate has insignificant errors (variations) as sample sizes grow larger. More specifically, the probability that those errors will vary by more than a given amount approaches zero as the sample size increases. In other words, the more data you collect, a consistent estimator will be close to the real population parameter you’re trying to measure. The sample mean and sample variance are two well-known consistent estimators.
The idea of consistency can also be applied to model selection, where you consistently select the “true” model with the associated “true” parameters. For example, a goodness of fit test can also be used as measure of consistency. One popular goodness of fit test is the chi-square test, which works on the premise that expected values for your data fit a normal distribution. And if you have data from a time-series model, data consistency can be measured with an autoregressive model. Many other measures of consistency for fitting to data to models exist. Which method you use depends on what you want your data to measure. For example, do you think your data follows a linear trend, an exponential trend, or a specific trend like the one seen in this paper, which outlines a consistent estimator for disturbance components in financial models?
The term consistent estimator is short for “consistent sequence of estimators,” an idea found in convergence in probability. The basic idea is that you repeat the estimator’s results over and over again, with steadily increasing sample sizes. Eventually — assuming that your estimator is consistent — the sequence will converge on the true population parameter. This convergence is called a limit, which is a fundamental building block of calculus.
Levinsohn, J. & MacKie-Mason, J. (1989). A simple, cons. est. for disturbance components in financial models. National Bureau of Economic Research. Technical working paper No. 80. Retrieved January 7, 2017 from http://www.nber.org/papers/t0080.pdf.
When you’re talking about a construct in relation to testing and construct validity, it has nothing to do with the way a test is designed or constructed. A construct is something that happens in the brain, like a skill, level of emotion, ability or proficiency. For example, proficiency in any language is a construct.
Construct validity is one way to test the validity of a test; it’s used in education, the social sciences, and psychology. It demonstrates that the test is actually measuring the construct it claims it’s measuring. For example, you might try to find out if an educational program increases emotional maturity in elementary school age children. Construct validity would measure if your research is actually measuring emotional maturity.