{smcl}
{* *! version 1.0.0 03Aug2022}{...}
{title:Title}

{p2colset 5 22 23 2}{...}
{p2col:{hi:power twosens} {hline 2}} Power and sample-size analysis for sensitivity between two diagnostic tests in two independent samples  {p_end}
{p2colreset}{...}


{marker syntax}{...}
{title:Syntax}

{phang}
Compute sample size

{p 8 43 2}
{opt power twosens} {it:sens1} {it:sens2}
[{cmd:,} {opth p:ower(numlist)} {opth a:lpha(numlist)} {opth prev(numlist)} {opth frac:tion(numlist)} {opt onesid:ed} 
{opt gr:aph}[{cmd:(}{it:{help power_optgraph##graphopts:graphopts}}{cmd:)}] ]

{phang}
Compute power 

{p 8 43 2}
{opt power twosens} {it:sens1} {it:sens2}
[{cmd:,} {opth n(numlist)} {opth a:lpha(numlist)} {opth prev(numlist)} {opth frac:tion(numlist)} {opt onesid:ed} 
{opt gr:aph}[{cmd:(}{it:{help power_optgraph##graphopts:graphopts}}{cmd:)}] ]


{phang}
where {it:sens1} is the sensitivity of the first diagnostic test and
{it:sens2} is the sensitivity of the second diagnostic test.
{it:sens1} and {it:sens2} may each be specified either as one 
number or as a list of values in parentheses (see {help numlist}).{p_end}



{synoptset 30 tabbed}{...}
{synopthdr}
{synoptline}
{p2coldent:* {opth a:lpha(numlist)}}significance level; default is {cmd:alpha(0.05)} {p_end}
{p2coldent:* {opth p:ower(numlist)}}power; default is {cmd:power(0.80)} {p_end}
{p2coldent:* {opth n(numlist)}}total sample size; required to compute power {p_end}
{p2coldent:* {opth prev(numlist)}}prevalence rate of disease in the population under study; default is {cmd:prev(0.50)}  {p_end}
{p2coldent:* {opth frac:tion(numlist)}}fraction of the sample assigned to test 1; default is {cmd:fraction(0.50)}  {p_end}
{synopt :{opt onesid:ed}}one-sided test; default is two sided{p_end}
{synopt :{cmdab:gr:aph}[{cmd:(}{it:{help power_optgraph##graphopts:graphopts}}{cmd:)}]}graph results; see {manhelp power_optgraph PSS-2:power, graph}{p_end}
{synopt :{opt init(#)}}initial value of the estimated power; default is {cmd:init(10)} {p_end}
{synoptline}
{p2colreset}{...}
{p 4 6 2}* Specifying a list of values in at least two starred options, or 
two command arguments, or at least one starred option and one argument
results in computations for all possible combinations of the values; see
{help numlist}.{p_end}


{marker description}{...}
{title:Description}

{pstd}
{opt power twosens} computes sample size or power for independent two-sample sensitivity of a diagnostic test,
accounting for the prevalence of the disease in the clinical population. Sensitivity is the ability 
of a test to correctly detect the disease when it is present. 

{pstd}
{opt power twosens} implements the naive prevalence inflation method introduced by Obuchowski and Zhou (2002). 
Li and Fine (2004) found this method (which they refer to as "Method 0") to be a useful approximation to exact 
sample-size calculations based on unconditional power, which are more computationally intensive. 
   


{title:Options}

{phang}
{opth alpha(numlist)} sets the significance level of the test.  The
default is {cmd:alpha(0.05)}.

{phang} 
{opth power(numlist)} specifies the desired power at which sample size is to be computed. 
The default is {cmd:power(0.80)}. If {cmd:power()} is specified in conjunction with {cmd:n()}, 
then the actual power of the test is presented. 

{phang} 
{opth n(numlist)} specifies the total number of subjects in the study to be used for determining power. 

{phang}
{opth prev(numlist)} specifies the conjectured prevalence of the disease in the clinical population. The default is {cmd:prev(0.50)}.

{phang}
{opth fraction(numlist)} specifies the fraction of the sample assigned to test 1. The default is {cmd:fraction(0.50)} (i.e. half the sample).

{phang} 
{cmd:onesided} indicates a one-sided test. The default is two sided. 

{phang}
{cmd:graph}, {cmd:graph()}; see {manhelp power_optgraph PSS-2: power, graph}.

{phang}
{opt init(#)} specifies an initial value for estimating power. 
The default value is {cmd:init(10)} which is a rescaled value of power = 0.001 (10/10,000). 
Increasing the initial value may be helpful if the reported power appears unreasonably low (e.g. 0.001).   


