Commentary
Success rates in the United States drug development system
Lorraine Sheck, Ph.D., Christopher Cox, Ph.D., Henry T. Davis, Ph.D.,
A. Gene Trimble, William M. Wardell, M.D., Ph.D., and Ronald Hansen, Ph.D.
Boston, Mass., and Rochester, N . Y .
Center for the Study of Drug Development, Tufts University, Boston, and the University of
Rochester, Rochester
Drug development in the United States has
been characterized by: (1) high attrition and correspondingly low success rates of drug candidates passing through the development sys(2) a steady decline in new chemical
entities (NCEs) entering clinical r e ~ e a r c h , ~ - ~
and (3) increasingly lengthy and more costly
periods required for clinical and regulatory review.3 These characteristics have raised the
concern that the n u m b e r ~ fNCEs reaching the
market in the future might remain low or decline even further unless compensatory ins
creases in NCE success rates
Although detailed information on the numbers of NCEs involved in preclinical testing is
difficult to obtain, success rates for the complete process of drug development from synthesis of a drug to market approval have been
estimated at less than 0.1 %.',
The filing
requirement of the 1962 investigational new
drug (IND) regulations has provided more reliable data on NCEs for the period from IND
filing to new drug application (NDA) approval,
so that success rates for NCEs in U. S. clinical
development and regulatory review have been
calculated with a greater degree of certainty.
From these data, success rates for drugs that
have reached the point of U. S. clinical study
have been calculated at about 9% to 12%.33
43
These success rates represent composite rates
for all NCEs receiving INDs between 1963 and
the early 1970s and hence do not reveal any
change in success rate specific to cohorts of
NCEs of the same IND age.
We examined rates in the United States at
which self-originated NCEs with IND filings
reach NDA approval by means of an improved
methodology for the determination of regulatory success rates. Success is defined as approval by the Food and Drug Administration;
success rate is defined as the cumulative percentage of NCEs that pass through IND filing
to submission and approval of the NDA (expressed as a function of time from IND filing).
Changes in success rates for NCEs with roughly
the same IND age are determined by stratifying
NCEs into 3-yr cohorts based on year of IND
filing. Success rates for the earlier IND cohorts
can be determined with reasonable certainty
from observed data, since few INDs remain active in these cohorts. However, for more recent
IND cohorts with greater numbers of active
INDs, a mathematic model is employed to estimate future success rates of NCEs currently in
drug development. The proportions of U. S.
NCE-INDs first studied abroad are also examined to evaluate the influence of foreign testing
on the success rate achieved by IND cohorts.
Methods
Reprint requests to: Louis Lasagna, M.D., Center for the Study of
Drug Development, Tufts University, 136 Harrison Ave., Boston,
MA 02111.
Criteria for inclusion of NCEs were as already described8: NCEs were defined as new
Volume 36
Number 5
molecular compounds not previously tested in
man and excluded new salts or esters of existing
drugs; surgical and diagnostic materials; certain
externally used compounds such as disinfectants, antiperspirants, and sunscreens; nutritional compounds such as natural forms of vitamins and sweetening agents; and certain biologic compounds such as vaccines, antigens,
antisera, immunoglobulins, or purified extracts
of existing drugs.
Data for this article were taken from our survey on U. S. investigational NCEss but were
restricted to information provided on 752 selforiginated NCEs (i.e., those owned and developed by a U. S. parent company) that had never
before been taken by man anywhere in the
world and had received an IND filing between
January 1, 1963 and December 31, 1979. Of
these 752 NCEs, 691 had received IND filings
and were subsequently first tested in man in the
United States and 61 were first tested abroad
and subsequently returned to the United States
for IND filing and continued U. S. investigational study.* For these NCEs, the primary
items of data analyzed included IND filing date,
country where first taken by man, and either
NDA approval date or the date of a firm's decision to cease clinical research without submitting an NDA. This latter information was available only from the firms and provides a more
accurate date of research abandonment than the
IND closure date, since firms often leave an
abandoned IND open to protect its trade secret
status.
In our previous articles, success rates on all
INDs filed between 1963 and the early 1970s
were determined from the observed number of
INDs reaching NDA approval, allowing at least
8 yr from IND filing to NDA a p p r ~ v a l . ~ ,In
this article we have refined this approach by
the 752
NCEs with
IND filings into 3-yr cohorts based on year of
IND
t' examine whether success rates
have changed with time. For each cohort, a suecess rate was calculated as the cumulative percentage of IND filings that reached NDA ap-
*An additional 69 NCEs, first taken by man abroad but as yet
without IND filings, were also considered in the foreign testing
analysis.
