Reference no: EM132353962

Assignment - Design of Experiments & Randomised Clinical Trials [DES]

Question 1 - (parts (a) through (f)) [present your answers up to 3 decimal places].

In a 2 treatment RCT using simple randomization, the probability of assignment to either treatment is 0.5. There are 10 dichotomous covariates (prognostic factors). The treatments are tested for balance on each of the covariates using a test with alpha = 0.05 for each test.

Show your working, and where appropriate both the algebraic expression and the final result (to a reasonable number of decimal places). You may assume, for the purposes of answering these questions, that the covariates are independent of one another. [Admittedly, this assumption is unlikely to be reasonable, but make it anyway.]

(a) What is the chance that all 10 of the covariates are balanced? [Provide your solution and working, both have to be correct for full mark allocation].

(b) What is the chance that exactly 7 are balanced? [Need the formula as well as the solution].

(c) What is the chance that none are balanced? [Write down the formula used in the computation and the solution].

(d) How many dichotomous covariates are needed such that the probability of finding at least one of them unbalanced is at least 0.4? [Formula, solution and provide justification exactly in four lines].

(e) How many dichotomous covariates are needed such that the probability of finding at least one of them unbalanced is at least 0.9? [Solution and formula are required to be presented for full marks].

(f) Explain how randomization, in general, can obtain balance on measured and un-measured confounding [Provide justification in exactly four lines].

Question 2 - (parts (b) through (c) with sub-parts) [all answers must be presented till 3 decimal places].

(a) In a RCT with randomisation in blocks within strata, what is the maximum imbalance in the number of treatment assignments that can occur if there are 2 treatments in blocks of varying size: 2, 4, 6 and 8, and there are 5 strata? (We assume that the trial ends randomly and uniformly within a block and the strata assignments are independent.)

(b) In a RCT with randomisation in blocks within strata, given that there are 3 treatments in blocks of uniform size: 3, and there are 10 strata:

(i) What is the maximum imbalance in treatment assignments that can occur between any 2 of the 3 treatments (given the trial ends randomly and uniformly within a block and the strata assignments are independent)?

(ii) Using the maximum imbalance, you found in (i), what is the probability that the trial will end exactly balanced for 2 of the 3 treatments and with the maximum excess for the other treatment?

(c) In a RCT with 2 treatment arms, blocks of uniform size: 2, and 3 strata, what is the chance that the trial will end exactly balanced

(i) Within each stratum and hence across all strata (assuming that when the trial ends, none of the strata are empty)?

(ii) Across all strata but not necessarily within each stratum (assuming that when the trial ends, none of the strata are empty)? [Hint: Start by listing each possible combination of stopping locations for the three strata.]

Question 3 - (parts (a) through (f)).

Patients in intensive care units (ICU) are often given "compression" stockings to prevent deep venous thrombosis (DVT). A randomised trial will be conducted in two large hospitals in order to address two questions of interest relating to using these compression stockings:

1. Is a thigh-length compression stocking better/worse than a knee-length stocking?

2. Is the position in which the patient lies important? (Two standard positions are used for unconscious ICU patients - either on their back with their legs out straight, or on their side with their knees bent at about 60 degrees.)

The trial investigators suspect that there is an interaction between compression stocking effectiveness and the position of the patient. The hypothesis is that the thigh- length stocking will be better when the legs are straight, and the knee-length one will be better when the knees are bent (due to excess compression behind the knee from the thigh-length stocking).

DVT may take time to develop and early clinical diagnosis is difficult, thus blood flow as measured by ultrasound will be used as a surrogate outcome measure.

(a) What type of study design would you recommend using? What are the advantages of using this type of design in this case? [Please provide your answer in no more than 10 lines].

(b) Suggest two baseline covariates that you would consider adjusting for in the analysis of the primary outcome (blood flow) and give a brief explanation as to why you think each covariate might be important in this context. [Please provide your answer in no more than 5 dot points].

(c) In dot point form, indicate the inclusion criteria you would use for this study [use up to 3 dot points].

(d) In dot point form, indicate the exclusion criteria you would use for this study.

(e) Outline a randomisation scheme to support the study. Your answer should outline both the logistics of the process from the trial staff's perspective and the technical details of groups, strata (should you choose to stratify), blocks (should you choose to block) etc.

(f) Produce a randomisation sequence to support your answer to part (e). Read the following note! [Code should be supplied and correct. If Stata was used, then provide the first 10 lines of your answer].

Note for Q3(f): This unit, DES, as such does not require you to have access to a statistics package (though I expect and would hope many of you will have some access to packages such as Stata and R at your work places). In any case, this question ought not disadvantage anyone who does not have a stats package. Let's look at some of the ways you could answer this question:

Case 1: You have Stata: code something yourself, or download -ralloc.ado- and -ralloc.hlp- from the SSC server (findit ralloc at the Stata dot prompt, this works fine in Stata 15 if you have Stata 13 and face problems please let me know) and use that.

Case 2: You have Excel: use its random number function, but be careful because Excel's random values, unlike a decent statistical package's random values, do not remain fixed after generation. They can change after seemingly completely unrelated operations on other cells. Sometimes this is referred to as a volatile function (A volatile function is a function that recalculates when you enter any data into any cell or take any other action. One of the few exceptions is changing the format of a cell.) If you use Excel you must ensure, somehow, that if you sent the spreadsheet off to the trial coordinator/trial pharmacy, the random values would not change. Imagine the chaos if they did....

Case 3: You have no stats package and not even Excel. Hmmm. Then go manual! Use random number tables, available in many stats texts or in books of tables or on-line. You will need to devise a system of randomly allocating the treatments to subjects within any strata you have designated and within any block pattern you may have specified.

You may assume that a total of about 400 patients will participate in the trial, but, especially, if you are doing things manually, you do not have to show me all 400 allocations. The first 10 or so in each stratum will suffice. Include the code you have written (or if doing things manually, exactly how you used the random digit tables), any output the code produces (e.g. if using Stata, the "notes" produced by ralloc.ado) and the first 10 allocations (of each stratum, should you have used more than one stratum). Ensure the allocations are labelled appropriately (Which treatment? Which stratum? Which block?).

In other words, however you do construct your schedule, imagine you will be audited by the FDA or the TGA and your randomisation schedule must be able to be reproduced by the auditing agents.

Question 4 - (parts (a) through (e)) [please provide your justification in more than 4 lines for each question].

Bipolar disorder is a recurrent psychiatric condition which is characterised by episodes of both mania and depression. Patients presenting with this disorder are typically treated with a mood stabiliser such as lithium. Antidepressants may also be prescribed, though their effectiveness has not been established for bipolar disorder.

A team of researchers is planning to conduct a study to evaluate the effectiveness of antidepressants combined with a mood stabiliser in the treatment of bipolar disorder compared to a mood stabiliser alone.

(a) Is a parallel design appropriate for this study? Give a reason for your answer and/or nominate any further information you might need before deciding.

(b) Is a crossover design appropriate for this study? Give a reason for your answer and/or nominate any further information you might need before deciding.

(c) Is a factorial design appropriate for this study? Give a reason for your answer and/or nominate any further information you might need before deciding.

(d) Is an n-of-1 design appropriate for this study? Give a reason for your answer and/or nominate any further information you might need before deciding.

(e) The study is intended to be a comparative study, where the aim is to show that antidepressants combined with a mood stabiliser is more effective in treating bipolar disorder than a mood stabiliser alone. Discuss the circumstances under which an equivalence study would be more appropriate.