help sampsi_sccs-------------------------------------------------------------------------------

Title

sampsi_sccs-Sample size estimation for the self-controlled case seriesstudy design

Syntax

sampsi_sccs[,options]

sampsi_sccs?where the second syntax displays the syntax diagram for the first syntax.

optionsDescription ------------------------------------------------------------------------- Optionsalpha(#)type 1 error levelpower(#)powerrho(#)relative incidence of outcome in post-exposure risk period compared to baselinemethod(string)method of sample size estimationonesideduse one-sided alpha-------------------------------------------------------------------------

Description

sampsi_sccsestimates the sample size for a self-controlled case series study design (see Whitaker et al (2006)). Optionally, one may control for the confounding effects of age. The formulae are taken from Musonda et al (2006). The program gives the required number of events rather than the number of subjects, but Musonda recommends (p2626) taking n_subjects= n_events.

Options+---------+ ----+ Options +----------------------------------------------------------

alpha(#)specifies the type 1 error level; default is 0.05

power(#)specifies the power; default is 0.90

rho(#)specifies the incidence rate of the event in the post-exposure risk period relative to that in the baseline (unexposed) period; default is 2

method(string)specifies the method of estimation.stringis one ofbin,srlorage; the default isbin.

binspecifies the binomial method [Eqns (6) and (3) of Musonda] using an arcsin transformation.srl(that's "el") specifies the signed root likelihood ratio method [Eqns (9) and (3) of Musonda].agespecifies the signed root likelihood ratio method with adjustment for the effect of age [Eqn (12) of Musonda].

onsesidedspecifies a one-sided alpha; the default is a two-sided alpha.

Examples(1) Use the binomial method to estimate the sample size required to show a 5-fold increase in incidence of disease during a 2 day period of risk following exposure when the entire observation period is 200 days and all subjects are exposed. Power is 0.9 for a two-tailed test at the 0.05 level. The program will prompt for relevant input.

. sampsi_sccs , rho(5)Binomial method

input duration of post-exposure risk period (e.g. 2) > . 2 input duration of entire observation period (e.g. 200) > . 200 input proportion of subjects exposed at all during obs period (e.g. 1 > ) . 1

================================================================== ========== sample size for SCCS Design: binomial method ========== ==================================================================

2-tailed alpha is: .05 power is: .9 relative incidence associated with exposure is: 5 post-exposure risk period is: 2

total number of events required in exposed subjects is: 94

total number of events required in unexposed subjects is: 0

Total number of events required is: 94 ==================================================================

Note 1: all subjects were exposed, so zero events would be seen in the unexposed. Note 2: the sample size depends,

inter alia, on the ratio of risk period to total observation period, and not on where within the observation period the risk is experienced.

(2) Use the signed root likelihood ratio method to estimate the sample size required to show a 3-fold increase in incidence of disease in infants during a 42 day post-exposure risk period when the observation period is the second year of life (days 366-730), and this total observation period is broken into 4 age sub-periods: the first 3 are of 91 days each, and the last is 92 days. The proportions exposed in each age group are 0.6, 0.2, 0.05 and 0.05 respectively. The incidence of disease within age groups, relative to the first age are 1, 0.6, 0.4 and 0.4 respectively. Desired power is 0.8 for a two-tailed test at the 0.05 level. This example is from Musonda section 7.3.

. sampsi_sccs , power(.8) rho(3) method(age)Signed root likelihood method controlling for age effects

input number of age groups (e.g. 5) > . 4

input age specific incidence [relative to age group 1] in age group 2 > . .6 input age specific incidence [relative to age group 1] in age group 3 > . .4 input age specific incidence [relative to age group 1] in age group 4 > . .4

input length of observation period for age group 1 > . 91 input length of observation period for age group 2 > . 91 input length of observation period for age group 3 > . 91 input length of observation period for age group 4 > . 92

input post-exposure risk period [assumed the same for each group] > . 42

input proportion of subjects exposed during obs period in age group 1 > . .6 input proportion of subjects exposed during obs period in age group 2 > . .2 input proportion of subjects exposed during obs period in age group 3 > . .05 input proportion of subjects exposed during obs period in age group 4 > . .05

================================================================== ========== sample size for SCCS Design with age effects ========== ==================================================================

2-tailed alpha is: .05 power is: .8 relative incidence associated with exposure is: 3 common post-exposure risk period is: 42

total number of events required in exposed subjects is: 35

total number of events required in unexposed subjects is: 2

Total number of events required is: 37 ==================================================================

Saved results

sampsi_sccssaves the following inr()Scalars

r(n_total)total sample sizer(n_exp)sample size required among the exposedr(n_unexp)sample size required among the unexposed

ReferencesWhitaker HJ, Farrington CP, Spiessens B, Musonda P [2006]. Tutorial in biostatistics: The self-controlled case series method. Statistics in Medicine 25(10), 1768–1797.

Musonda P, Farrington CP, Whitaker HJ [2006]. Sample sizes for self-controlled case series studies. Statistics in Medicine 25(15), 2618–2631.

AcknowledgementsThanks to Tony Lachenbruch, Oregon State University, for pointing out an error in an early version of the code and for other helpful comments and assistance with testing. Thanks also to Paddy Farrington, Open University UK, for suggesting an approach to resolving the aforementioned error.

AuthorPhilip Ryan Data Management & Analysis Centre Discipline of Public Health Faculty of Health Sciences University of Adelaide South Australia philip.ryan@adelaide.edu.au