{smcl} {* *! version 0.9 31 Jan 2019}{...} {vieweralsosee "" "--"}{...} {vieweralsosee "Install sim_ma" "ssc install des_ma"}{...} {vieweralsosee "Help des_ma (if installed)" "help des_ma"}{...} {viewerjumpto "Syntax" "des_ma##syntax"}{...} {viewerjumpto "Description" "des_ma##description"}{...} {viewerjumpto "Options" "des_ma##options"}{...} {viewerjumpto "Examples" "des_ma##examples"}{...} {title:Title} {phang} {bf:des_ma} {hline 2} Single-stage multi-arm trial simulation for normally distributed outcomes {marker syntax}{...} {title:Syntax} {p 8 17 2} {cmdab:des_ma}{cmd:,} [{it:options}] {synoptset 20 tabbed}{...} {synopthdr} {synoptline} {syntab:Optional} {synopt:{opt n(#)}} Stage-wise group size in the control arm. Default value is 34.{p_end} {synopt:{opt tau(numlist)}} Treatment effects. Default value is (0, 0, 0).{p_end} {synopt:{opt sd(#)}} Standard deviation of the responses. Default value is 1.{p_end} {synopt:{opt rat:io(#)}} Allocation ratio between the experimental arms and the shared control arm. Default value is 1.{p_end} {synopt:{opt alp:ha(#)}} Chosen significance level. Default value is 0.05.{p_end} {synopt:{opt cor:rection(string)}} Multiple comparison correction. Default value is dunnett.{p_end} {synopt:{opt replicates(#)}} Number of replicate simulations. Default value is 10000.{p_end} {marker description}{...} {title:Description} {pstd} {cmd:sim_ma} simulated multi-arm trials with {it:K} experimental (see option {opt k}) and a single control treatment. The outcome variable of interest is assumed to be normally distributed.{p_end} {pstd} It is assumed that {it:K} null hypotheses are to be tested, given by {it:H_}{it:k}: {it:τ}_{it:k} = {it:μ}_{it:k} - {it:μ}_0 ≤ 0, {it:k} = 1,..., {it:K}, where {it:μ}_{it:k} is the mean response on arm {it:k}. Thus, arm 0 is assumed to be the control arm. A set of (computed) p-values are used in combination with a chosen multiple comparison procedure in order to determine which of the null hypotheses to reject.{p_end} {pstd} Note that it is assumed {it:n} patients will be recruited to the control arm, and {it:rn} patients to each experimental arm (see option {opt rat:io}). It is also assumed that the standard deviation of the accrued responses is known (see option {opt sd}). {p_end} {pstd} The operating characteristics are evaluated at a specified vector of treatment effects ({it:τ}_1, ..., {it:τ}_{it:K}) (see option {opt tau}), using a particular number of replicate simulations (see option {opt rep:licates}). {p_end} {pstd} Several multiple comparison procedures are supported (see {opt cor:rection}), which in general work to control a particular error-rate to a specified significance level (see option {opt a:lpha}): {p_end} {pstd} • benjamini: Control the false-discovery rate using the Benjamini-Hochberg procedure (Benjamini and Hochberg, 1995). {p_end}{pstd} • bonferroni: Control the familywise error-rate using Bonferroni's correction (Bonferroni, 1936; Dunn, 1958; Dunn, 1961). {p_end}{pstd} • dunnett: Control the familywise error-rate using Dunnett's correction (Dunnett, 1955; Dunnett, 1964). {p_end}{pstd} • holm: Control the familywise error-rate using the Holm-Bonferroni method (Holm, 1979). {p_end}{pstd} • none: Do not apply a multiple comparison procedure (i.e., test each hypothesis at level {opt alp:ha}). {p_end}{pstd} • sidak: Control the familywise error-rate using Šidák's correction (Šidák, 1967). {p_end}{pstd} • step_down_dunnett: Control the familywise error-rate using the step-down Dunnett correction (Naik, 1975; Marcus {it:et al}, 1976). {p_end} {marker options}{...} {title:Options} {break} {phang} {opt n(#)} An integer giving the group size in the control arm. Should be greater than or equal to 1. The default value is 68. {p_end}{break}{phang} {opt tau(#)} A numlist (vector) giving the treatment effects. It can be of length 1. Thus, {cmd:sim_ma} will simulate single-stage two-arm trials. However, if such simulations are required, the user is recommended to use {help sim_fixed} (available from the author) instead, which is optimised for such scenarios. The (internally specified) default value is (0, 0, 0). {p_end}{break}{phang} {opt sd(#)} A real giving the assumed value of the standard deviation of the responses in the control and experimental arms. It should be strictly greater than 0. The default value is 1. {p_end}{break}{phang} {opt rat:io(#)} A real giving the allocation ratio between the experimental arms and the shared control arm. That is, {opt rat:io} patients are allocated to each experimental arm for every one patient allocated to the control arm. It should be strictly positive. The default value is 1. {p_end}{break}{phang} {opt alp:ha(#)} A real giving the chosen significance level to use in the chosen multiple comparison procedure (see option {opt cor:rection}). It should be strictly between 0 and 1. The default value is 0.05. {p_end}{break}{phang} {opt cor:rection(string)} A string giving the multiple comparison procedure to use. It should be one of benjamini, bonferroni, dunnett, holm, none, sidak, or step_down_dunnett. The default value is dunnett. Note used if option {opt k} is equal to 1. {p_end}{break}{phang} {opt rep:licates(#)} An integer giving the number of replicate simulations to use to evaluate required error-rates and sample sizes. It should be an integer greater than or equal to 1. The default value is 10000. {p_end} {marker examples}{...