Success rates in U . S . drug development
575
proval at any given number of years from IND
filing. Observed success rates are based on the
full data base of 752 NCEs and 69 NDA approvals as of March 31, 1984. Since observations cease at a fixed point in time (March 31,
1984), the data are right-censored because additional approvals are expected to occur beyond
March 31, 1984, particularly in more recent
cohorts.
To test our observed data statistically and to
predict success rates in more recent IND cohorts
beyond the range of observation, a mathematical model was developed to describe the
manner in which NCEs progress through the
IND and NDA phases of drug development.
Two aspects of the IND phase were considered
separately: residence time (the time from IND
filing until termination) and fate (i.e., whether
the termination took the form of research abandonment or NDA approval). Thus the model
has two stages, with the first stage describing
the residence time of an NCE as a function of
year of IND filing and the second stage describing the fate of an NCE as a function of residence
time. When the two stages are combined, the
model* allows us to estimate the average residence times and success rates of compounds in
the system for any particular year (or group of
years) of IND filing. Because research termination dates required for the development of the
first stage of the model were missing for 43
NCE-INDs, the model is based on a data base of
709 NCEs with IND filings between 1963 and
1979 and on approval data for 52 NCEs as of
December 31, 1979.t
To evaluate the influence of foreign testing
on observed success rates, cumulative success
rates for INDs first tested abroad and for INDs
first tested in the United States were compared
*From a statistical point of view, the need for a two-stage model
arises from the difficulty of modeling the IND phase, which can
terminate either in research abandonment or in NDA approval. Because the orobabilitv structure of a ~rocesswith multi~leoutcomes is
comp~ex,'ourtwo-stage model represents a practiA solution for
dealing with this complexity. Mathematic details of the model are
discussed in the Appendix.
tThe lower number of approved NCEs considered in the model
and the larger number for the observed success rates are because the
model required complete data on both research abandonment and
approval. Status of clinical research for those NCEs that were not
approved was only available through the end of our investigational
survey period (December 31, 1979), while dates of approval were
available through March 31, 1984.
Clin. Pharmacol. Ther.
November 1984
576 Sheck et al.
TIME FROM IND FILING TO NDA APPROVAL (YEARS)
Fig. 1. Observed success rates for four cohorts of self-originated U. S. NCE-INDs.
Table I. Current cumulative and highest possible regulatory success rates for cohorts
of IND filings
Highest
lND cohort
1
INDs
$led
I
No. of
approvals*
I
Current cumulative
success rates*
No. of INDs
still active?
Possible success
rate (%)$
*As of March 31, 1984.
+Number may be fewer than shown because research abandonment data are known only up to December 31, 1979, while NDA approval
data are known up to March 31, 1984.
$The highest possible success rate for the cohorts is calculated by assuming that the active NCEs for each cohort will all eventually be
approved. This rate is not shown for cohorts of INDs filed after 1971, which are too recent for the attrition evident in the earlier cohorts to have
occurred.
§Incomplete cohort with respect to 3-yr intervals of IND filings.
and the overall effect of foreign screening of
NCEs was examined.
Results
Fig. 1 compares observed cumulative success
rates for four 3-year cohorts of self-originated
NCE-INDs reaching NDA approval after different elapsed times from IND filing. Intermediate
success rates 6 yr after IND filing were similar
for all four cohorts (3.5% to 4.2%). However,
with additional time from IND filing, "final"
cumulative success rates have increased in more
recent cohorts. The 1963-65 cohort required 17
yr from the end of 1965 to obtain a 9.4% success rate, whereas the 1969-71 cohort required
only 12 yr to reach a 13.7% success rate. The
1972-74 cohort also shows a rising trend toward
a 9.5% success rate after 8 yr; whether this
curve will eventually exceed its predecessors
cannot yet be determined. Fig. 1 also illustrates
that shorter residence times were required to
reach a given success rate for more recent IND
cohorts: To reach an 8% cumulative success
rate, the 1963-65 cohort required about 13 yr,
the 1966-68 cohort required about 12 yr, and
both the 1969-71 and 1972-74 cohorts required
less than 8 yr.
In our survey, only 20 NCE-INDs filed during the period 1963 through 1971 were still active and not approved as of the end of December
Volume 36
Number 5
1979. Table I shows by cohort current cumulative success rates and those that would be
reached if all remaining active NCEs were approved. Thus for the 1963-65 cohort with only
one active IND, a 9.9% success rate is the maximum success rate expected if that IND were
eventually approved. For the 1966-68 cohort
with five active INDs, a 12.1% success rate is
the maximum success rate achievable. For the
1969-71 cohort, the maximum success rate
would be 22.9%. For these earlier cohorts with
fewer active INDs, estimation of the maximum
success rate of an IND cohort seems reasonable.
