# How does procedure failure rate affect sample size in a randomized clinical trial?

I am currently conducting medical research. It is a randomized blinded clinical trial to compare patient indicators of rehabilitation after a surgical procedure . One group of patients receives an injection of local anesthetic near a sensory nerve; the second group of patients receives the same injection of local anesthetic near the same nerve but also receives a catheter near the nerve to provide a continuous infusion of local anesthetic. The two groups are measured on certain parameters of rehabilitation over a 24-hour period and data from both groups will be compared. The injections and catheter placement are done using ultrasound and there is a failure rate--either because the medication was not placed in the right place (primary failure) or the catheter becomes dislodged (under the skin) at some point during the study period(secondary failure) We will not know if the injection was improperly placed or if the catheter became dislodged during the 24 hour period.(The catheter could also work initially and become dislodged at some unknown point during the study) If the study is randomized is it necessary to know (or have an estimate of ) the failure rate of injections of local anesthetic and catheter placements in order to determine the appropriate number of study patients to ensure that the results will be sufficiently powered?

• What sorts of outcomes are you looking at? I ask because the effect size you want to detect is an important part of power analysis. For the study more broadly, are you looking at the effects of using the catheter specifically, or are you looking at patient outcomes with and without the catheter? – Upper_Case-Stop Harming Monica Dec 30 '16 at 15:05
• What is not clear to me is what you do with the data from patients that have the secondary failure. Throwing out the data could create unknown bias. Such problems are sometimes remedied by imputation if there are characteristics of the patients that have secondary failures that can relate to the patients with primary failures. – Michael R. Chernick Dec 30 '16 at 15:08
• As I read Upper_Case's comment and review the question again. I am wondering whether or not the objective is to see if the adding of the catheter reduces or increases the chance of failure compared to the injection alone. Does the type of failure really matter? If not maybe you can lump primary and secondary failures as simply failures. Are you trying to compare treatments with respect to efficacy and safety? If so failures might be a safety issue. But you also say you have several measures of rehabilitation (a measure of efficacy). Maybe you need to concentrate on one measure. – Michael R. Chernick Dec 30 '16 at 15:23
• @mcmillc With that information in mind I will strongly endorse mdewey's answer. Intent to treat seems like the right approach, in which case the failure rate (unknown or otherwise) will be represented in your data by a change in the average effect of the catheter on your outcomes. Since the catheterization fails some of the time, applicable results will reflect that real-world condition rather than the "pure" effect of failure-less catheter placement. So your study population size shouldn't change (from this, at least). – Upper_Case-Stop Harming Monica Dec 30 '16 at 16:42
• @EdM That's my argument, so I think we agree (provided I am interpreting your comment correctly). The examination isn't of the performance of a catheterization that is known to be successful but rather of how use of a catheter affects outcomes. The failure rate of catheterization in the study should be similar to that in the field. So even if power to detect the effect of successful catheterization decreases as a result of increased variance due to catheterization failures, the power to detect the effect of catheterization (given that failures sometimes occur) should be the same. Right? – Upper_Case-Stop Harming Monica Dec 30 '16 at 20:30

From the point of intention to treat it is not necessary to take this into account because everybody should be included in the analysis in the arm to which they are randomised. The failure rate is an inherent part of the treatment. If you want to compare the effect of actually receiving the treatment in the two arms that is a different mater but from your description I assume that is unknowable.

As a side issue I do not see how you can maintain masking if you are catheterising in one group but not the other. You can, and should, mask the outcome assessors but surely everybody else: patients, investigators, clinical team, ... will know.

My last paragraph is not relevant now as the OP has kindly elaborated on their ingenious scheme for employing a sham catheter.

Just for reference for people coming upon this who may not know about it intention to treat is described in this Wikipedia article and the alternative complier average causal effect is outlined in many articles including this open access one. There does not seem to be a Wikipedia entry for it.

