## Monday, October 03, 2016

### Type III or Type 3 Error in Clinical Trials

Anybody who learns the statistics will be familiar with the concept of type I and type II error. In hypothesis testing, Type I error, also known as a “false positive”: the error of rejecting a null hypothesis when it is actually true. In other words, this is the error of accepting an alternative hypothesis (the real hypothesis of interest) when the results can be attributed to chance. Plainly speaking, it occurs when we are observing a difference when in truth there is none (or more specifically - no statistically significant difference).

Type II error, also known as a "false negative": the error of not rejecting a null hypothesis when the alternative hypothesis is the true state of nature. In other words, this is the error of failing to accept an alternative hypothesis when you don't have adequate power. Plainly speaking, it occurs when we are failing to observe a difference when in truth there is one. In practice, the statistical power (equals to 1 - type II error) is commonly used. Power is the probability of rejecting the null hypothesis when the null hypothesis is indeed not true (i.e., the alternative hypothesis is true).

Now, there are also a concept of type III error. Fundamentally, Type III errors occur when researchers provide the right answer to the wrong question. While the term ‘type III error’ has been used in literature and presentations, the true meaning of ‘type III error’ is not clearly or consistently defined. People may use the term “type III error” to refer to different things.

In one of presentations, the type III error was used to describe those clinical trials that would have been successful but were not performed due to resource constraint

We make type III error when conclusion is not supported by the data

Type III error referring to an error by rejecting a null hypothesis but inferring the incorrect alternative hypothesis.

A type III error is where you correctly reject the null hypothesis, but it’s rejected for the wrong reason. This compares to a Type I error (incorrectly rejecting the null hypothesis) and a Type II error (not rejecting the null when you should). Type III errors are not considered serious, as they do mean you arrive at the correct decision. They usually happen because of random chance and are a rare occurrence. You can also think of a Type III error as giving the right answer (i.e. correctly rejecting the null) to the wrong question. Either way, you’re still arriving at the correct conclusion for the wrong reason. When we say the “wrong question”, that normally means you’ve formulated your hypotheses incorrectly. In other words, both your null and alternate hypotheses may be poorly worded or completely incorrect.

In a presentation slides titled “Type III and Type IV Errors: Statistical Decision-Making Considerations in addition to Rejecting and Retaining the Null Hypothesis”, type III error was used to refer to the wrong model, right answer and common influences on type III error would be:
• ·         Incorrect operationalization of variables
• ·         Poor theory (e.g., ad hoc explanations of findings)
• ·         Mis-identifying causal architecture (Schwartz & Carpenter, 1999)

In an editorial article of Arch Surg, the type III error was described as “the type III error occurs whenever the conclusions drawn are not supported by the data presented”. The author presented 5 examples using the published articles.

Type III error is solving the wrong problem precisely  – from Raiffa – 1968

Solving the wrong problem is defined as a Type III error by Howard Raiffa (1968, p. 264) and Ian Mitroff (1974). Type III errors are different from Type I and Type II errors, which involve setting the significance level too high or too low in testing the null hypothesis.

“The second trial (the HEMO study) committed a Type III statistical error asking the wrong question and did not bring any valuable results, but at least it did not lead to deterioration of dialysis outcomes in the USA”
Type III error — asking the wrong question and achieving the correct answer:

Kimball [7] postulated a Type III error, an error that gives the right answer to the wrong problem. A Type IV error was subsequently postulated as a type of error that solved the right problem too late [8].

in Flick, U. (2006). An introduction to qualitative research (3rd ed.). Thousand Oaks, CA: Sage.
Flick (2006), for example, discusses qualitative validity in terms of “whether researchers see what they think they see” (p. 371). Moreover, he and others (Kirk & Miller, 1986) argue that three types of error may occur as regards qualitative validity: seeing a relationship, a principle, and so on when they are not correct (Type I error); to reject them when they are correct (Type II error); and asking the wrong questions (Type III error).

Discussion so far has essentially been concerned with assessing the outcome of interventions and has ignored the nature of the intervention itself. Type III error refers to rejection of the effectiveness of a programme when the programme was inadequate in terms of design or delivery. This is neatly encapsulated in the acronym GIGO – garbage in, garbage out!

The real worry clinically is the type III error, in which a clinically significantly inferior treatment is preferred to a superior one on the basis of insufficient dataTraditional Type I and II error describe the false positive and negative rates, Type III error describes the opportunity cost of not investigating valid hypotheses due to budgetary limitations
Predictor variables must be easy to collect (to minimize missing data), clinically relevant, and reliable.The number of variables in multiple regression analyses must also be carefully controlled. Too few variables means that important predictors may be omitted, while too many variables can result in overfitting (a type I error in which false-positive predictors are erroneously included in the model); underfitting (a type II error in which important variables are omitted from the final model); and paradoxical fitting (a type III error in which a variable that, in truth, has a positive association with the outcome is found to have a negative association).The risk of these problems increases as the ratio of outcome events to the number of predictor variables becomes smaller (the events per variable [EPV] ratio, in which the number of events is the lower figure for binary outcomes). The risk of error is especially high with EPVs <10 .="" span="">
In an article by Robin et al (1990) “Type 3 and type 4 errors in the statistical evaluation of clinical trials”, the type III error was referred to
Type 3 errors, then, are errors in which the risks of a given medical or public health approach is underestimated, undetected or not specifically sought, leading to an underestimate of the risk-benefit balance.”. The type 3 error was further classified as three categories: type 3A errors arise from a failure to obtain sufficient data to determine the statistical significance of a given risk in an experimental versus a control group.  Type 3-B errors involve failures to look for or detect specific risks in an experimental versus a control group. Type 3-C errors involve risks in which the harm to subjects occurs months to years after the initial use of the modality As a result, the risk-benefit ratio of the modality is seriously underestimated.

Obviously, type III error from clinical trials has greater impact on health policy and medical practice because it involves in making the right decision. While the impact of type I and type II errors are the issues within a clinical trial, the impact of type III error goes beyond a clinical trial - if a type III error is committed, we could potentially adopted a wrong practice due to insufficient information .