On the Use of the Accelerated Failure Time Model as an Alternative to the Proportional Hazards Model in the Treatment of Time to Event Data: A Case Study in Influenza

Article (PDF Available)inTherapeutic Innovation and Regulatory Science 36(3):571-579 · July 2002with 1,910 Reads
DOI: 10.1177/009286150203600312
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Abstract
The accelerated failure time model is presented as an alternative to the proportional hazards model in the analysis of time to event data. A case study in influenza looking at the time to resolution of influenza symptoms is used to illustrate these considerations. The proportional hazards model displays significant lack of fit while the accelerated failure time model describes the data well. From a clinical perspective the accelerated failure time model in this and other applications is seen to be a more appropriate modeling framework and has the added advantage of being easier to interpret. It is concluded that the accelerated failure time model should be considered as an alternative to the proportional hazards model in the analysis of time to event data, especially in applications where the effects of treatment are to accelerate (or delay) the event of interest with no permanent effect in the context of the follow-up period.
Drug Information Journal, Vol. 36, pp. 571579, 2002 0092-8615/2002
Printed in the USA. All rights reserved. Copyright 2002 Drug Information Association Inc.
ON THE USE OF THE ACCELERATED
FAILURE TIME MODEL AS AN
ALTERNATIVE TO THE PROPORTIONAL
HAZARDS MODEL IN THE TREATMENT
OF TIME TO EVENT DATA: A CASE
STUDY IN INFLUENZA
R
ICHARD
K
AY
PAREXEL International, Sheffield, United Kingdom
N
ELSON
K
INNERSLEY
Roche Global Development, Welwyn Garden City, United Kingdom
The accelerated failure time model is presented as an alternative to the proportional
hazards model in the analysis of time to event data. A case study in influenza looking
at the time to resolution of influenza symptoms is used to illustrate these considerations.
The proportional hazards model displays significant lack of fit while the accelerated
failure time model describes the data well. From a clinical perspective the accelerated
failure time model in this and other applications is seen to be a more appropriate modeling
framework and has the added advantage of being easier to interpret. It is concluded that
the accelerated failure time model should be considered as an alternative to the propor-
tional hazards model in the analysis of time to event data, especially in applications
where the effects of treatment are to accelerate (or delay) the event of interest with no
permanent effect in the context of the follow-up period.
Key Words: Accelerated failure time model; Proportional hazards model; Influenza
INTRODUCTION effects of oseltamivir in the time to resolution
of symptoms in influenza.
THE PROPORTIONAL HAZARDS model
The first section provides details of the
has become the model of choice in the analy-
case study while the second section critiques
sis of time to event data in clinical trials. It
the proportional hazards model. The third
is argued in this paper that this is not always
section introduces the accelerated failure time
appropriate and that the accelerated failure
model. The fourth section discusses good-
time model in many applications provides a
ness of fit methods for both models. The
more appropriate modeling framework. These
analysis of the case study is presented in
points are illustrated through a case study
the fifth section. The sixth section describes
that involves a clinical trial evaluating the
software that may be used to fit the models.
The seventh section provides some conclud-
ing remarks.
Reprint address: Dr. Richard Kay, PAREXEL, Naviga-
The general conclusion from this applica-
tion House, 1 South Quay Drive, Sheffield S2 5SU,
United Kingdom (e-mail: richard.kay@parexel.com). tion is that in many settings the accelerated
571
572 Richard Kay and Nelson Kinnersley
failure time model provides a better descrip- Study Endpoints
tion of data than the proportional hazards
The primary efficacy endpoint was time to
model and that the routine use of the more
resolution of illness, defined as the time from
common proportional hazards model should
study drug initiation to the time of alleviation
be considered carefully in all cases. In the
of symptoms, among individuals with influ-
pharmaceutical setting, regulatory require-
enza infection. Symptom alleviation was con-
ments mean that considerations of model
sidered to occur at the start of the first 24-
choice should take place in advance of seeing
hour period in which all influenza symptoms
the data. If the effects of treatment are to
were scored ‘mild’ or none’ and remained
accelerate (or delay) the event of interest
so for 24 hours. For the purposes of this
rather than having a longer term impact, in
article only the market dose of 75 mg bid is
the context of the trial duration, on the occur-
compared with placebo.
rence of the event, then the accelerated fail-
ure time model should replace the propor-
Summary of the Primary Analysis
tional hazards model as the model of choice.
