Shih/SIZE: A User's Guide

Introduction

Shih/SIZE is an internet-based program that provides a simple user-interface for Size, a SAS macro written my Joanna Shih. SIZE calculates sample size and power in a two-group design, based on either a non-proportional or proportional hazards model, using the standard log-rank or binomial test. It allows for unequal sample sizes, crossovers, losses to follow-up, and lag in treatment effects.  It utilizes the methods of Lakatos (1986, 1988).

 

The user interface

The user interface is the same for both the proportional hazards version and the non-proportional hazards version of Shih/SIZE. There are a total of 15 fields for the user to enter parameters where the user can calculate power or sample size given the other. There are fields in which numbers must be entered, as well as fields that are drop-down menus containing the proper choices for the user to scroll through. Positioning the arrow over the name field and then left-clicking anywhere inside that field will place the cursor inside. Once the name is entered, the user must tab over once or left-click on the next parameter field to enter values for the calculator. The user must then enter an appropriate value, continuing this process until all fields are completed. Next to each field is a link to the web page of definitions for each parameter. The user can tab over to any link and hit enter, or left-click on any link, to proceed to that page. Each parameter is defined, and some examples are given of appropriate values. The user must click the "Back" button on the browser in order to return to the Shih/SIZE user interface.

 

The methods and assumptions for Shih/SIZE

Shih/SIZE provides a simple user interface to Size, a SAS macro that calculates power and sample size for studies involving two groups with a survival outcome. Though it does not allow for all of the capabilities of Size, it still allows for many of the common complexities of randomized clinical trials.

 Shih/SIZE calculates power and sample size for studies involving two groups with a survival outcome, using the methods developed by Lakatos (1986, 1988). A Markov chain model is used to account for time-dependent hazard rates and event rates in the control group, and assumes that loss to follow-up and noncompliance rates are independent of time. Shih/SIZE also allows for the user to specify simultaneous entry or a uniform accrual period, the number of periods required to reach full treatment effect, as well as a gradual or immediate reduction in treatment effect after crossing over to the control group.

 

The parameters to calculate power and sample size

Number of periods. The number of time periods in which patients are to be enrolled and followed, usually expressed in months or years. The hazard is constant within each period.

Control event rate. The conditional probability of having an event, given having survived the previous periods. In the "Proportional hazards" calculator, only a single entry is allowed, which is the constant conditional probability. In the "Non-proportional hazards" calculator, the number of conditional probabilities specified must match number of periods in the study. Each entry can be a unique probability. The rates entered must be separated by spaces.

Hazard ratio, treated-to-control. The ratio of the hazard rates in each period. In the "Proportional hazards" calculator, only a single entry is allowed, which represents the constant ratio of the hazard rates in each period for the treated group to the control group. In the "Non-proportional hazards" calculator, the number of hazard ratios specified must match the number of periods in the study. Each entry can be a unique hazard ratio. The ratios entered must be separated by spaces.

Two-sided type I error. Probability of falsely rejecting the null hypothesis.

Test statistic. The test statistic used to calculate power or sample size. Either the standard log-rank test or the binomial test can be used.

Patient entry. Describes how patients enter the study. Patients either enter simultaneously or uniformly over an accrual period.

Number of time periods for uniform patient entry. The number of periods for patient recruitment. Must be specified if patient entry is not simultaneous.

Ratio of sample size, control:treated. The number of patients assigned to the control group for each patient assigned to the treated group. In general, if R=n/m, then the total sample size N is n(R+1)/R, where n and m are the sample sizes of the control & treated groups, respectively.

Lag in treatment effect. The number of periods to achieve full treatment effect. An entry of 0 indicates full treatment effect is achieved immediately. In the "Non-proportional hazards" calculator, it adjusts the event rate for crossovers. If 0 is entered, then patients return to the efficacy level comparable to the level in the opposite group immediately after crossover. This number should less than or equal to the number of periods in the study.

Lagged effect of drop-out. Describes how the treatment vanishes for those who cross over to the control group. A gradual lagged effect describes the treatment level of the those who drop out of the treated group to return to the level of the control group in the same way the treatment reached its full effect. An immediate effect describes the treatment level vanishing completely when a patient drops out of the treated group.

Rate of crossover to treated in each period. The conditional probability of patients crossing over to the treatment assigned to the treated group, given having complied with the treatment assigned in the previous periods. The number of probabilities specified must match the number of periods in the study. The probabilities entered must be separated by spaces.

Rate of crossover to control in each period. The conditional probability of patients crossing over to the treatment assigned to the control group, given having complied with the treatment assigned in the previous periods. The number of probabilities specified must match the number of periods in the study. The probabilities entered must be separated by spaces.

Loss to follow-up rate in each period. The conditional probability of patients becoming lost to follow-up, given having been followed in the previous periods. The number of probabilities specified must match the number of periods in the study. The probabilities entered must be separated by spaces.

Power. Probability of correctly rejecting the null hypothesis under the specified assumptions.

Total sample size. The sum of the sample sizes in the control and treated groups.

 

Executing the calculation, modifying the parameters, and exiting Shih/SIZE

Once all parameter values are entered, and assuming the values are valid, simply positioning the arrow with the mouse over the "Calculate" button and left-clicking on it, or tabbing over until the button is highlighted and pressing "Enter" on the keyboard, executes the calculation process. If any of the values are invalid, Shih/SIZE will not display the SAS output correctly. See section 2.4 of the Appendix for the correct SAS output. To modify one or more of the parameter values, the user must hit the "Back" button on the web browser. The cursor must then be placed in the appropriate number field by positioning the arrow with the mouse and left-clicking anywhere inside the number field, and modifying as necessary with the delete or backspace keys. The user can also clear all values by pressing the "Reset" button. At any time, the user can close Shih/SIZE by simply navigating to another web page, or closing the web browser.


 

Proceed to Shih/SIZE 

Proportional Hazards

Non-proportional Hazards

Power

Power

Sample Size

Sample Size