byars_lower

Calculates the lower confidence limits for observed numbers of events using Byar's method (1).

Functions to calculate commonly used public health statistics and
their confidence intervals using methods approved for use in the production
of Public Health England indicators such as those presented via Fingertips
(<http://fingertips.phe.org.uk/>). It provides functions for the generation
of proportions, crude rates, means, directly standardised rates, indirectly
standardised rates, standardised mortality ratios, slope and relative index
of inequality and life expectancy.
Statistical methods are referenced in the following publications.
Breslow NE, Day NE (1987) <doi:10.1002/sim.4780080614>.
Dobson et al (1991) <doi:10.1002/sim.4780100317>.
Armitage P, Berry G (2002) <doi:10.1002/9780470773666>.
Wilson EB. (1927) <doi:10.1080/01621459.1927.10502953>.
Altman DG et al (2000, ISBN: 978-0-727-91375-3).
Chiang CL. (1968, ISBN: 978-0-882-75200-6).
Newell C. (1994, ISBN: 978-0-898-62451-9).
Eayres DP, Williams ES (2004) <doi:10.1136/jech.2003.009654>.
Silcocks PBS et al (2001) <doi:10.1136/jech.55.1.38>.
Low and Low (2004) <doi:10.1093/pubmed/fdh175>.

Anderson Georgina

PHEindicatormethods

Common Public Health Statistics and their Confidence Intervals

Fox Sebastian

Francis Matthew

Fryers Paul

Clegg Emma

byars_lower function

<dl><dt>x</dt>
<dd>the observed numbers of events; numeric vector; no default</dd>
<dt>confidence</dt>
<dd>the required level of confidence expressed as a number
between 0.9 and 1 or a number between 90 and 100 or can be a vector of 0.95
and 0.998, for example, to output both 95 percent and 99.8 percent percent CIs; numeric;
default 0.95</dd></dl>

Arguments

This is an internal package function that is appropriately called by exported
'phe_' prefixed functions within the PHEindicatormethods package. 
<code>byars_lower</code> and <code>byars_upper</code> together return symmetric confidence
intervals around counts, therefore
for a specified confidence level, \(\alpha\), the probability that, by chance, the lower limit returned
will be above the true underlying value, is \(\alpha\)/2.
If the confidence level is very close to 1 or the number of events is very small
Byar's method is inaccurate and may return a negative number - in these cases an error is returned.

Notes