In total, 209 patients were randomized to
placebo (198 completed) and 211 were ran-
domized to oseltamivir 75 mg bid (195 com-
THE CASE STUDY
pleted). Laboratory-documented influenza was
confirmed in 129 (62%) placebo recipients
Protocol Design
and 124 (59%) 75 mg bid recipients.
Kaplan-Meier estimates of the time to al-
Data were analyzed from a placebo-controlled,
leviation were constructed for each treatment
double-blind study to investigate the effects
group, and subjects who withdrew before
of oral oseltamivir (Tamiflu
TM
) on symptoms
symptoms were alleviated were censored at
of influenza. The findings of this trial con-
the time of withdrawal. Figure 1 displays the
ducted in the United States have been de-
resulting Kaplan-Meier curves. Treatment
scribed elsewhere (1) as have the results from
groups were compared using the Generalized
an identically designed study (2) (the non-
Wilcoxon test stratified for region and smok-
United States study is not discussed further
ing status (3).
here). In brief, previously healthy, nonimmu-
The Kaplan-Meier curves show the early
nized adults (1865 years) with a tempera-
benefit of treatment and support for the a
ture of 38°C and symptoms of influenza
priori belief of nonproportional hazards. From
were randomized to receive oral oseltamivir
a clinical perspective it was anticipated that
(Tamiflu
TM
) 75 mg, 150 mg, or matching pla-
resolution of symptoms would be achieved
cebo twice daily for 5 days. The study was
in most subjects within the timeframe of the
designed to assess the effect of treatment on
trial, irrespective of treatment, and that any
the duration and severity of the symptoms of
differences between the groups would be in
influenza.
terms of a faster resolution within the active
Participants recorded the severity of seven
group. Table 1 shows a summary of the anal-
influenza symptoms (cough, nasal conges-
ysis.
tion, sore throat, fatigue, headache, myalgia,
and feverishness) using a 4-point scale (0,
THE PROPORTIONAL HAZARDS
absent; 3, severe) twice daily for 21 days.
MODELA CRITIQUE
Swabs from the nose and throat were taken
in order to isolate influenza virus. Serum The proportional hazards model, introduced
by Cox (4), has become the model of choicesamples for HAI antibody titer were also ob-
tained. An influenza-infected subject was de- for the analysis of time to event data. In this
model the hazard function for a patient withfined as isolation of influenza virus from
nasal/throat secretions and/or a four-fold or treatment indicator and baseline covariates
vector x is given bygreater HAI antibody response.
Accelerated Failure Time Model and Influenza 573
FIGURE 1. Kaplan-Meier curves for the time to alleviation of all seven influenza symp-
toms (influenza infected population).
λ(t;x)
0
(t) e
βx
. the hazard rate in one treatment group is al-
ways a constant multiple of the hazard rate
in the other treatment group. Selection effects
Estimation of the coefficients β of the xs
over time, however, make this approach un-
proceeds by the method of partial likelihood
realistic.
(5) and in this the underlying hazard func-
Aalen (6), in the context of frailty model-
tion, λ
0
(t), remains unspecified. The model is
ling, discusses these points at length. Keid-
considered, therefore, to be semi-parametric
ing, Anderson, and Klein (7) propose use of
and as such has the advantage of being able
the accelerated failure time model as a way
to cope with a variety of basic shapes for the
of dealing with these selection effects and
common hazard function across patients.
Hougaard (8) notes the value of this model
One disadvantage of the model, however,
in overcoming problems in the selection of
is that this underlying hazard function is
covariates.
common across all patients. The hazard func-
tions for any two patients with baseline x
vectors x
1
and x
2
are constrained to be propor-
THE ACCELERATED FAILURE
tional and the method of estimation is based
TIME MODEL
on this. The method of estimation depends
In the accelerated failure time model the time
critically on evolving risk sets through time.
to event variable T is modelled, on the log
The risk set at time t contains those patients
scale, directly in terms of x:
who are alive and in the trial just prior to
time t and, therefore, at risk of suffering the
event and the likelihood terms assume that Y = log T = a + bx error
574 Richard Kay and Nelson Kinnersley
TABLE 1
Summary of the Time to Alleviation of All Seven
Influenza Symptoms (Influenza Infected Population)
Oseltamivir
Placebo 75 mg bid
N* 128 121
Kaplan-Meier median (hours) 103.3 71.5
Difference between medians (hours) 31.8
95% C.I. for difference between
medians (hours)
16.2 to 52.6
p-value
<0.0001
*one placebo subject and three 75 mg bid subjects failed to return their diary
cards
bootstrap estimate (percentile method, 2000 samples)
Generalized Wilcoxon test, stratified for region and smoking status
where the distribution of the ‘error term is for data. In addition, it has a straightforward
interpretation in terms of measuring treat-some specified function. In this paper, we
will assume that this distribution is the stan- ment differences. If x
1
is the indicator for
the treatment group then b
1
is the (adjusted)dard normal. Other forms for this are possible
but these will not be discussed further within treatment difference in means on the log scale
this case study.
