{smcl} {* *! version 3.1.4 09oct2023}{...} {cmd:help tostrrp} {hline} {title:Title} {p2colset 5 16 18 2}{...} {p2col:{cmd:tostrrp} {hline 2}}Test for equivalence of relative risk and unity in paired binary data {p_end} {p2colreset}{...} {marker syntax}{...} {title:Syntax} {p 8 14 2}{cmd:tostrrp} {it:treatment_1_outcome_variable} {it:treatment_2_outcome_variable} {ifin} , {opt delta0(#)} [{cmd:,} {opt deltau:pper(#)} {opt a:lpha(#)} {opt rel:evance} {opt treatment1(treatment 1 name)} {opt treatment2(treatment 2 name)} {opt out:come(positive outcome label)} {opt noo:utcome(negative outcome label)}] {p 8 14 2}{cmd:tostrrpi} {it:#a #b #c #n #delta0} [{cmd:,} {opt deltau:pper(#)} {opt a:lpha(#)} {opt rel:evance} {opt treatment1(treatment 1 name)} {opt treatment2(treatment 2 name)} {opt out:come(positive outcome label)} {opt noo:utcome(negative outcome label)}] {synoptset 21 tabbed}{...} {synopthdr:tostrrp options} {synoptline} {syntab:Main} {synopt :{opt delta0(#)}}the value defining an equivalence interval (the lower value, if {opt deltau:pper} is used){p_end} {synoptline} {p2colreset}{...} {synoptset 21 tabbed}{...} {synopthdr:tostrrp and tostrrpi options} {synoptline} {syntab:Main} {synopt :{opt deltau:pper(#)}}the upper value of a geometrically asymmetric equivalence interval{p_end} {synopt :{opt a:lpha(#)}}set nominal type I level; default is {opt a:lpha(0.05)}{p_end} {synopt :{opt rel:evance}}perform & report combined tests for difference and equivalence{p_end} {synopt :{opt treatment1(string)}}The name of the first treatment group{p_end} {synopt :{opt treatment2(string)}}The name of the second treatment group{p_end} {synopt :{opt out:come(string)}}The label for having a positive outcome{p_end} {synopt :{opt noo:utcome(string)}}The label for having a negative outcome{p_end} {synoptline} {p2colreset}{...} {marker description}{...} {title:Description} {pstd} {cmd:tostrrp} test for equivalence of the relative risk of a positive outcome and unity in paired (or matched) randomized control trial or paired (or matched) cohort design data. It calculates an asymptotic {it:z} test statistic based on a reparameterized multinomial model ({help tostrrp##Tang2003:Tang, et al., 2003}) in a two one-sided tests approach ({help tostrrp##Schuirmann1987:Schuirmann, 1987}). {cmd:tostrrpi} is the immediate form of {cmd:tostrrp}; see {help immed}. The equivalence interval for the test is defined by a chosen level of tolerance, as specified by {cmd: delta0}, or by {it:#delta0} in the immediate form of the command.{p_end} {pstd} The two one-sided null hypotheses take on the following form based on the relative risk (RR), and the threshold {opt delta0}: {p 12} Ho1: RR <= {opt delta0}, or{p_end} {p 12} Ho2: RR >= 1/{opt delta0},{p_end} {p 8 8}where the equivalence interval ranges from {opt delta0} to 1/{opt delta0}.{p_end} {pstd} When a geometrically asymmetric equivalence interval is defined using the {opt deltau:pper} option the two one-sided null hypotheses become:{p_end} {p 12} Ho1: RR <= {opt delta0}, or{p_end} {p 12} Ho2: RR >= {opt deltaupper},{p_end} {p 8} where the equivalence interval ranges from {opt delta0} to {opt deltaupper}.