• I was going to ask: what is "blinded" supposed to mean in this context? (But perhaps there is a standard answer? This is far from my field!) – GeoMatt22 Dec 30 '16 at 15:20
• I think we are jumping the gun by providing answers before we really understand the study more clearly. Specifically what is the ultimate objective (as Upper Case mentioned). Is safety part of the objective? Does type of failure matter? What statistical methods are being used (hypothesis testing, survival analysis, etc.)? – Michael R. Chernick Dec 30 '16 at 15:30
• @GeoMatt22 I prefer the term masking as I find it offensive to speak of blinding patients but it is the standard term unfortunately except in ophthalmology for obvious reasons. – mdewey Dec 30 '16 at 15:40
• Sorry, I did understand the use of blinding = masking. But in controlled studies, I thought "blind" meant the patients did not know which group the were in (treatment vs. control), and if "double blind" then the doctors also did not know. So I was agreeing with your 2nd paragraph ... but not sure if there was another meaning to "blinded" that I was missing. – GeoMatt22 Dec 30 '16 at 16:04

The power of your study depends on the magnitude of the difference you hope to detect between the two treatments, the variability among participants in terms of their responses to the treatments, and the number of participants. Insofar as the possibility of placement failure increases the variability of responses among participants, it will necessarily decrease the power for detecting a particular difference between the treatments, given the same number of participants. As an extreme example, if there always was placement failure you would be unable to detect any differences at all.

That said, placement failure seems inherent in these treatments so this would seem to be a fair test of their differences in clinical practice (except for the caution raised by @mdewey about whether this is really masked, unless all get catheterized but some receive placebo instead of anesthetic, or unless you are willing to accept a possible placebo effect simply due to catheterization that doesn't correspond to the continued anesthetic infusion). With treatment failure you may not be able to detect as small a difference as you might like, so an estimate of treatment failure should be considered in your design.

• Random uncertainty decreases the precision of an experiment.
• Systematic uncertainty decreases the accuracy of an experiment.

The Standard deviation , $s$ equals the square root of the sum of squares of differences $/ N$ (population).

The standard deviation of the mean value of a set of measurements $σ_m$ , (“sigma-em”)

$σ_m=s/√N$

When we speak of the uncertainty σ of a set of measurements made under identical conditions, we mean that number $σ_m$ and not $s$. There are two common ways to state the uncertainty of a result: in terms of a $σ$, like the standard deviation of the mean $σ_m$, or in terms of a percent or fractional uncertainty, “epsilon”, $\epsilon$.

If the uncertainty of results does not change with quality or experience then the rate of change of standard deviation of the mean value with growing data set size will be small. It is both an indicator of process quality and significant population size.

Referring to Shannon's Law and digital communication we know that the Noise to Signal ratio or standard deviation is arithmetically related to the error rate is directly proportional on a log-log scale ( although we usually use the inverse or S to N ratio (SNR)) where 10:1 or 10dB to 15 dB or 30:1 is usually the threshold of noise where you have a 50/50 chance of error depending how how you discriminate the results "good or bad" and 20dB is 1% noise, the error rate is quite small. (more astute statisticians are welcome improve or correct this description)

You must decide your own population size and and error threshold and thus population size for significant results depending on the weight of the error. ( longer recovery period vs loss of added cost, infection or whatever)

A typical calculation is a measure of the improved recovery time with a standard deviation with and without additional treatment. Then plotting the standard deviation over time for each medical team is an indicator of their treatment efficacy improvement rate.

IMHO, blinding the test is less important than defining the measurement methods of observation of recovery accurately, confidence in skill , if this can be measured somehow with measurable thresholds, tolerances and bias inputs. (neglect or more attention may bias the results in either direction) (blind test results are somewhat meaningless without these details because they only apply to the team that repeated the process and not all teams unless a larger measurement takes place.)

Even with a large sample base, every precedure must be a measurable parameter with a tolerance to obtain a reliable prediction of the outcome. ( e.g. placement, adhesion secured, patient motion etc.) Reducing the deviation improves the success rate. Design of Experiments (DoE) can be done to optimize the process. (beyond scope of this answer)