so that e
b
1
is the (adjusted) ratio of geometric
Standard likelihood methods of estima-
means.
tion can easily incorporate censoring and the
likelihood function is given by:
ASSESSING MODEL FIT
One approach to assessing the fit of the pro-
L(a, b) f(t
i
)
events
Π S(t
i
)
censorings
=
portional hazards model is to fit a more gen-
eral model, which allows the effects of treat-
ment to vary with time, and to then compare
Π
events
φ
log t
i
(a + bx
i
)
σ
the fit of this to the standard model. This
more general model is often specified by de-
fining k cut points τ
1
, τ
2
,...,τ
k
, on the time
Π
censorings
1 −Φ
log t
i
(a + bx
i
)
σ
冎冊
axis and allowing the coefficient β
1
of the
treatment indicator to be different across the
intervals defined by those cut points:
where f() and S() are probability density
and survivor functions, respectively, for Y =
β
1
10
0 <τ≤τ
1
log T, t
i
is the exact or censored event time
for patient i with covariates vector x
i
,and
11
τ
1
<τ≤τ
2
where φ() and Φ() are density and distribu-
tion functions, respectively, for the standard
normal distribution.
1k
τ
k
.
The likelihood function is fully specified
and maximum likelihood estimates a
ˆ
, b
ˆ
, and In the application in this paper, three cut
points were defined resulting in four inter-σ
ˆ
of a, b,andσ are obtained through maximi-
zation of this. vals. The cut points were chosen to ensure
that each of the intervals contained approxi-In many clinical trial applications this
model provides a more appropriate model mately equal numbers of events. A chi-
Accelerated Failure Time Model and Influenza 575
TABLE 2
squared goodness of fit statistic is then con-
Summary of the Proportional Hazards
structed on three degrees of freedom as twice
Model Fitting for Time to Alleviation of All
the absolute difference in the maximized log-
Seven Influenza Symptoms (Influenza
likelihoods under the standard and more gen-
Infected Population)
eral model. Goodness of fit of the accelerated
Standard
failure time model can be assessed graphi-
Effect Estimate Error p-value
cally through a generalization of the normal
probability plot. Differences between fitted
Smoking 0.188 0.165 0.26
Treatment 0.410 0.135 0.0024
and observed values of Y define residuals on
the log scale, and these are standardized in
the usual way using (observed Y fitted Y)/
residual SD, that is, r
i
= {y
i
(a
ˆ
+ b
ˆ
x
i
)} σ
ˆ
.
ference between the treatment groups. The
These will be a mixture of exact and cen-
estimated hazard ratio is e
0.410
= 1.51. The ef-
sored residuals, the censored residuals being
fect of baseline smoking status is nonsignifi-
obtained from the original censored observa-
cant (p = 0.26).
tions. The only information that we have on
the censored residuals is that the correspond-
ing exact value is larger than the observed The Accelerated Failure Time Model
censored value. If the model is a valid de-
Details of the fit of the accelerated failure
scription, then the residuals will form a cen-
time model are given in Table 3. The treat-
sored sample from a standard normal distri-
ment effect is seen to be highly significant
bution. The estimated distribution function,
with p < 0.0001, with smoking status margin-
F(r), of these residuals can then be compared
ally nonsignificant (p = 0.08). The group es-
to the distribution function, Φ(r), of the stan-
timated (adjusted) ratio of geometric means
dard normal. The Kaplan-Meier method of
is e
0.433
= 0.65 so that the ‘mean’ time to
estimation can be used to estimate 1 F(r)
alleviation of influenza illness in the active
giving the distribution function by subtrac-
(75 mg bid) group is estimated to be 0.65
tion. In terms of the plot, Φ
1
(F
ˆ
(r)) can be
times that in the placebo group. The direction
plotted against r and an approximate straight
of the smoking status effect suggests a slightly
line indicates that the model provides an ade-
longer time to resolution of illness among
quate fit to the data. The plotting points cor-
smokers.
