Ultrasound is no different to any other imaging modality in this perspective. You seem to have multiple questions to answer. Typically your data collection will measure image interpetation accuracy, sensitivity and specificity. You could just focus on the abnormal cases (sensitivity) or normal cases (specificity) but typically researchers don't do this because the whole is a more interesting study.

You need to know the 'ground truth' of each case; typically by agreed blind double reporting but correlation with histology is even better because of course both viewers could be wrong. A decision, typically on a 5 point scale, is recorded by the respondent for each case. The 'truth' is typically recorded in a seperate column in a binary fashion (eg 0=normal, 1=abnormal). You can then sort and copy the data into an ROC calculator and plot the accuracy of TPF against FPF (eg JROCFIT from Johns Hopkins University).   

From the raw data you can now define the TP,FP,TN,FN decisions and calculate accuracy, sensititivity and specificity. Do this for eacg respondent to create a string of data. Now you can test your hypothesis (or Null) and analyse using SPSS or similar, for example you might want to compare radiologists and radiographers, or look for variation by gender, age group, training etc

Hope this helps

Ultrasound has one difference to other imaging modalities - that it is a subjective investigation in that you cannot reproduce precisely the same conditions. Furthermore ultrasound has a multitude of uses.

I suggest that you need to define precisely which ultrasound investigation you refer to and make sure that you compare it to a gold standard - if you can ("ground truth") as above.

Thank you Chris wright and Markus Maiden-Tilsen..... What i would like to know is if i am comparing the result of Ultrasound with MRI and check sensitivity and specificity of Ultrasound to detect Muskuloskeletal Injury. How should i form the Hypothesis for the same. Should i write the Null hypothesis as 'Sensitivity = 90%' and Alternative Hypothesis as 'Sensitivity  is not equal to 90%'... Or is there any other way of writing it? Or is there no hypothesis to be written for such studies?

NOTE: The percentage given here is just an example taken based on other studies.

You need to establish the 'ground truth' ie what is the true diagnosis per case. Argueable a blind double reported MRI might be more reliable than a subjective ultrasound scan which is more operator sensitive. You would need to ground this in the literature. Bear in mind though that all modalities have error, which is why whenever possible the histology is a better 'truth'. The analysis is really about comparative accuracy and so your null hypothesis is that ultrasound is less sensitive than MRI for MSK injuries. Test it statistically using the raw decision data to get an overall accuracy correlation then drill down to looking at normal verus abnormal decisions if necessary. With skilled operators, don't be suprised if you find no significant differences (regardless of the % you set - so don't do this) but you might see a trend from a box plot. You might find that if you had the same subject scanned by many operators (could use phantom) you might be able to see differences in performance highlighting the subjective nature of ultrasound but again experts will almost cenrtainly all be above 90% so you probably need some trainees in the population.

Thank you Chris Wright. The picture is clear now. cheers

agreed with chris-- if you have written any hypothesis you can share with me to give advise if needed

the Null hypothesis as 'Sensitivity = 90%' and Alternative Hypothesis as 'Sensitivity  is not equal to 90%

This question was asked several years ago but, maybe, still should be answered. It appears that Arakkal wanted to compare the accuracy (sensitivity and specificity) of US vs MRI in diagnosing a certain condition. Please note that H0 typically tests the claim that there is NO difference between the two modalities, while H1 states there is. You need to decide whether your test is one-sided (the difference is in one direction) or two-sided (in two directions). You may want to test H0 for specificity and sensitivity separately because specificity could be the same within statistical limits, whereas sensitivity could be significantly different. Note that the outcome of your test is binary (disease present or absent) which determines the choice of the test. You also need to tell whether the patient samples to which you apply the test are the same (repeated measures) or two independent samples; different tests will be used. I intentionally did not give a more definitive answer, to keep the learning opportunity open.

I have been designing a diagnostic study currently and have struggled with what is the null hypothesis and how to write the null hypothesis when using PASS 11 to calculate the sample size. I came across this question asked years ago, but find it still needs a further answer.

I recommend the following reference, which answered this question perfectly:

Leeflang, M.M.G.Allerberger, F. et al.Sample size calculations for diagnostic studies.Clinical Microbiology and Infection, Volume 25, Issue 7, 777 - 778. DOI:https://doi.org/10.1016/j.cmi.2019.04.011

In summary, as quote "the first step is to decide what type of study is planned, and whether the study is hypothesis driven or not". As in the question of Arakkal, the aim of the study is to investigate whether ultrasound has a higher sensitivity than MRI in MSK injuries. Then the null hypothesis may be that there is no difference in sensitivity between the two tests. If in practice a specificity of at least 95% is required, then the null hypothesis may be that the specificity of the new test is not different from 95%.

However, in a study that is not hypothesis-driven (like the study I am designing), the aim is to estimate the sensitivity or specificity of a new test. In that case, "the sample size will focus on the precision of these estimates, i.e. the width of the confidence interval around the sensitivity and the specificity."