For more recent cohorts, however, the estimation of ultimate success rate becomes less certain because too little time has elapsed to allow
for attrition through research abandonment. Not
all active INDs will reach NDA approval, and
some will almost certainly experience research
abandonment without NDA approval. Because
of this phenomenon, a mathematic model was
constructed to estimate current and future cumulative regulatory success rates for more recent
cohorts (Fig. 2).
The first stage of the model involves survival
distribution analysis (see Appendix) to estimate
the residence time distributions for IND terminations (either by NDA approval or by research
abandonment) based on year of IND filing. As
shown in Fig. 2, top panel, residence times
from IND filing to time of termination increase
for more recent cohorts. Although this seems to
contradict the trend toward shorter residence
times described in Fig. 1, it should be noted that
the termination rates shown in Fig. 2 are based
both on INDs reaching NDA approval (10%)
and on those abandoned in research (90%). In
contrast, rates shown in Fig. 1 are based only on
approval data. This paradox is explained by the
larger proportion of INDs that remain in the
system for a longer time before being abandoned and overshadow the smaller proportion
that successfully reaches NDA approval. A
likelihood ratio test proved the statistical significance (P < 0.01) of these increases, indicating that more recent NCEs are remaining in the
system longer before a decision on their termination is made. When observed termination
rates are superimposed on estimate curves, observed and estimated data are in good agree-
Success rates in U . S . drug development
577
63-65
66 - 68
69-71
72 74
ALL TERMINATED NCEs
(STAGE 1 OF THE MODEL)
O f ' , ! , , , , , , , , , , , , ,, ,
5
10
15
TlME FROM IND FILING TO TERMINATION
/
NCEs TERMINATED
BY APPROVAL
(STAGE 2 OF THE MODEL)
3
- 1
-
TlME FROM IND FILING TO NDA APPROVAL
(years)
/
APPROVAL RATES
OF NCEs
(COMBINED VERSION OF
THE MODEL)
10
20
TlME FROM IND FILING TO NDA APPROVAL
(years)
Fig. 2. Mathematic model for estimation of success
rates.
ment (Fig. 2), thus supporting the choice of
survival distribution analysis for this stage of
the model.
The second stage of our mathematical model
distinguishes between the two alternative endpoints of IND termination (approval or abandonment) and indicates a modified logistic regression analysis (see Appendix) to estimate the
probability of NDA approval as a function of
residence time. As shown in Fig. 2, middle
578 Sheck et a / .
Cfin. Pharmacof. Ther.
November I984
- PREDICTED
1148 1 196365
---
I
?
OBSERVED
18-
1972- 74
1969-71
v)
v)
LU
14-
' . I
/'
0
0
14
3 IO-
10
l8I
U)
6-
.
J
2-
2
07
,
5
10
15
0
i
5
10
15
TIME FROM IND FILING TO NDA APPROVAL
Fig. 3. Predicted and observed success rates for four IND cohorts
panel, the probability of NDA approval increases significantly with increasing residence
time. Of those NCEs with residence times of 3
yr or less, fewer than 5% terminate in NDA
approval (the remaining 95% terminate by research abandonment), whereas 34% of those
NCEs with residence times of 7 yr or more are
estimated to terminate in NDA approval. The
curve levels off at 36%-the estimated maximal percentage of NDA approvals as described
in the Appendix. Unlike the survival functions
described in stage I of the model, this modified
logistic regression function was not found to
depend on year of IND filing. Thus regardless of
year of IND filing, an approval is more likely the
longer an NCE remains in the system; termination by research abandonment is more likely at
earlier points in the development process.
Fig. 2, middle panel, also shows that the
modified logistic regression function closely
approximates the grouped observed data for the
earlier part of the curve but deviates somewhat
from the later data points. This is in part because the later points are based on very few
approvals at the longer residence times, thus
introducing more potential error into the righthand portion of the curve. Because the probability of NDA approval increases the longer an
NCE remains in the system and only very few
NCEs are left at the latest time point (the fate of
most of them having been decided much earlier), the number of NDA approvals with longer
(8 to 10 yr) residence times is very small and
does not influence the overall trend toward
shorter residence times shown by the observed
success rates of the more recent IND cohorts in
Fig. 1.
The two stages of the model were combined
to estimate success rates as a function of time
from IND filing for each cohort of IND filings
Volume 36
Number 5
Success rates in U. S . drug development
579
FOREIGN-TESTED NCEs WITHOUT INDs
FOREIGN-TESTED NCEs WITH lNDs
US-TESTED NCEs WITH lNDs
COHORTS BY YEAR OF IND FILING
Fig. 4. NCEs tested anywhere in the world with or without INDs
included in this study. As shown in Fig. 2, bortom panel, the estimated success rate increases
from about 9.9% for the 1963-65 IND cohort
(after 17 yr) to 13% for the 1969-71 cohort (after 12 yr). For the 1963-65 IND cohort, the
estimated success rate is only slightly higher
than the current observed success rate of 9.4%
(after 17 yr) and will in fact be reached if the
last active IND of that cohort is approved. For
the 1969-71 cohort, the estimated success rate is
about 0.5% lower than the current observed
success rate of 13.7% (after approximately
12 yr).