respond to the steps where the Kaplan-Meier
Table 4 provides (adjusted) group geomet-
curve changes, that is, at the exact residuals.
ric means and their ratio from the model. The
In addition, survival curves obtained from
group geometric means have been evaluated
the fitted model can be compared directly
at ‘average’ values for the covariates, calcu-
to the Kaplan-Meier curves to evaluate the
lated according to the actual proportions in
validity of the modelling.
the different categories in the data as a whole,
namely 0.23 for the smokers indicator and
APPLICATION TO THE
INFLUENZA DATA
TABLE 3
Summary of the Accelerated Failure Time
The Proportional Hazards Model
Model Fitting for Time to Alleviation of All
Seven Influenza Symptoms (Influenza
The estimated coefficients of the treatment
Infected Population)
indicator and the covariate, smoking status,
are given in Table 2. Region (west coast,
Standard
mid-west, east coast, and southern United
Effect Estimate Error p-value
States) was also included as a factor in the
Smoking 0.212 0.121 0.08
model. The p-value for treatment is signifi-
Treatment 0.433 0.101 <0.0001
cant with p = 0.0024, indicating a clear dif-
576 Richard Kay and Nelson Kinnersley
TABLE 4
Summary of the Accelerated Failure Time Model Fitting
for Time to Alleviation of All Seven Influenza Symptoms
(Influenza Infected Population)
Oseltamivir
Placebo 75 mg bid
(Adjusted) geometric mean (hours) 103.8 67.3
Ratio of (adjusted) geometric means 0.65
95% C.I. for ratio of (adjusted)
geometric means 0.53 to 0.79
0.34, 0.15, 0.33, and 0.19 for the four region the estimated coefficients vary, starting
around 0.6/0.8 early on in time, falling to 0.4indicators.
The Kaplan-Meier curves indicate sub- in the third interval, and becoming negative
(0.6) in the final interval. The chi-squaredstantial differences between the two groups
and indeed both models have picked this up. goodness of fit statistic on three degrees of
freedom gives a p-value of 0.016, indicatingWe will see, however, in a later section that
the proportional hazards model displays sig- a significant lack of fit of the proportional
hazards model to these data. The model fitnificant lack of fit and for this reason is not
an appropriate description of these data. Also here with the four intervals illustrates the
common problem with the proportional haz-in more marginal situations where the differ-
ences between the treatments are not quite ards model in its standard form. As time goes
on, the make-up of the subjects in the twoso great the choice of a ‘correct’ model will
become critical. treatment groups will change and the chang-
ing coefficients of the treatment indicator are
a result of these selection effects. Although
Model Checking
the treatment ‘effect’ appears to be in favor
of the active treatment in the first three inter-Table 5 provides details of the fit of the pro-
portional hazards model in which the coeffi- vals and in favor of placebo in the final inter-
val, this is a false interpretation. In the earliercient of treatment is allowed to vary with
time. Choosing approximately equal num- period, the active treatment was seen to have
a dramatic effect on more rapid resolution ofbers of events in the 4 intervals gave cut
points of 50, 87, and 131 hours. Note that symptoms while fewer patients on placebo
had their symptoms resolved. In the final
interval, the placebo patients are simply play-
ing ‘catch-up.’
TABLE 5
Figure 2 gives the generalized normal
Summary of the Piecewise Proportional
probability plot for these data. This is seen
Hazards Model Fitting for Time to
to approximate reasonably well to a linear
Alleviation of All Seven Influenza
Symptoms (Influenza Infected Population)
relationship, suggesting that the accelerated
failure time model provides an adequate de-
Time Estimated Standard
scription of the data. Further, the fitted sur-
(Hours) Log-hazard Ratio Error
vival curves from the accelerated failure time
(0, 50) 0.586 0.261 model for the two treatment groups, utilizing
[50, 87) 0.779 0.260
‘average’ covariate values are as shown in
[87, 131) 0.423 0.259
Figure 3, together with the treatment group
[131, ) 0.561 0.371
Kaplan-Meier curves. These are seen to ap-
Accelerated Failure Time Model and Influenza 577
FIGURE 2. Generalized normal probability plot for the accelerated failure time model
when fitted to the time to alleviation of all seven influenza symptoms (influenza in-
fected population).
