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I'm part of a team of medical doctors designing a study. but nobody seems to get statistics and the study might result in a huge waste of time, so that's why I'm here.

Our pediatric patients suffer from a heart disease. We clinically noticed that they have a reduction of pulmonary function. We would want to know if a pulmonary screening is needed for these patients.

Our plan is to run pulmonary tests on patients (two or three times, in different days, since the test can have some variability) and on healthy controls matched by age (we will probably end up with 10:7 patients:controls).

Reference ranges for pulmonary tests are determined based on sex, weight etc. and results of the tests are expressed as % of predicted value. A test is considered pathological if the result is < x% than predicted (x varies from test to test).

There are two issues that bug me.

1) Patients are at different stages of the disease, so I do not know if a normal test means that the disease has no pulmonary effect or if it's just at an early stage.

2) Puberty, oh damn puberty, screws up everything and we will probably end up having to divide our sample into prepubescent-pubescent-postpubescent.

Does the design of the study make sense?

How do we determine the sample size needed?

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    $\begingroup$ Hey, welcome to the site. Question: why are you comparing diseased patients to healthy controls, when reference ranges (based on sex, weight, etc.) already exist? How were those reference ranges determined? If the goal is to determine whether your patients need a full screening, won't comparing their cursory pulmonary test results to the reference range suffice? $\endgroup$ – Anson Call Feb 6 '18 at 23:16
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To answer question 1, the project design needs to established first, including the issues. The statistical design of the study would come afterwards.

You have noted a clinical reduction in pulmonary function. I am guessing that your aim is "To determine if pulmonary screening can detect the loss in pulmonary function before it is clinically detectable." This is crucial for guiding the design.

Issue 1) You would need to do testing to see if the tests correlate with either no pulmonary effect or an early stage of disease. I suspect this would involve, after establishing a "screening diagnosis of decrease pulmonary function," following up on these patients to determine if they later develop decreased pulmonary function i.e. a later-stage.

Issue 2). I suspect that puberty would be partially considered in the pulmonary test reference ranges as the ranges would include age. If age isn't included in the range, then you may need healthy controls to reduce the confounding effect of age and puberty; otherwise the ranges would suffice as control for this specific study.

Given this, I can answer your questions:

Question 1: You would use an unpaired, two-tailed, t-test, comparing your patients to either the healthy controls or parameters. You need two-tailed as opposed to one-tailed, unless it is 100% impossible that the patients could have an improved clinical function, which cannot be ruled out. You need unpaired, as you are comparing different groups of people. You use a t-test to compare two groups (patients vs controls/parameters).

Question 2: For-testing, there is no minimum sample size required. t-tests are designed to be able to work with small samples. However, a large sample size is still helpful as it will result in more power and a greater chance of statistical significance.

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