help tostrrp
--------------------------------------------------------------------------------------------------------------------------------------
Title
tostrrp -- Test for equivalence of relative risk and unity in paired binary data
Syntax
tostrrp treatment_1_outcome_variable treatment_2_outcome_variable [if] [in] , delta0(#) [, deltaupper(#) alpha(#) relevance
treatment1(treatment 1 name) treatment2(treatment 2 name) outcome(positive outcome label) nooutcome(negative outcome
label)]
tostrrpi #a #b #c #n #delta0 [, deltaupper(#) alpha(#) relevance treatment1(treatment 1 name) treatment2(treatment 2 name)
outcome(positive outcome label) nooutcome(negative outcome label)]
tostrrp options Description
--------------------------------------------------------------------------------------------------------------------------------
Main
delta0(#) the value defining an equivalence interval (the lower value, if deltaupper is used)
--------------------------------------------------------------------------------------------------------------------------------
tostrrp and tostrrpi options Description
--------------------------------------------------------------------------------------------------------------------------------
Main
deltaupper(#) the upper value of a geometrically asymmetric equivalence interval
alpha(#) set nominal type I level; default is alpha(0.05)
relevance perform & report combined tests for difference and equivalence
treatment1(string) The name of the first treatment group
treatment2(string) The name of the second treatment group
outcome(string) The label for having a positive outcome
nooutcome(string) The label for having a negative outcome
--------------------------------------------------------------------------------------------------------------------------------
Description
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 z test statistic based on a reparameterized
multinomial model (Tang, et al., 2003) in a two one-sided tests approach (Schuirmann, 1987). tostrrpi is the immediate form of
tostrrp; see immed. The equivalence interval for the test is defined by a chosen level of tolerance, as specified by delta0, or
by #delta0 in the immediate form of the command.
The two one-sided null hypotheses take on the following form based on the relative risk (RR), and the threshold delta0:
Ho1: RR <= delta0, or
Ho2: RR >= 1/delta0,
where the equivalence interval ranges from delta0 to 1/delta0.
When a geometrically asymmetric equivalence interval is defined using the deltaupper option the two one-sided null hypotheses
become:
Ho1: RR <= delta0, or
Ho2: RR >= deltaupper,
where the equivalence interval ranges from delta0 to deltaupper.
The two z test statistics, z1 and z2, are both constructed with rejection probabilities in the upper tails. So p1 = P(Z >= z1),
and p2 = P(Z >= z2).
NOTES: When delta0 = 1, the Tang, Tang and Chan test statistic reduces to McNemar's test statistic (McNemar, 1947). When a = b
= c = 0, there are no positve outcomes in either treatment group, and the RR and test statistics become undefined. If a > 0,
and b = c = 0, then there is complete concordance, and z1 = z2, so p1 = p2. 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 p-value to 0.05 (Wellek, 2010).
Options for tostrrp and tostrrpi
+------+
----+ Main +--------------------------------------------------------------------------------------------------------------------
delta0(#) defines the equivalence threshold for the tests, with the lower boundary of equivalence equal to delta0, and the upper
boundary equal to 1/delta0. For example, 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 delta0.
deltaupper(#) defines the upper equivalence threshold for the test, and restricts the meaning of delta0 to the lower equivalence
threshold for the test. Also, delta0 must be a positive value less than or equal to 1, and deltaupper must be a positive
value that is greater than or equal to 1. Taken together, these correspond to geometrically asymmetric equivalence
intervals.
alpha(#) specifies the nominal type I error rate. The default is alpha(0.05).
relevance reports results and inference for combined tests for difference and equivalence of marginal probabilities (of
exposure) for a specific alpha, and delta0. See the end of the Discussion section in tost for more details on inference
from combined tests.
treatment1(string) labels the name of the first treatment group in the output table. For tostppr this defaults to the variable
label for treatment_1_outcome_variable.
treatment2(string) labels the name of the second treatment group in the output table. For tostppr this defaults to the variable
label for treatment_2_outcome_variable.
outcome(string) labels the value corresponding to positive for the outcome. For tostppr this defaults to the label for the
value = 1 in treatment_1_outcome_variable (or in treatment_2_outcome_variable if treatment_1_outcome_variable is unlabeled).
nooutcome(string) labels the value corresponding to negative for the outcome. For tostppr this defaults to the label for the
value = 0 in treatment_1_outcome_variable (or in treatment_2_outcome_variable if treatment_1_outcome_variable is unlabeled).
Examples
Setup
. use hivfluid (requires that you install hivfluid.dta)
Relevance test example from Tang, et al., 2003, Table II, based on data from Lachenbruch and Lynch, 1998
. tostrrp plasma alternate, delta0(0.95) rel
Same as above command, but using immediate form
. tostrrpi 446 5 16 1157 0.95, rel treatment1("Plasma sample") treatment2("Alternative fluid") outcome("HIV Positive")
nooutcome("HIV Negative")
Example from Tang, et al., 2003, Table V, based on data from Tango, 1998
. tostrrpi 43 0 1 44 0.9, treatment1("Thermal") treatment2("Chemical") outcome("Effective") nooutcome("Ineffective")
Saved results
tostrrp and tostrrpi save the following in r():
Scalars
r(RR) relative risk (aka incidence rate ratio) of positive outcome for treatment 2 vs. treatment 1
r(sdRR) standard deviation of relative risk based on the score statistic per (Tang, et al., 2003)
r(z1) z test statistic for Ho1 (upper)
r(z2) z test statistic for Ho2 (lower)
r(p1) P(Z >= z1)
r(p2) P(Z >= z2)
r(delta0) delta0, tolerance level defining the equivalence interval; OR
r(deltalower) delta_lower, tolerance level defining the equivalence interval's lower side; AND
r(deltaupper) delta_upper, tolerance level defining the equivalence interval's upper side
r(relevance) Relevance test conclusion for given alpha and delta0
Author
Alexis Dinno
Portland State University
alexis.dinno@pdx.edu
Development of tost is ongoing, please contact me with any questions, bug reports or suggestions for improvement. Fixing bugs
will be facilitated by sending along:
(1) a copy of the data (de-labeled or anonymized is fine),
(2) a copy of the command used, and
(3) a copy of the exact output of the command.
Suggested citation
Dinno A. 2017. tostrrp: Test for equivalence of relative risk and unity in paired designs. Stata software package. URL:
https://www.alexisdinno.com/stata/tost.html
Reference
Lachenbruch, P. A. and Lynch, C. J. 1998. Assessing screening tests: Extensions of McNemarâ€™s test. Statistics In Medicine 17:
2207-2217
McNemar, Q. 1947. Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika
12: 153-157
Schuirmann, D. A. 1987. A comparison of the two one-sided tests procedure and the power approach for assessing the
equivalence of average bioavailability Journal of Pharmacokinetics and Biopharmaceutics. 15: 657-680
Tang, N.-S., Tang, M.-L., and Chan, I. S. F. 2003. On tests of equivalence via non-unity relative risk for matched-pair
design. Statistics In Medicine 22: 1217-1233.
Tango, T. 1998. Equivalence test and confidence interval for the difference in proportions for the paired-sample design.
Statistics In Medicine, 17: 891-908
Wellek, S. 2010. Testing Statistical Hypotheses of Equivalence and Noninferiority, second edition. Chapman and Hall/CRC
Press. p. 31
Also See
Help: tost, mcc, tostmcc