proximate the Kaplan-Meier curves well, namely PROBPLOT, which produces a vari-
ety of probability plots to assess model fit.supported this modelling framework for
these data. The exact format of the PROBPLOT output
differs from the plots programmed by the
authors using SAS version 6.12 and pre-
SOFTWARE
sented here. SAS version 8.2 also allows
specification of interaction model terms
The SAS system, version 6.12 (9), was used
whereas in previous releases the user had to
to perform all of the analyses and graphical
code dummy (or indicator) variables to fit
presentations in this paper. In particular, the
interaction terms. A wide variety of acceler-
Proc Lifereg procedure was used to fit the
ated failure time models can also be fitted
accelerated failure time models, Proc Phreg
using S-Plus software.
was used to fit proportional hazards models,
and Proc Lifetest was used to compute
Kaplan-Meier estimates. Furthermore, Proc
CONCLUDING REMARKS
Lifetest was used in the computation of the
residuals plotted in the generalized normal In many clinical trial applications the accel-
erated failure time model is often a moreprobability plot described in the section on
“Assessing Model Fit.” realistic model than the proportional hazards
model in the analysis of time to event data.In version 8.2 of the SAS system a new
statement has been added to Proc Lifereg, The proportional hazards model is appro-
578 Richard Kay and Nelson Kinnersley
FIGURE 3. Fitted survival curves from the accelerated failure time model at ‘average’
covariate values for each treatment group and Kaplan-Meier curves for the treatment
groups.
priate when there is a permanent difference perspective is based on more realistic as-
sumptions regarding the effects of treatment,between the groups in the longer term in the
context of the follow-up period. The acceler- that effect being one of faster resolution
rather than a more permanent effect. The ac-ated failure time model is more appropriate
when the group differences are seen over a celerated failure time model in addition, has
a more straightforward interpretation asshorter timeframe while in the longer term
the probability of remaining event free is compared to proportional hazards model in
terms of (adjusted, geometric) means andsimilar in the two groups. This is consistent
with there being a delay in the event occur- their ratio.
The proportional hazards model is rou-ring in one group compared to the other but
no permanent effect. The presence of such a tinely applied to the analysis of time to event
data. The case study considered here pro-delay is seen in many therapeutic settings
and a range of time to event endpoints. vides an example of a situation where this
model is inappropriate and where the acceler-In the analysis of time to alleviation of
influenza illness outlined here the propor- ated failure time model provides a better de-
scription. Further, the basis of this alternativetional hazards model is seen to display signif-
icant lack of fit. In contrast, the accelerated modeling framework is clinically more ap-
propriate in this setting. It is the authors’failure time model provides an adequate de-
scription of these data and from a clinical view that in many clinical trial applications
Accelerated Failure Time Model and Influenza 579
Carewicz O, Mercier CH, Rode A, Kinnersley N,
the accelerated failure time model provides a
Ward P. Efficacy and safety of oseltamivir in treatment
more appropriate modelling framework than
of acute influenza: a randomised controlled trial.
the proportional hazards model for the analy-
Neuraminidase Inhibitor Flu Treatment Investigator
sis of time to event data and should, there-
Group. The Lancet. 2000;355:18451850.
3. Kalbfleisch JD, Prentice RL. The Statistical Analysis
fore, be viewed as a potential alternative ap-
of Failure Time Data. New York, NY: Wiley; 1972:
proach.
144147.
4. Cox DR. Regression models and life-tables (with dis-
cussion). J Roy Stat Society, Series B. 1972;34:187
AcknowledgmentsThe influenza study was sponsored
220.
by F. Hoffman-La Roche, Basel, Switzerland. The au-
5. Cox DR. Partial likelihood. Biometrika. 1975;62:
thors would like to thank Lesley Struthers at Roche
269276.
Global Development and the reviewers for their valuable
6. Aalen OO. Effects of frailty in survival analysis. Stat
comments on the manuscript.
Methods Med Res. 1994;3:227243.
7. Keiding N, Anderson PK, Klein JP. The role of frailty
models and accelerated failure time models in describ-
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    TheSurveillance, Epidemiology and End Results (SEER) cancer database contains survival data for US individuals diagnosed with cancer. Semiparametric Bayesian methods are computationally expensive to fit for such large data-sets. This paper develops a cost-effective Markov chain Monte Carlo strategy for censored outcomes to fit a semiparametric bayesian analysis of SEER data of New Mexico. We use an accelerated failure time model, with Dirichlet process random effects for inter-subject variation, and intrinsic conditionally autoregressive random effects for spatial correlations. The results offer insights into differences in breast cancer mortality rates between ethnic groups, tumor grade and spatial effect of counties.