{p_end} {pstd} The two {it:z} test statistics, {it:z}1 and {it:z}2, are both constructed with rejection probabilities in the upper tails. So {it:p}1 = P(Z >= {it:z}1), and {it:p}2 = P(Z >= {it:z}2). {pstd} NOTES: When delta0 = 1, the Tang, Tang and Chan test statistic reduces to McNemar's test statistic ({help tostrrp##McNemar1947:McNemar, 1947}). When {it:a} = {it:b} = {it:c} = 0, there are no positve outcomes in either treatment group, and the RR and test statistics become undefined. If {it:a} > 0, and {it:b} = {it:c} = 0, then there is complete concordance, and {it:z}1 = {it:z}2, so {it:p}1 = {it:p}2. As is standard with two one-sided tests for equivalence, if one wishes to make a type I error %5 of the time, one simply conducts both of the one-sided tests of Ho1 and Ho2 by comparing the resulting {it:p}-value to 0.05 ({help tostrrp##Wellek2010:Wellek, 2010}).{p_end} {marker options}{...} {title:Options for tostrrp and tostrrpi} {dlgtab:Main} {phang} {opth delta0(#)} defines the equivalence threshold for the tests, with the lower boundary of equivalence equal to {opt delta0}, and the upper boundary equal to 1/{opt delta0}. For example, {opt delta0} = 0.8 gives an equivalence interval of 0.8, 1.25 (because 1.25 = 1/0.8). Researchers are responsible for choosing meaningful values of {opt delta0}.{p_end} {phang} {opt deltau:pper(#)} defines the {it: upper} equivalence threshold for the test, and restricts the meaning of {opt delta0} to the {it: lower} equivalence threshold for the test. Also, {opt delta0} must be a positive value less than or equal to 1, and {opt deltau:pper} must be a positive value that is greater than or equal to 1. Taken together, these correspond to geometrically asymmetric equivalence intervals.{p_end} {phang} {opt a:lpha(#)} specifies the nominal type I error rate. The default is {opt a:lpha(0.05)}.{p_end} {phang} {opt rel:evance} reports results and inference for combined tests for difference and equivalence of marginal probabilities (of exposure) for a specific {opt a:lpha}, and {opt delta0}. See the end of the Discussion section in {help tost} for more details on inference from combined tests. {phang} {opt treatment1(string)} labels the name of the first treatment group in the output table. For {cmd:tostppr} this defaults to the variable label for {it:treatment_1_outcome_variable}. {phang} {opt treatment2(string)} labels the name of the second treatment group in the output table. For {cmd:tostppr} this defaults to the variable label for {it:treatment_2_outcome_variable}. {phang} {opt out:come(string)} labels the value corresponding to positive for the outcome. For {cmd:tostppr} this defaults to the label for the value = 1 in {it:treatment_1_outcome_variable} (or in {it:treatment_2_outcome_variable} if {it:treatment_1_outcome_variable} is unlabeled). {phang} {opt noout:come(string)} labels the value corresponding to negative for the outcome. For {cmd:tostppr} this defaults to the label for the value = 0 in {it:treatment_1_outcome_variable} (or in {it:treatment_2_outcome_variable} if {it:treatment_1_outcome_variable} is unlabeled). {marker examples}{...} {title:Examples} {pstd} Setup{p_end} {phang2}{cmd:. use hivfluid} (requires that you {net "get tost, from(https://alexisdinno.com/stata/)":install hivfluid.dta}) {pstd} Relevance test example from Tang, et al., 2003, Table II, based on data from {help tostrrp##Lachenbruch1998:Lachenbruch and Lynch, 1998}{p_end} {phang2}{cmd:. tostrrp plasma alternate, delta0(0.95) rel} {pstd} Same as above command, but using immediate form{p_end} {phang2}{cmd:. tostrrpi 446 5 16 1157 0.95, rel treatment1("Plasma sample") treatment2("Alternative fluid") outcome("HIV Positive") nooutcome("HIV Negative")} {pstd} Example from Tang, et al., 2003, Table V, based on data from {help tostrrp##Tango1998:Tango, 1998}{p_end} {phang2}{cmd:. tostrrpi 43 0 1 44 0.9, treatment1("Thermal") treatment2("Chemical") outcome("Effective") nooutcome("Ineffective")} {marker saved_results}{...