Systems and methods for designing randomized controlled studies

A method for evaluating sample size at an interim stage of an ongoing randomized controlled trial (RCT), said method comprising:

• selecting a covariate for adjustment;
• obtaining blinded RCT data;
• and
• performing a blinded sample size reestimation, at the interim stage, using RCS2 and a formula:
• Nadjusted=Noriginal(1−RCS2);
• wherein
• the RCT is further conducted using the blinded sample size reestimation,
• wherein the Noriginal is an original number of events required to obtain the statistical power without covariate adjustment,
• wherein the Nadjusted is a reestimated number of events required to obtain the statistical power;
• wherein the RCS2 is computed, at the interim stage, on the blinded RCT data based on a formula:
• R
• CS
• 2
• =
• 1
• -
• exp
• [
• -
• 2
• n
• ⁢
• (
• l
• 1
• -
• l
• 0
• )
• ]
• ,
• wherein
• the RCS2 is a Cox-Snell R2,
• the n is a number of participants,
• the l0 is a log-likelihood of a Cox model to explain the time-to-event outcome with an intercept only, and
• the l1 is a log-likelihood of a Cox model to explain the time-to-event outcome with an intercept and with covariate adjustment.

A machine readable medium having executable instructions to cause one or more processing units to perform a method of designing a randomized controlled trial (RCT), the method comprising:

• selecting a covariate for adjustment;
• and
• calculating a sample size required to obtain a statistical power based on a formula:
• Nadjusted=Noriginal (1−RCS2);
• wherein
• the RCT is conducted using the calculated sample size,
• wherein the Noriginal is an original number of events required to obtain the statistical power without covariate adjustment,
• wherein the Nadjusted is an adjusted number of events required to obtain the statistical power with covariate adjustment, and
• wherein the RCS2 is computed on data external to the RCT based on a formula:
• R
• CS
• 2
• =
• 1
• -
• exp
• [
• -
• 2
• n
• ⁢
• (
• l
• 1
• -
• l
• 0
• )
• ]
• ,
• wherein
• the RCS2 is a Cox-Snell R2,
• the n is a number of participants,
• the l0 is a log-likelihood of a Cox model to explain the time-to-event outcome with an intercept only, and
• the l1 is a log-likelihood of a Cox model to explain the time-to-event outcome with an intercept and with covariate adjustment.

A machine readable medium having executable instructions to cause one or more processing units to perform a method of evaluating sample size required to obtain a statistical power at an interim stage of an ongoing randomized controlled trial (RCT), the method comprising:

• selecting a covariate for adjustment;
• obtaining blinded RCT data;
• and
• performing a blinded sample size reestimation, at the interim stage, using RCS2 and a formula:
• Nadjusted=Noriginal(1−RCS2);
• wherein
• the RCT is further conducted using the blinded sample size reestimation,
• wherein the Noriginal is an original number of events required to obtain the statistical power without covariate adjustment,
• wherein the Nadjusted is a reestimated number of events required to obtain the statistical power;
• wherein the RCS2 is computed, at the interim stage, on the blinded RCT data based on a formula:
• R
• CS
• 2
• =
• 1
• -
• exp
• [
• -
• 2
• n
• ⁢
• (
• l
• 1
• -
• l
• 0
• )
• ]
• ,
• wherein
• the RCS2 is a Cox-Snell R2,
• the n is a number of participants,
• the l0 is a log-likelihood of a Cox model to explain the time-to-event outcome with an intercept only, and
• the l1 is a log-likelihood of a Cox model to explain the time-to-event outcome with an intercept and with covariate adjustment.