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    Objective: To evaluate the efficacy and safety of caffeine citrate in the treatment of apnea in bronchiolitis. Study design: Eligible infants aged ≤4 months presenting to the main pediatric emergency service with apnea associated bronchiolitis were stratified by gestational age (<34 weeks or longer) and randomized to receive a single dose of intravenous 25 mg/kg caffeine citrate or saline placebo. The primary efficacy outcome was a 24-hour apnea-free period beginning after completion of the blinded study drug infusion. Secondary outcomes were frequency of apnea by 24, 48, and 72 hours after study medication, need for noninvasive/invasive ventilation, and length of stay in the hospital's pediatric intensive care/step-down unit. Results: A total of 90 infants diagnosed with viral bronchiolitis associated with apnea (median age, 38 days) were enrolled. The rate of respiratory virus panel positivity was similar in the 2 groups (78% for the placebo group vs 84% for the caffeine group). The geometric mean duration to a 24-hour apnea-free period was 28.1 hours (95% CI, 25.6-32.3 hours) for the caffeine group and 29.1 hours (95% CI, 25.7-32.9 hours) for the placebo group (P = .88; OR, 0.99; 95% CI, 0.83-1.17). The frequency of apnea at 24 hours, 24-48 hours, and 48-72 hours after enrollment and the need for noninvasive and invasive ventilation were similar in the 2 groups. No safety issues were reported. Conclusions: A single dose of caffeine citrate did not significantly reduce apnea episodes associated with bronchiolitis. Trial registration: Clinicaltrials.gov: NCT01435486.
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    The study conducted on internship program that is under coordination of National Capacity Building Secretariat (NCBS), data was collected from fresh graduates, who have applied for internship program on the period from July 2014 to June 2015. In our study the sampled individuals are interns who were placed in different institutions and finalized the program before completing the period of 6 months, the list was extracted in internship database. The total number of 7000 graduates or students were hosted in different institutions in Rwanda in the period of 6 years, but the number that was used in our study is composed by 786 interns who hosted and completed the internship in the period of July 2014-2015, among them 119 were found a job and are conserved as censored cases to our study. The Kaplan Meier and Cox regression models will be used to analysis data collected. (IBM SPSS Statistics V20.0) software was be used to do the analysis in this study. In this research, we have introduced section, the literature review is the second while the third is the data collection and the forth as data analysis and interpretation of data analyzed. The final is the conclusion of the whole research and recommendations to address issues on internship program. The work plan and budget for this research were developed; the research is worth 1,280,000 Rwandan francs that was utilized to collect data, communication, stationary, publishing, etc. Keywords: Analysis of Internship Program in Rwanda internship program that is under coordination of National Capacity.
  • Chapter
    This chapter introduces how to analyze nonstandard data types, like binary, categorical, ordinal, and time to event data through generalized linear models (GLMs) and their extension. Logistic regression of binary or ordinal data, Poisson regression of count data, beta regression of proportions, and parametric modeling of survival data are discussed, as are generalized estimating equations. GLMs are then extended to nonlinear GLMs. Three case studies are presented: analysis of adverse event data from a clinical trial, analysis of the frequency of seizure data, and ordinal regression analysis of neutropenia and time to event data from a clinical study with a new anticancer drug.
  • Regression models and life-tables (with discussion )– Acknowledgments—The influenza study was sponsored 220
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    Cox DR. Regression models and life-tables (with discussion ). J Roy Stat Society, Series B. 1972;34:187– Acknowledgments—The influenza study was sponsored 220. by F. Hoffman-La Roche, Basel, Switzerland. The
  • The Statistical Analysis fore, be viewed as a potential alternative apof Failure Time Data
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    Kalbfleisch JD, Prentice RL. The Statistical Analysis fore, be viewed as a potential alternative apof Failure Time Data. New York, NY: Wiley; 1972: proach. 144–147.
  • Version randomized controlled trial. US Oral Neuraminidase Study Group
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    • Sas
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    SAS Institute Inc. SAS/STAT User's Guide. Version randomized controlled trial. US Oral Neuraminidase Study Group. JAMA. 2000;283:1016–1024. 6, Fourth Edition, Volume 2. Cary, NC: SAS Institute Inc.;1989.
