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

{p2colset 5 22 23 2}{...}
{p2col:{hi:power onesens} {hline 2}} Power and sample-size analysis for sensitivity of a one-sample diagnostic test  {p_end}
{p2colreset}{...}


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

{phang}
Compute sample size

{p 8 43 2}
{opt power onesens} {it:sens0} {it:sens1}
[{cmd:,} {opth p:ower(numlist)} {opth a:lpha(numlist)} {opth prev(numlist)} {opt onesid:ed} {opt gr:aph}[{cmd:(}{it:{help power_optgraph##graphopts:graphopts}}{cmd:)}] ]

{phang}
Compute power 

{p 8 43 2}
{opt power onesens} {it:sens0} {it:sens1}
[{cmd:,} {opth n(numlist)} {opth a:lpha(numlist)} {opth prev(numlist)} {opt onesid:ed} {opt gr:aph}[{cmd:(}{it:{help power_optgraph##graphopts:graphopts}}{cmd:)}] ]


{phang}
where {it:sens0} is the null (hypothesized) sensitivity, and
{it:sens1} is the alternative (target) sensitivity.
{it:sens0} and {it:sens1} 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}
{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}
{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 onesens} computes sample size or power for one-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 onesens} 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} 
{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}.



{title:Examples}

    {title:Examples: Computing sample size}

{pstd}
    Compute the sample size required to detect a sensitivity of 0.90 given a
    sensitivity of 0.70 under the null hypothesis using a two-sided test;
    assume a 5% significance level, 80% power and a conjectured disease prevalence of 0.50 (the defaults) {p_end}
{phang2}{cmd:. power onesens 0.70 0.90} 

{pstd}
    Same as above, using a power of 90%, a one-sided test, and a prevalence of 0.10 {p_end}
{phang2}{cmd:. power onesens 0.70 0.90, power(0.90) prev(0.10) onesided}

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

{pstd}
    Applying a range of sensitivity values under the alternative hypothesis
	and setting alpha levels to 0.05 and 0.01 with a prevalence of 0.10. Here we graph the results {p_end}
{phang2}{cmd:. power onesens (0.60(0.05).80) 0.90, power(0.90) onesided alpha(0.01 0.05) prev(0.10) 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 onesens 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 onesens (0.60(.10)0.80) 0.90, n(5(5)80) onesided graph}


{title:Stored results}

{pstd}
{cmd:power onesens} 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(sens0)}}null sensitivity{p_end}
{synopt:{cmd: r(sens1)}}alternative sensitivity{p_end}
{synopt:{cmd: r(delta)}}effect size{p_end}
{synopt:{cmd: r(prev)}}prevalence of disease{p_end}
{synopt:{cmd: r(divider)}}1 if divider is requested in the table, 0 otherwise{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:onesens}{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 onesens}}

{p 4 8 2}{cmd:power onesens} 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 ONESENS: Stata module to compute power and sample size for sensitivity of a one-sample diagnostic test



{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 onespec} (if installed), 
{helpb power twosens} (if installed), {helpb power twospec} (if installed), {helpb power pairsens} (if installed), 
{helpb power pairspec} (if installed){p_end}