Definitions

Shih/Size

Power In the sample size calculator, the probability of correctly rejecting the null hypothesis, under the specified assumptions. Example, for 80% power, enter 0.80.
   
Sample size in control/treated group In the power calculator, the sample size in either the control or treated groups.
   
Ratio of sample size, control to 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.
   
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. Example: for a 5-period study with the probability of an event in the first two periods as 0.3 and 0.25 in the final 3 periods, enter 0.3  0.3  0.25   0.25  0.25.
                      
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. Example: for a 5-period study with a constant hazard ratio of 0.85, enter 0.85  0.85  0.85  0.85  0.85.
   
Number equal length study 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.
                       
Type of patient entry Description of patient entry into the study. "Staggered, uniform" implies patients enter uniformly over the number of periods allotted for recruitment. "Simultaneous" implies all patients are recruited by the beginning of the study.
   
Number study periods for uniform patient entry The number of periods allotted for patient recruitment. Enter 0 if patient entry is simultaneous.
   
Two-sided Type I error Probability of falsely rejecting the null hypothesis. For example, enter 0.05 or 0.01.
   
Test statistic Either the standard log-rank test or the binomial test can be used..
                                                        
Periods to achieve full 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. This entry is ignored in the "Proportional hazards" calculator.
   
List loss to follow-up rates for 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. For no losses to follow-up, enter 0.
   
List rates of crossover to treated for 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. For 100% compliance, enter 0.
                                                       
Lag in effect of crossover to treated 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. This entry is ignored in the "Proportional hazards" calculator.
                                                       
List rates of crossover to control for 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. For 100% compliance, enter 0.