  • Article
    Context Previous studies have shown oseltamivir, a neuraminidase inhibitor, to be effective in preventing influenza and treating experimental influenza.Objective To evaluate the efficacy and safety of oseltamivir in the treatment of naturally acquired influenza infection.Design Randomized, placebo-controlled, double-blind study conducted January through March 1998.Setting Sixty primary care and university health centers throughout the United States.Participants A total of 629 healthy nonimmunized adults aged 18 to 65 years with febrile respiratory illness of no more than 36 hours' duration with temperature of 38°C or more plus at least 1 respiratory symptom and 1 constitutional symptom.Interventions Individuals were randomized to 1 of 3 treatment groups with identical appearing pills: oral oseltamivir phosphate, 75 mg twice daily (n = 211) or 150 mg (n = 209) twice daily, or placebo (n = 209).Main Outcome Measures Duration and severity of illness in individuals infected with influenza.Results Two individuals withdrew before receiving medication and were excluded from further analyses. A total of 374 individuals (59.6%) were infected with influenza. Their duration of illness was reduced by more than 30% with both oseltamivir, 75 mg twice daily (median, 71.5 hours; P<.001), and oseltamivir, 150 mg twice daily (median, 69.9 hours; P = .006), compared with placebo (median, 103.3 hours). Severity of illness was reduced by 38% (median score, 597 score-hours; P<.001) with oseltamivir, 75 mg twice daily, and by 35% (median score, 626 score-hours; P<.001) with oseltamivir, 150 mg twice daily, vs placebo (median score, 963 score-hours). Oseltamivir treatment reduced the duration of fever and oseltamivir recipients returned to usual activities 2 to 3 days earlier than placebo recipients (P≤.05). Secondary complications such as bronchitis and sinusitis occurred in 15% of placebo recipients compared with 7% of combined oseltamivir recipients (P = .03). Among all 629 subjects, oseltamivir reduced illness duration (76.3 hours and 74.3 hours for 75 mg and 150 mg, respectively, vs 97.0 hours for placebo; P = .004 for both comparisons) and illness severity (686 score-hours and 629 score-hours for 75 mg and 150 mg, respectively, vs 887 score-hours for placebo; P<.001 for both comparisons). Nausea and vomiting occurred more frequently in both oseltamivir groups (combined, 18.0% and 14.1%, respectively; P = .002) than in the placebo group (7.4% and 3.4%; P<.001).Conclusions Our data suggest that oral oseltamivir treatment reduces the duration and severity of acute influenza in healthy adults and may decrease the incidence of secondary complications.
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    A definition is given of partial likelihood generalizing the ideas of conditional and marginal likelihood. Applications include life tables and inference in stochastic processes. It is shown that the usual large-sample properties of maximum likelihood estimates and tests apply when partial likelihood is used.
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    It is not, in general, possible to include all relevant risk factors in a model of survival or disease incidence. This heterogeneity must be accounted for in the interpretation, as it can imply otherwise unexpected results. This is illustrated by diabetic nephropathy, a serious complication experienced by some diabetic patients. A mathematical model with varying susceptibility can explain that the incidence increases until 20 years duration of diabetes and later decreases. The hospital-based data cover patients diagnosed during 1933-1972. They are interval censored, because early detection of nephropathy requires chemical analysis of urine samples. The data are consistent with a model where less than half of the patients are susceptible, and for each of these the hazard is increasing. The estimated degree of heterogeneity markedly depends on the assumed model. The dependence on age at onset and calendar time of onset is examined. The highest risk is seen at onset age 13-17 years, and the risk decreases with calendar time. The effect of covariates on the hazard is markedly different for the various models, but this is partly a matter of parametrization, as the disagreement is reduced by a reparametrization inspired by accelerated failure time models.
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    Unobserved individual heterogeneity, also called frailty, is a major concern in the application of survival analysis. Hazard rates do not give direct information on the change over time in the individual risk, but are strongly influenced by selection effects operating in the population. The individuals surviving up to a certain time will on average be less frail than the original population. Models are reviewed that account for this phenomenon, and some medical examples are discussed. It is emphasized that the frailty phenomenon may be modelled in many different ways, and a stochastic process approach is discussed as an alternative to the common proportional frailty model.
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    In survival analysis, deviations from proportional hazards may sometimes be explained by unaccounted random heterogeneity, or frailty. This paper recalls the literature on omitted covariates in survival analysis and shows in a case study how unstably frailty models might behave when asked to account for unobserved heterogeneity in standard survival analysis with no replications per heterogeneity unit. Accelerated failure time modelling seems to avoid these difficulties and also to yield easily interpretable results. We propose that it would be advantageous to upgrade the accelerated failure time approach alongside the hazard modelling approach to survival analysis.
