------------------------------------------------------------------------------------------------------------------- name: log: C:\git\artbin\examples\artbin_examples.log log type: text opened on: 23 May 2023, 17:06:31 . . . which artbin c:\ado\personal\a\artbin.ado *!version 2.0.2 EMZ 23may2023 . which art2bin c:\ado\personal\a\art2bin.ado *!version 1.01 09june2022 . . . . /*** > \subsection{Binary outcome and comparison with published sample size} > We reproduce the sample size calculation in \citet{Pocock83} for a 2-arm superiority trial comparing the efficacy > of therapeutic doses of anturan in patients after a myocardial infarction with the placebo standard treatment. > The primary outcome was death from any cause within one year of first treatment. The control (placebo) arm was e > xpected to have a 10\% probability of death within one year and the anturan treatment arm a 5\% probability, with > the trial powered at 90\%. The patient outcome was binary; either failure (death in a year) or success (surviva > l). The published sample size was 578 patients per arm (1156 patients in total). > In the below \texttt{artbin} example we do not specify in the syntax whether the outcome is favourable or unfavou > rable, rather we let the program infer it. The aim of a clinical trial is always to improve patient outcome, the > refore as the experimental arm anticipated probability ($\pi_2 = 0.05$) is $less$ $than$ the control arm anticipa > ted probability ($\pi_1 = 0.1$) then the outcome is inferred to be unfavourable (i.e. the trial is aiming to $red > uce$ the probability of the event occurring, in this case, death). > ***/ . . . artbin, pr(0.1 0.05) alpha(0.05) power(0.9) wald ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.0.2 23may2023) ------------------------------------------------------------------------------ A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, Ella Marley-Zagar and Ian White MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK. ------------------------------------------------------------------------------ Type of trial superiority Number of groups 2 Favourable/unfavourable outcome unfavourable Inferred by the program Allocation ratio equal group sizes Statistical test assumed unconditional comparison of 2 binomial proportions using the wald test Local or distant distant Continuity correction no Anticipated event probabilities 0.100 0.050 Alpha 0.050 (two-sided) (taken as .025 one-sided) Power (designed) 0.900 Total sample size (calculated) 1156 Sample size per group (calculated) 578 578 Expected total number of events 86.70 ------------------------------------------------------------------------------ . local n=r(n) . . . /*** > The \texttt{artbin} output table shows the trial set-up information including the study design, statistical tests > and methods used. The hypothesis tests are shown with the calculated sample size and events based on the select > ed power. > A total sample size of 1156 participants is required, as per the published sample size given by Pocock. > The same result is achieved by the code \texttt{artbin, pr(0.9 0.95) alpha(0.05) power(0.9) wald} assuming a favo > urable outcome (survival) instead. > The Wald test is used instead of the default score test as Pocock used the sample estimate in the method of estim > ating the variance of the difference in proportions under the null hypothesis $H_{0}$. > > \subsection{Binary outcome and comparison with \texttt{power}} > We compare the output of \texttt{artbin} to Stata's \texttt{power} command, which like \texttt{artbin} uses the s > core test as the default. > ***/ . . . power twoproportions 0.1 0.05, alpha(0.05) power(0.9) Performing iteration ... Estimated sample sizes for a two-sample proportions test Pearson's chi-squared test Ho: p2 = p1 versus Ha: p2 != p1 Study parameters: alpha = 0.0500 power = 0.9000 delta = -0.0500 (difference) p1 = 0.1000 p2 = 0.0500 Estimated sample sizes: N = 1,164 N per group = 582 . local npower=r(N) . . artbin, pr(0.1 0.05) alpha(0.05) power(0.9) ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.0.2 23may2023) ------------------------------------------------------------------------------ A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, Ella Marley-Zagar and Ian White MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK. ------------------------------------------------------------------------------ Type of trial superiority Number of groups 2 Favourable/unfavourable outcome unfavourable Inferred by the program Allocation ratio equal group sizes Statistical test assumed unconditional comparison of 2 binomial proportions using the score test Local or distant distant Continuity correction no Anticipated event probabilities 0.100 0.050 Alpha 0.050 (two-sided) (taken as .025 one-sided) Power (designed) 0.900 Total sample size (calculated) 1164 Sample size per group (calculated) 582 582 Expected total number of events 87.30 ------------------------------------------------------------------------------ . local nartbin=r(n) . . . /*** > Both give a total sample size of `nartbin'. > > \subsection{One-sided non-inferiority trial} > Next we show a one-sided non-inferiority trial with the 'onesided' option. We assume a 90\% probability of survi > val in both the control and treatment arms, with the treatment arm being no more than 5\% less effective than the > control. > ***/ . . artbin, pr(0.9 0.9) margin(-0.05) onesided ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.0.2 23may2023) ------------------------------------------------------------------------------ A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, Ella