} {title:Saved results} {pstd} {cmd:tostrrp} and {cmd:tostrrpi} save the following in {cmd:r()}: {synoptset 15 tabbed}{...} {p2col 5 15 19 2: Scalars}{p_end} {synopt:{cmd:r(RR)}}relative risk (aka incidence rate ratio) of positive outcome for treatment 2 vs. treatment 1{p_end} {synopt:{cmd:r(sdRR)}}standard deviation of relative risk based on the score statistic per ({help tostrrp##Tang2003:Tang, et al., 2003}){p_end} {synopt:{cmd:r(z1)}}{it:z} test statistic for Ho1 (upper){p_end} {synopt:{cmd:r(z2)}}{it:z} test statistic for Ho2 (lower){p_end} {synopt:{cmd:r(p1)}}P({it:Z} >= {it:z}1){p_end} {synopt:{cmd:r(p2)}}P({it:Z} >= {it:z}2){p_end} {synopt:{cmd:r(delta0)}}delta0, tolerance level defining the equivalence interval; OR{p_end} {synopt:{cmd:r(deltalower)}}delta_lower, tolerance level defining the equivalence interval's lower side; AND{p_end} {synopt:{cmd:r(deltaupper)}}delta_upper, tolerance level defining the equivalence interval's upper side{p_end} {synopt:{cmd:r(relevance)}}Relevance test conclusion for given alpha and delta0{p_end} {p2colreset}{...} {title:Author} {pstd}Alexis Dinno{p_end} {pstd}Portland State University{p_end} {pstd}alexis.dinno@pdx.edu{p_end} {pstd} Development of {net "describe tost, from(https://alexisdinno.com/stata/)":tost} is ongoing, please contact me with any questions, bug reports or suggestions for improvement. Fixing bugs will be facilitated by sending along:{p_end} {p 8 8 4}(1) a copy of the data (de-labeled or anonymized is fine),{p_end} {p 8 8 4}(2) a copy of the command used, and{p_end} {p 8 8 4}(3) a copy of the exact output of the command.{p_end} {title:Suggested citation} {p 4 8} Dinno A. 2017. {bf:tostrrp}: Test for equivalence of relative risk and unity in paired designs. Stata software package. URL: {view "https://www.alexisdinno.com/stata/tost.html"} {marker reference}{...} {title:Reference} {marker Lachenbruch1998}{...} {phang} Lachenbruch, P. A. and Lynch, C. J. 1998. {browse "https://sci-hub.io":Assessing screening tests: Extensions of McNemar’s test}. {it:Statistics In Medicine} 17: 2207-2217 {marker McNemar1947}{...} {phang} McNemar, Q. 1947. {browse "https://sci-hub.io":Note on the sampling error of the difference between correlated proportions or percentages}. {it:Psychometrika} 12: 153-157 {marker Schuirmann1987}{...} {phang} Schuirmann, D. A. 1987. {browse "https://pdfs.semanticscholar.org/053b/97e316fc43588e6235f88a1a7a4077342de7.pdf":A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability}. {it:Journal of Pharmacokinetics and Biopharmaceutics}. 15: 657-680 {marker Tang2003}{...} {phang} Tang, N.-S., Tang, M.-L., and Chan, I. S. F. 2003. {browse "https://sci-hub.io":On tests of equivalence via non-unity relative risk for matched-pair design}. {it:Statistics In Medicine} 22: 1217-1233. {marker Tango1998}{...} {phang} Tango, T. 1998. {browse "https://sci-hub.io":Equivalence test and confidence interval for the difference in proportions for the paired-sample design}. {it:Statistics In Medicine}, 17: 891-908{p_end} {marker Wellek2010}{...} {phang} Wellek, S. 2010. {browse "https://www.crcpress.com/product/isbn/9781439808184":{it:Testing Statistical Hypotheses of Equivalence and Noninferiority}}, second edition. Chapman and Hall/CRC Press. p. 31{p_end} {title:Also See} {psee} {space 2}Help: {help tost:tost}, {help mcc:mcc}, {help tostmcc:tostmcc}