} {title:Examples} {phang} {it:Note:} Depending on the available processing power, each of the following examples could take several minutes to run. {p_end} /// Example 1: Find a 3-experimental treatment multi-arm design, and simulate /// its operating characteristics under the global null hypothesis. {phang}{stata des_ma}{p_end} {phang}{stata sim_ma}{p_end} /// Example 2: Find a design with modified multiplicity correction, and /// simulate its operating characteristics under the least /// favourable configuration. {phang}{stata des_ma, correction(holm)}{p_end} {phang}{stata sim_ma, n(71) tau(0.5, 0, 0) correction(holm)}{p_end} /// Example 3: Find a 2-experimental treatment multi-arm design using /// Bonferroni's correction, with unequal allocation to the /// experimental and control arms, and simulate its operating /// characteristics under the global null hypothesis. {phang}{stata des_ma, k(2) ratio(0.5) correction(bonferroni)}{p_end} {phang}{stata sim_ma, n(96) tau(0, 0) ratio(0.5) correction(bonferroni)}{p_end} {marker results}{...} {title:Stored results} {pstd} {cmd:des_ma} stores the following in {cmd:r()}: {synoptset 15 tabbed}{...} {p2col 5 15 19 2: scalars:}{p_end} {synopt:{cmd:r(P_HA)}} Estimated probability that at least one null hypothesis is rejected.{p_end} {synopt:{cmd:r(P_H1)}} Estimated probability that {it:H}_1 is rejected.{p_end} {synopt:{cmd:r(FDR_HG)}} Estimated false discovery rate.{p_end} {title:Author} {p} Dr Michael J Grayling Institute of Health & Society, Newcastle University, UK Email: {browse "michael.grayling@newcastle.ac.uk":michael.grayling@newcastle.ac.uk} {title:See also} {bf:References:} {phang} Benjamini Y, Hochberg Y (1995) {browse "https://www.jstor.org/stable/2346101":Controlling the false discovery rate: a practical and powerful approach to multiple testing}. {it:J Roy Stat Soc B} {bf:57}(1){bf::}289–300. {phang} Bonferroni CE (1936) Teoria statistica delle classi e calcolo delle probabilità. {it:Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commerciali di Firenze} {bf:8:}3-62. {phang} Dunn OJ (1958) {browse "https://www.jstor.org/stable/2236948":Estimation of the means for dependent variables}. {it:Ann Math Stat} {bf:29}(4){bf::}1095–111. {phang} Dunn OJ (1961) {browse "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.309.1277":Multiple comparisons among means}. {it:J Am Stat Assoc} {bf:56}(293){bf::}52–64. {phang} Dunnett CW (1955) {browse "https://www.jstor.org/stable/pdf/2281208.pdf":A multiple comparison procedure for comparing several treatments with a control}. {it:J Am Stat Assoc} {bf:50}(272){bf::}1096–121. {phang} Dunnett CW (1964) {browse "https://www.jstor.org/stable/2528490#metadata_info_tab_contents":New tables for multiple comparisons with a control}. {it:Biometrics} {bf:20}(3){bf::}482–91. {phang} Holm S (1979) {browse "https://www.ime.usp.br/~abe/lista/pdf4R8xPVzCnX.pdf":A simple sequentially rejective multiple test procedure}. {it:Scand J Stat} {bf:6}(2){bf::}65–70. {phang} Marcus R, Peritz E, Gabriel KR (1976) {browse "https://www.jstor.org/stable/2335748#metadata_info_tab_contents":On closed testing procedures with special reference to ordered analysis of variance}. {it:Biometrika} {bf:63}(3){bf::}655–60. {phang} Naik UD (1975) {browse "https://www.tandfonline.com/doi/abs/10.1080/03610927508827267":Some selection rules for comparing p processes with a standard}. {it:Commun Stat A} {bf:4}(6){bf::}519–35. {phang} Šidák ZK (1967) {browse "https://www.jstor.org/stable/2283989#metadata_info_tab_contents":Rectangular confidence regions for the means of multivariate normal distributions}. {it:J Am Stat Assoc} {bf:62}(318){bf::}626–33. {bf:Related commands:} {help des_dtl} (a command for designing multi-stage drop-the-losers trials) {help des_ma} (a command for designing single-stage multi-arm trials) {help des_mams} (a command for designing multi-arm multi-stage trials) {help sim_dtl} (a command for simulating multi-stage drop-the-losers trials) {help sim_fixed} (a command for simulating single-stage two-arm trials) {help sim_mams} (a command for simulating multi-arm multi-stage trials)