Marley-Zagar and Ian White MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK. ------------------------------------------------------------------------------ Type of trial non-inferiority Number of groups 2 Favourable/unfavourable outcome favourable Inferred by the program Allocation ratio equal group sizes Statistical test assumed unconditional comparison of 2 binomial proportions using the score test Local or distant distant Continuity correction no Null hypothesis H0: H0: pi2 - pi1 <= -.05 Alternative hypothesis H1: H1: pi2 - pi1 > -.05 Anticipated event probabilities 0.900 0.900 Alpha 0.050 (one-sided) Power (designed) 0.800 Total sample size (calculated) 914 Sample size per group (calculated) 457 457 Expected total number of events 822.60 ------------------------------------------------------------------------------ . . . /*** > > A sample size of 457 is required in each group. > > \subsection{Superiority trial with multiple arms} > Next we demonstrate a superiority trial with more than 2 arms. Instead of comparing each of the treatment arms t > o the control group, \texttt{artbin} uses a global test to assess if there is $any$ difference among the groups. > ***/ . . . artbin, pr(0.1 0.2 0.3 0.4) alpha(0.1) power(0.9) ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.0.2 23may2023) ------------------------------------------------------------------------------ A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, Ella Marley-Zagar and Ian White MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK. ------------------------------------------------------------------------------ Type of trial superiority Number of groups 4 Favourable/unfavourable outcome not determined Allocation ratio equal group sizes Statistical test assumed unconditional comparison of 4 binomial proportions using the score test Local or distant distant Continuity correction no Anticipated event probabilities 0.100 0.200 0.300 0.400 Alpha 0.100 (two-sided) Power (designed) 0.900 Total sample size (calculated) 176 Sample size per group (calculated) 44 44 44 44 Expected total number of events 44.00 ------------------------------------------------------------------------------ . . . /*** > > A sample size of 44 is required in each of the four groups. > > \subsection{Complex non-inferiority trial in a real-life setting} \label{sec:complexNIexample} > Finally, we demonstrate a more complex non-inferiority design from the STREAM trial. The need for the STREAM tri > al arose from the increase of multi-drug resistant strains of Tuberculosis, especially in countries without robus > t health care systems unable to administer and follow up treatment over long periods of time. The STREAM trial e > valuated a shorter more intensive treatment for multi-drug resistant Tuberculosis compared to the lengthier treat > ment recommended by the World Health Organization. > The trial used an expected 0.7 probability on control ($\pi_1$) and 0.75 on treatment ($\pi_2$), hence it was ass > umed that 70\% in the long-regimen group and 75\% of the participants in the short-regimen group would attain a f > avourable outcome. A favourable outcome was defined as cultures negative for $Mycobacterium$ $tuberculosis$ at 1 > 32 weeks and at a previous occasion, with no intervening positive culture or previous unfavourable outcome \citep > {Nunn2019}. A 10 percentage-point non-inferiority margin was considered to be an acceptable difference in effica > cy, given the shorter treatment duration ($m =$ -0.1 defined as $\pi_2$-$\pi_1$), with twice as many patients in > treatment compared to control. The \texttt{wald} test was applied as it is often used in non-inferiority trials. > > ***/ . . . artbin, pr(0.7 0.75) margin(-0.1) power(0.8) ar(1 2) wald ltfu(0.2) ART - ANALYSIS OF RESOURCES FOR TRIALS (binary version 2.0.2 23may2023) ------------------------------------------------------------------------------ A sample size program by Abdel Babiker, Patrick Royston, Friederike Barthel, Ella Marley-Zagar and Ian White MRC Clinical Trials Unit at UCL, London WC1V 6LJ, UK. ------------------------------------------------------------------------------ Type of trial non-inferiority Number of groups 2 Favourable/unfavourable outcome favourable Inferred by the program Allocation ratio 1:2 Statistical test assumed unconditional comparison of 2 binomial proportions using the wald test Local or distant distant Continuity correction no Null hypothesis H0: H0: pi2 - pi1 <= -.1 Alternative hypothesis H1: H1: pi2 - pi1 > -.1 Anticipated event probabilities 0.700 0.750 Alpha 0.050 (two-sided) (taken as .025 one-sided) Power (designed) 0.800 Loss to follow up assumed: 20 % Total sample size (calculated) 399 Sample size per group (calculated) 133 266 Expected total number of events 292.60 ------------------------------------------------------------------------------ . local n=r(n) . . /*** > The non-inferiority trial required a total sample size of 399 (133 in control, 266 in intervention), assuming 20\ > % of patients were not accessible in primary analysis. When the STREAM trial concluded, it estimated that a shor > ter more intensive treatment for multi-drug resistant Tuberculosis was only 1\% less effective than the lengthier > treatment recommended by the World Health Organization, and demonstrated significant evidence of non-inferiority > . > > > ***/ . . log close name: log: C:\git\artbin\examples\artbin_examples.log log type: text closed on: 23 May 2023, 17:06:32 -------------------------------------------------------------------------------------------------------------------