  • Article
    Previous studies have shown oseltamivir, a neuraminidase inhibitor, to be effective in preventing influenza and treating experimental influenza. To evaluate the efficacy and safety of oseltamivir in the treatment of naturally acquired influenza infection. Randomized, placebo-controlled, double-blind study conducted January through March 1998. Sixty primary care and university health centers throughout the United States. A total of 629 healthy nonimmunized adults aged 18 to 65 years with febrile respiratory illness of no more than 36 hours' duration with temperature of 38 degrees C or more plus at least 1 respiratory symptom and 1 constitutional symptom. Individuals were randomized to 1 of 3 treatment groups with identical appearing pills: oral oseltamivir phosphate, 75 mg twice daily (n = 211) or 150 mg (n = 209) twice daily, or placebo (n = 209). Duration and severity of illness in individuals infected with influenza. Two individuals withdrew before receiving medication and were excluded from further analyses. A total of 374 individuals (59.6%) were infected with influenza. Their duration of illness was reduced by more than 30% with both oseltamivir, 75 mg twice daily (median, 71.5 hours; P < .001), and oseltamivir, 150 mg twice daily (median, 69.9 hours; P = .006), compared with placebo (median, 103.3 hours). Severity of illness was reduced by 38% (median score, 597 score-hours; P < .001) with oseltamivir, 75 mg twice daily, and by 35% (median score, 626 score-hours; P < .001) with oseltamivir, 150 mg twice daily, vs placebo (median score, 963 score-hours). Oseltamivir treatment reduced the duration of fever and oseltamivir recipients returned to usual activities 2 to 3 days earlier than placebo recipients (P < or = .05). Secondary complications such as bronchitis and sinusitis occurred in 15% of placebo recipients compared with 7% of combined oseltamivir recipients (P = .03). Among all 629 subjects, oseltamivir reduced illness duration (76.3 hours and 74.3 hours for 75 mg and 150 mg, respectively, vs 97.0 hours for placebo; P = .004 for both comparisons) and illness severity (686 score-hours and 629 score-hours for 75 mg and 150 mg, respectively, vs 887 score-hours for placebo; P < .001 for both comparisons). Nausea and vomiting occurred more frequently in both oseltamivir groups (combined, 18.0% and 14.1%, respectively; P = .002) than in the placebo group (7.4% and 3.4%; P < .001). Our data suggest that oral oseltamivir treatment reduces the duration and severity of acute influenza in healthy adults and may decrease the incidence of secondary complications.
  • Article
    Use of some antiviral drugs for influenza infection is limited by potential rapid emergence of resistance. We studied the efficacy and safety of oseltamivir, the oral prodrug of the neuraminidase inhibitor GS4071, in adults with naturally acquired laboratory-confirmed influenza. We did a randomised controlled trial of 726 previously healthy non-immunised adults with febrile influenza-like illness of up to 36 h duration. Patients were assigned oral oseltamivir 75 mg (n=243), oseltamivir 150 mg (n=245), or placebo (n=238) twice daily for 5 days. We assessed recovery by questionnaire and temperature recordings. The primary endpoint was time to resolution of illness in influenza-infected patients. 475 (66%) patients had confirmed infection. Duration of illness was significantly shorter by 29 h (25% reduction, median duration 87.4 h [95% CI 73.3-104.7], p=0.02) with oseltamivir 75 mg and by 35 h (30%, 81.8 h [68.2-100.0], p=0.01) with oseltamivir 150 mg than with placebo (116.5 h [101.5-137.8]). The effect of oseltamivir was apparent within 24 h of the start of treatment. In patients treated within 24 h of symptom onset, symptoms were alleviated 43 h (37% reduction) and 47 h (40%) earlier with oseltamivir 75 mg and 150 mg, respectively, compared with placebo (75 mg 74.5 h [68.2-98.0], p=0.02; 150 mg 70.7 h [54.0-89.4], p=0.01; placebo 117.5 h [103.0-143.8]). Oseltamivir was associated with lower [corrected] symptom scores, less viral shedding, and improved health, activity, and sleep quality, and was well tolerated. Oseltamivir was effective and well tolerated in the treatment of natural influenza infection in adults. The efficacy, tolerability, and ease of administration warrant further investigation in children, elderly patients, and at-risk patients.