# Model based estimates of sample size and power for group sequential designs with early outcomes Provides sample sizes and power for group sequential designs with early outcomes defined by a recruitment and correlation model, recruitment period and interim analysis time-points. ```r gsearlyModel(rmodel="fix", trecruit, s, tfu, tinterims, pow=0.9, n=NULL, theta, tref=c(1,2), vphi=0.5, m=2, cmodel="uniform", sd=1, rho=0.5, fp, tn, treatnames=c("control", "treat"), sopt=list(r=18, bisect=list(min=20, max=10000, niter=1000, tol=0.001))) ``` ## Arguments - `rmodel`: Recruitment model, options are c(`"fix"`, `"dlin"`, `"ilin"`, `"dquad"`, `"iquad"`, `"dilin"`, `"idlin"`, `"diquad"`, `"idquad"`, `"filin"`, `"fdlin"`, `"ilinf"`, `"dlinf"`) with default=`"fix"`. - `trecruit`: The recruitment period (an integer >1) which is used to define the base units for all analyses and plotting functions (which are on a scale of `1:trecruit`) and is usually the smallest practical study time unit; e.g. if `trecruit=30` months, then `tinterims` and `tfu` should also be set in units of months. - `s`: The study outcome is observed at a sequence of `s` occasions, with `s - 1` early outcomes. An integer value, 2 <= `s` <= 10, the upper limit is purely for reasons of practical implementation. - `tfu`: A vector of length `s`, of follow-up time points, in the same units as `trecruit`. - `tinterims`: A vector of ordered numeric interim analysis time-points, in the same units as `trecruit`. - `pow`: The study target power. If `n` is set, then this is ignored and the study power is reported. - `n`: The total study sample size (control + treatment groups). If this is set to `NULL` then the bisection algorithm is used to find `n` to give power `pow`. - `theta`: The treatment effect, in the same units as `sd`. Current implementation forces a positive value for `theta`. - `tref`: A vector of integers of length 2 that defines the correlation parameter `rho` for the exponential model; the parameter `rho` is the correlation between data at times `tfu[tref[1]]` and `tfu[tref[2]]`, with default `c(1,2)`; see `tfuStandard`. - `vphi`: A weight for unequal group sizes 0 < `vphi` < 1 where the ratio of control to treatment group participants is `vphi` / (1 - `vphi`), with default of 0.5 (equal group sizes). - `m`: A parameter (1 <= `m` < `Inf`) that sets the recruitment model breakpoint for those models that have two phases (e.g. `"diquad"` or `"dilin"`). Ignored for models that do not have two phases. - `cmodel`: The correlation model is set to either `"uniform"` or `"exponential"`; see `corrExp`, `corrUnif`. - `sd`: The standard deviation (0 < `sd` < `Inf`) of the outcome, that is assumed to be the same in both arms and at each time-point. - `rho`: The correlation parameter (0 <= `rho` < 1) associated with correlation model `cmodel`. - `fp`: A vector (of length `tinterims + 1`) of false positive rates; see `Examples`. - `tn`: A vector (of length `tinterims + 1`) of true negative rates; see `Examples`. - `treatnames`: Names used for the two study groups, referred to elsewhere as the first (or 0) and second (or 1) groups, with default `c("control","treat")`. - `sopt`: List of settings for the `gsBound` and `gsProbability` functions in the `gsDesign` package and settings for the bisection algorithm with default `list(r=18, bisect=list(min=20, max=10000, niter=1000, tol=0.001))`. The `min`, `max`, `niter` and `tol` settings represent the minimum and maximum starting points, maximum number of iterations and tolerance for the bisection algorithm. ## Returns An object of class gsearly is a list containing the following components. - **title**: Package title and version number. - **call**: Call to `gsearlyModel`. - **rdata**: A list of the recruitment model (`rmodel`), the recruitment period (`trecruit`), the number of follow-up time-points (`s`), the follow-up time points (`tfu`), on the scale of `trecruit` (`tfu$tfu`) and on the standardized scale (`tfu$stfu`), the study sample size (`n`) for the control and treatment groups and the total (control, treat, total), the weight for the unequal group sizes (`vphi`), the recruitment model parameter (`m`), the interims analyses time-points (`tinterims`), in the units of `trecruit`, and the numbers of study participants recruited and with outcome data at each of the interims (`interims`). - **idata**: A list of the correlation model (`cmodel`), consisting of the correlation model type (`cmodel$type`), parameter (`cmodel$rho`) and correlation matrix (`cmodel$corrmat`), the standard deviation (`sd`), interim and final analysis times (`tinterims`) and the information fraction (`tau`) and variance of the treatment effect estimate (`vbeta`) at times `tinterims`. - **power**: A list of the total number of the looks (`nlooks`), treatment effect (`theta`), the target power (`setpow`), the false positive (`fp`) and true negative rates (`tn`), the lower (`lowerror`) and upper (`upperror`) boundaries and stopping probabilities (`bound`, `prob`) for each look and the total stopping probabilities (`totalerror`) summed across looks (`futility`, `efficacy`). ## See Also `expectSampsize`, `fixedSampsize`, `roundInterims`, `corrExp`, `corrUnif` ## Examples ```r # RCT planning: # Recruitment is expected to take 36 months (trecruit) with three # follow-up times (s) for outcomes at 3, 6 and 12 months (tfu) and # interim analyses (tinterims) at 18 and 30 months. # Study procedures and experience suggest that "dilin" (m=2) is likely # to be a good approximation to temporal patterns of recruitment and data # accrual (rmodel). Correlations between outcomes at 3, 6 and 12 are # assumed to follow a uniform model (cmodel) with parameter (rho) set to 0.5. # Randomisation to the two study arms will be on a 1:1 basis (vphi=0.5). # The standard deviation of the final 12m outcome is expected to be 20, # and the anticipated treatment effect (theta) 8. # Primary interest for the RCT is in stopping early for futility. # Therefore the following values for the false positive and true # negative rates were selected. # Vectors of cumulative probabilities for crossing boundaries under the # null hypothesis (of no treatment difference). fp <- c(0.0000,0.0010,0.0250) tn <- c(0.2400,0.7200,0.9750) # For 90 percent power (pow), a call to gsearlyModel provides a feasible design rctdesign <- gsearlyModel(rmodel="dilin", trecruit=36, s=3, tfu=c(3,6,12), tinterims=c(18,30), pow=0.9, vphi=0.5, m=2, cmodel="uniform", sd=20, rho=0.5, theta=8, fp=fp, tn=tn) rctdesign # If n is set, rather than pow, then we can explore power for lower n update(rctdesign, n=136) # Expected numbers of participants at interim analyses rctdesign$rdata$interims # Information at these interims and final analysis rctdesign$idata$interims # Upper and lower stopping boundaries and probabilities rctdesign$power$lowerror rctdesign$power$upperror ```

gsearlyModel function