{title:Examples}

    {title:Examples: Computing sample size}

{pstd}
    Compute the sample size required to detect a statistical difference in sensitivity between
	two tests, where the first test is hypothesized to have a sensitivity of 0.70 and the second
	test is hypothesized to have a sensitivity of 0.90 using a two-sided test;
    assume a 5% significance level, 80% power, a conjectured disease prevalence of 0.50,
	and 50% of the sample assigned to test 1 (the defaults) {p_end}
{phang2}{cmd:. power twosens 0.70 0.90} 

{pstd}
    Same as above, using a power of 90% and a prevalence of 0.10 {p_end}
{phang2}{cmd:. power twosens 0.70 0.90, power(0.90) prev(0.10)}

{pstd}
    Computing sample size for a range of prevalence rates {p_end}
{phang2}{cmd:. power twosens 0.70 0.90, power(0.90) prev(0.10(.10).90)}

{pstd}
    Applying a range of sensitivity values for test 1
	and setting alpha levels to 0.05 and 0.01 with a prevalence of 0.10, and 33% of the sample assigned
	to test 1. Here we graph the results {p_end}
{phang2}{cmd:. power twosens (0.60(0.05).80) 0.90, power(0.90) alpha(0.01 0.05) prev(0.10) frac(0.33) graph}


    {title:Examples: Computing power}

{pstd}
    For a total sample of 50 subjects, compute the power of a two-sided test to 
    detect a sensitivity of 0.90 given a null sensitivity of 0.70; assume a 5%
    significance level and a prevalence of 0.50 (the default){p_end}
{phang2}{cmd:. power onesens 0.70 0.90, n(50)}

{pstd}
    Same as above, but change the prevalence to 0.20 and use a one-sided test {p_end}
{phang2}{cmd:. power twosens 0.70 0.90, n(50) prev(0.20) onesided }

{pstd}
    Same as above, but apply a range prevalence rates {p_end}
{phang2}{cmd:. power onesens 0.70 0.90, n(50) prev(0.20 0.50 0.70) onesided }

{pstd}
	Compute powers for a range of null sensitivities and total sample sizes, 
	graphing the results{p_end}
{phang2}{cmd:. power twosens (0.60(.10)0.80) 0.90, n(5(5)80) onesided graph}


{title:Stored results}

{pstd}
{cmd:power twosens} stores the following in {cmd:r()}:

{synoptset 20 tabbed}{...}
{p2col 5 20 24 2: Scalars}{p_end}
{synopt:{cmd: r(alpha)}}significance level{p_end}
{synopt:{cmd: r(power)}}power{p_end}
{synopt:{cmd: r(beta)}}probability of a type II error{p_end}
{synopt:{cmd: r(sens1)}}sensitivity of test 1{p_end}
{synopt:{cmd: r(sens2)}}sensitivity of test 2{p_end}
{synopt:{cmd: r(delta)}}effect size{p_end}
{synopt:{cmd: r(prev)}}prevalence of disease{p_end}
{synopt:{cmd: r(fraction)}}fraction of sample assigned to test 1{p_end}
{synopt:{cmd: r(divider)}}1 if divider is requested in the table, 0 otherwise{p_end}
{synopt:{cmd: r(init)}}initial value of the estimated power {p_end}
{synopt:{cmd: r(N)}}total sample size{p_end}
{synopt:{cmd: r(N0)}}sample size of the non-diseased group{p_end}
{synopt:{cmd: r(N1)}}sample size of the diseased group{p_end}
{synopt:{cmd: r(onesided)}}1 for a one-sided test, 0 otherwise{p_end}

{synoptset 20 tabbed}{...}
{p2col 5 20 24 2: Macros}{p_end}
{synopt:{cmd:r(type)}}{cmd:test}{p_end}
{synopt:{cmd:r(method)}}{cmd:twosens}{p_end}
{synopt:{cmd:r(columns)}}displayed table columns{p_end}
{synopt:{cmd:r(labels)}}table column labels{p_end}
{synopt:{cmd:r(widths)}}table column widths{p_end}
{synopt:{cmd:r(formats)}}table column formats{p_end}

{synoptset 20 tabbed}{...}
{p2col 5 15 19 2: Matrices}{p_end}
{synopt:{cmd:r(pss_table)}}table of results{p_end}
{p2colreset}{...}


{title:References}

{p 4 8 2} Li, J. and J. Fine. 2004. On sample size for sensitivity and specificity in prospective diagnostic accuracy studies. {it: Statistics in Medicine} 23:2537-2550.{p_end}

{p 4 8 2} Obuchowski, N.A. and X. H. Zhou. 2002. Prospective studies of diagnostic test accuracy when disease prevalence is low. {it:Biostatistics} 3:477-492.{p_end}


{marker citation}{title:Citation of {cmd:power twosens}}

{p 4 8 2}{cmd:power twosens} is not an official Stata command. It is a free contribution
to the research community, like a paper. Please cite it as such: {p_end}

{p 4 8 2}
Linden, A. 2022. POWER TWOSENS: Stata module to compute power and sample size for sensitivity between two diagnostic tests in two independent samples



{title:Authors}

{p 4 4 2}
Ariel Linden{break}
President, Linden Consulting Group, LLC{break}
alinden@lindenconsulting.org{break}



{title:Also see}

{p 4 8 2} Online: {helpb estat classification}, {helpb lsens}, {helpb power}, {helpb power onesens} (if installed), 
{helpb power onespec} (if installed), {helpb power twospec} (if installed), {helpb power pairsens} (if installed), 
{helpb power pairspec} (if installed){p_end}