ST 520 Statistical Principles of Clinical Trials - NCSU Statistics ...

More documents

Recommendations

Info

CHAPTER 9 ST 520, A. TSIATIS and D. Zhang The LIFETEST Procedure Product-Limit Survival Estimates Survival Standard Number Number SURVTIME Survival Failure Error Failed Left 0.0000 1.0000 0 0 0 10 4.5000 0.9000 0.1000 0.0949 1 9 7.5000 0.8000 0.2000 0.1265 2 8 8.5000* . . . 2 7 11.5000 0.6857 0.3143 0.1515 3 6 13.5000* . . . 3 5 15.5000 0.5486 0.4514 0.1724 4 4 16.5000 0.4114 0.5886 0.1756 5 3 17.5000* . . . 5 2 19.5000 0.2057 0.7943 0.1699 6 1 21.5000* . . . 6 0 * Censored Observation 9.4 Two-sample Tests The major objective of many Phase III clinical trials is to compare two or more treatments with respect to some primary endpoint. If the primary endpoint is time to an event (e.g. survival time), then interest will focus on whether one treatment will increase or decrease the distribution of this time as compared to some standard or control treatment. Let us begin by considering the comparison of two treatments. Let the variable A denote treatment group, where we take A = 0 to denote the control group or standard treatment and A = 1 the new treatment. The problem of comparing two treatments is often cast as a hypothesis testing question. The null hypothesis being that the distribution of time to death (event) is the same for both treatments. Letting T denote a patient’s underlying survival time, we define the treatment specific survival distributions by S1(t) = P(T ≥ t|A = 1) and S0(t) = P(T ≥ t|A = 0). The null hypothesis is given as or equivalently H0 : S1(t) = S0(t) = S(t), t > 0, H0 : λ1(t) = λ0(t) = λ(t), where λj(t), j = 0, 1 denote the treatment-specific hazard rates. PAGE 144
CHAPTER 9 ST 520, A. TSIATIS and D. Zhang The alternative hypothesis of most interest in such trials is that the survival time for one treatment is stochastically larger than the survival time for the other treatment. Specifically, we say the survival time for treatment 1 is stochastically larger than the survival time for treatment 0 if S1(t) ≥ S0(t) for all t > 0 with strict inequality for at least one value of t. It has become standard practice in clinical trials to use nonparametric tests; that is, tests based on statistics whose distribution under the null hypothesis does not depend on the underlying survival distribution S(t) (At least asymptotically). The most widely used test with censored survival data is the logrank test which we now describe. Data from a clinical trial comparing the survival distribution between two treatments can be viewed as realizations of the random triplets where • Ui = min(Ti, Ci) – Ti denotes the latent failure time – Ci denotes the latent censoring time • ∆i = I(Ti ≤ Ci) denotes failure indicator • Ai denotes treatment indicator We also define the following notation: (Ui, ∆i, Ai), i = 1, . . .,n, • nj = � n i=1 I(Ai = j) denotes the number of patients assigned treatment j = 0, 1; n = n0+n1 • nj(u) = � n i=1 I(Ui ≥ u, Ai = j) denotes the number at risk at time u from treatment j = 0, 1 • n(u) = n0(u) + n1(u) denotes the total number at risk at time u from both treatments • dj(u) = � n i=1 I(Ui = u, ∆i = 1, Ai = j) denotes the number of observed deaths at time u from treatment j = 0, 1 PAGE 145
Page 1 and 2:
ST 520 Statistical Principles of Cl
Page 3 and 4:
TABLE OF CONTENTS ST 520, A. Tsiati
Page 5 and 6:
CHAPTER 1 ST 520, A. TSIATIS and D.
Page 7 and 8:
Page 9 and 10:
Page 11 and 12:
Page 13 and 14:
Page 15 and 16:
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98: CHAPTER 6 ST 520, A. TSIATIS and D.
Page 147: CHAPTER 9 ST 520, A. TSIATIS and D.
Page 169 and 170: CHAPTER 10 ST 520, A. TSIATIS and D
Page 199 and 200:
CHAPTER 10 ST 520, A. TSIATIS and D
show all

ST 520 Statistical Principles of Clinical Trials - NCSU Statistics ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?