Time-to-event analysis

6-week treatment period Would your view of the relationship between the active treatment and the risk of headache change A methodology called time-to-event analysis is useful here. 

This example suffers from an oversimplification that we have to deal with in the real world, namely that study participants do not always complete the study for the full length of the follow-up period. Participants may drop out of studies for a number of reasons, some of which reflect their experience with the drug (for example, it may be poorly tolerated). Therefore, the time at risk differs from individual to individual within the same trial, and it can differ to a considerable degree from trial to trial throughout a clinical development program. 

The most important points to remember here are as follows. Simply comparing the relative frequency (that is, the proportion of participants reporting the AE) of the AE between two groups does not tell the whole story Such an analysis does not address the potential temporal relationship between exposure to the study treatment and the AE of interest. As we saw in this 

Chapter 8 Confirmatory clinical trials Safety data I 

A more informative approach would be to take into account the time of the event relative to the start of treatment. Ideally, we should use the data from all participants in this approach and should account for varying lengths of time at risk for experiencing the event. O Neill 1987) advocated 

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A time-to-event analysis data set captures the information about the time distance between therapeutic intervention and some other particular event. There are two time-to-event analysis variables that deserve special attention and definition. They are as follows ... 

Note that the term censor is introduced in the preceding table. The log-rank test (invoked in SAS with PROC LIFETEST) and the Cox proportional hazards model (invoked in SAS with PROC PHREG) allow for censoring observations in a time-to-event analysis. These tests adjust for the fact that at some point a patient may no longer be able to experience an event. The censor date is the last known time that the patient did not experience a given event and the point at which the patient is no longer considered able to experience the event. Often the censor date is the last known date of patient follow-up, but a patient could be censored for other reasons, such as having taken a protocol-prohibited medication. 

Time-to-event analysis in clinical trials is concerned with comparing the distributions of time to some event for various treatment regimens. The two nonparametric tests used to compare distributions are the log-rank test and the Cox proportional hazards model. The Cox proportional hazards model is more useful when you need to adjust your model for covariates. 

Fig. 17.8 Schematic representation of the PK/PD model. C = model predicted drug concentrations in plasma R = the free form of the calcitonine gene-related peptide (CGRP) receptor R = the blocked form of the CGRP receptor, which has been related to the severity of headache and time to rescue medication using logistic regression and time-to-event analysis.

Bedaux and Kooijman 1994 Kooijman 1996 Newman and McCloskey 1996, 2000 Zhao and Newman 2007). This is not just an academic discussion the 2 theories lead to different time courses of mortality at constant exposure (Kooijman 1996) (see Figure 2.10) and have very different consequences for sequential exposure (Newman and McCloskey 2000 Zhao and Newman 2007). In reality, both sensitivity difference and stochasticity are likely to play a role in mortality. Individuals also differ in sensitivity, especially in field populations, but there is clearly a substantial stochastic component involved in mortality that cannot be ignored. The method to deal with stochastic events in time is survival analysis or time-to-event analysis (see Bedaux and Kooijman 1994 Newman and McCloskey 1996). For industrial practices, this method has a long history as failure time analysis (see, e.g., Muenchow 1986). Bedaux and Kooijman (1994) link survival analysis to a TK model to describe survival as a function of time (i.e., the hazard rate is taken proportional to the concentration above a threshold value). Newman and McCloskey (1996) take an empirical relationship between external concentration and hazard rate. 

The lack of participant-level data limits assessment of the role of important covariates such as age and sex, as well as precluding time-to-event analysis. 

The study termination form data may be used for efficacy or safety analysis purposes. With regard to safety, if patients discontinue a study medication earlier than patients on standard therapy or placebo, then that is important to know. For efficacy analyses, patients who withdraw due to a lack of efficacy or adverse event may be precluded from being considered a treatment responder or success. Also, often the study termination date is used as a censor date in time-to-event analyses for therapy efficacy. Study termination forms play a key role in patient disposition summaries found at the start of a clinical study report. From a CDISC perspective, the study termination form is a finding. 

Categorical Data and Why Zero and Missing Results Differ Greatly 102 Performing Many-to-Many Comparisons/Joins 106 Using Medical Dictionaries 108 Other Tricks and Traps in Data Manipulation 112 Common Analysis Data Sets 118 Critical Variables Data Set 118 Change-from-Baseline Data Set 118 Time-to-Event Data Set 121... 

In this section we take the aforementioned principles and guidelines for analysis data sets and apply them to creating the most common analysis data sets. The critical variables, change-from-baseline, and time-to-event data sets are presented. Although these are the most common analysis data sets that a statistical programmer will encounter, they are by no means all of the possible analysis data sets. When it comes to analysis data sets, there is no limit to the diversity of data that you may have to create. 

Comparison of Kaplan-Meier survival estimates is often called for in clinical trial analysis. With survival analysis, you are trying to determine which treatment group displays a better time-to-event distribution than another. Part of this analysis is the production of Kaplan-Meier estimates plots that show the probability of a given event over time for each treatment group. In the following example you see that New Drug displays better survival estimates over time than either Old Drug or Placebo. ... 

There are also special considerations as to how to statistically evaluate specific aspects of these studies. Specifically, analysis of time to event becomes very important (Anderson et al., 2000). 

Anderson, H., Spliid, H., Larsen, S. and Dali, V (2000). Statistical analysis of time to event data from preclinical safety pharmacology studies. Tox. Methods 10 111-125. 

In order to illustrate the kinds of arguments and considerations which are needed in relation to intention-to-treat, the discussion in this section will consider a set of applications where problems frequently arise. In Chapter 13 we will cover methods for the analysis of time-to-event or so-called survival data, but for the moment I would like to focus on endpoints within these areas that do not use the time-point at which randomisation occurs as the start point for the time-to-event measure. Examples include the time from rash healing to complete cessation of pain in Herpes Zoster, the time from six weeks after start of treatment to first seizure in epilepsy and time from eight weeks to relapse amongst responders at week 8 in severe depression. 

The special methods we are going to discuss in this section were first developed primarily in the 1970s and applied in the context of analysing time to death and this is why we generally refer to the topic as survival analysis . As time has gone on, however, we have applied these same techniques to a wide range of time-to-event type endpoints. The list below gives some examples ... 

Incorrect analysis of time-to-event data in terms of the definition for the origin of the measurement - the point of randomisation is the only origin that can be used in a randomised trial... 

Cox EH, Veyrat-FoIIet C, Beal SL, Fuseau E, Kenkare S, Sheiner LB. A population pharmacokinetic-pharmacodynamic analysis of repeated measures time-to-event pharmacodynamic responses The antiemetic effect of ondansetron. J Pharmacokinet Biopharm 1999 27 625M4. 

Survival analysis. The analysis of time to event data in particular, but not exclusively, where the event is death. A common feature of such data is that they are very skewed and that there are many censored values. Survival analysis is one of the single most important topics in medical statistics, although its importance to pharmaceutical statistics is, because of the nature of the trials usually run in drug development, relatively less important than the contents of standard textbooks on medical statistics might suggest. 

The same issue exists for time-to-event endpoints. While the most common metric for trials with these endpoints is the hazard ratio evaluated using survival analysis (usually a Cox proportional hazards model), absolute measures, such as the difference in event rates at a fixed follow-up time, are sometimes used. 

Moore, K.L. and M.J. van der Laan. Application of time-to-event methods in the assessment of safety in clinical trials. In K.E. Peace (ed.). Design, Summarization, Analysis Interpretation of Clinical Trials with Time-to-Event Endpoints. Chapman Hall, Boca Raton, FL, 2009a. 

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