In a similar manner as was shown with observed success rates in Fig. 1 , shorter residence
times are required to reach a given estimated
success rate for more recent IND cohorts: the
1963-65 cohort requires about 9 yr, while the
1972-74 cohort requires less than 8 yr to reach
an 8% cumulative success rate. However, because Fig. 2 shows success rates projected over
17 yr for all IND cohorts, we can discern
plateau areas that represent the maximum success rate for each cohort when all INDs have
either been abandoned or approved. Given these
plateau areas, median residence times for IND
cohorts required to reach maximum success
rates are increasing for more recent IND
cohorts, reflecting the longer times required for
decisions to continue or abandon research.
To evaluate the extent to which the model
adequately estimates the observed data, esti-
mated success rates have been plotted with the
corresponding observed success rates (as in Fig.
1). Fig. 3 shows differences between observed
and estimated NCE success rates. In general,
however, the estimated success rates describe
increasing success rates after shorter residence
times for more recent IND cohorts in the fashion of the observed success rates. Furthermore,
the model predicts that success rates will continue to increase for more recent INDs (e.g.,
INDs filed after 1972 for which few observed
data are yet available). Agreement between observed and estimated rates is satisfactory given
the complexities of the process being modeled
and the relatively simple structure of the model.
When a discrepancy occurs, however, the observed value is usually lower than the expected
value. This could in part be a result of missing
data on research abandonment, resulting in a
smaller denominator (709). This smaller denominator produces an upward bias for the estimated values but has no effect on the calculation of observed success rates, since this is with
the larger denominator (752).
The increase in success rates for the 1969-7 1
and 1972-74 IND cohorts coincides with an increase in initial clinical study abroad. Less than
2% of the NCEs in the two earlier cohorts were
first clinically studied abroad, compared to 6%
for the 1969-71 cohort and 18% for the 1972-74
cohort. We would expect the probability of success to be higher for NCEs that were first tested
Clin. Pharmacol. Ther.
November 1984
580 Sheck et al.
1969-1971 COHORT
p
i
FIRST STUDIED ABROAD
i
(3 Of 9)
STUDY)
TIME (YEARS)
1972- 1974 COHORT
2
30:
5
p FIRST STUDIED ABROAD
0
39
Z
i
20;
,
/
./'
;
16 01
23)
.i
/
0
,./
0
2
4
COMBINED (FOREIGN 1 US STUDY)
(12 01 126)
6
8
10
12
14
TIME (YEARS)
Fig. 5. Approval rates for INDs by first study location.
abroad because of a screening effect. Based on
initial foreign clinic trials, firms will stop research on less promising candidates without
applying for an IND and select the more promising candidates for further study under an IND.
Fig. 4 shows both the increase in initial foreign
clinical testing and the growth in the number of
NCEs that have been clinically tested abroad
without an IND. To investigate the effect of this
screening on IND success rates, we separated
the 1969-71 and 1972-74 IND cohorts by location of first clinical testing. As indicated in Fig.
5, INDs with previous foreign study have a
much higher success rate than those first studied
in the United States: 33% vs 12.7% for the
1969-71 cohort and 26% vs 6% for the 197274 cohort. If we limit our analysis to those
NCEs first tested in man in the United States,
the differences in success rates among cohorts
is significantly narrowed (Fig. 6). The 196971 cohort still exhibits a higher success rate,
but the 1972-74 cohort is within the range of
the first two. These results indicate that
NCEs screened abroad contribute substantially
to the observed rise in IND success rates and
underscore the importance of including for-
Volume 36
Number 5
Success rutes in U . S . drug development
0
2
4
8
6
10
12
14
16
581
18
TIME (YEARS)
Fig. 6. Approval rates for INDs first tested in the United States only
eign study data in future studies of success
rates.
Discussion
Various estimates and calculations of the
percentage of INDs that reach NDA approval
have been made. In previous reports we have
calculated success rates by a simple descriptive
analysis that determines success rate for all
INDs filed between 1963 and the early 1970s,
allowing at least 8 yr from IND filing to NDA
a p p r ~ v a l . ~This
,
method had two limitations: It
calculated a rate for a large group of INDs of
different IND ages so that the important question of whether NCE success rates may be
changing with time remained unanswered, and
it provided no estimates of eventual success
rates. We have here made a comprehensive
examination of success rates that calculates
separate success rates for 3-yr cohorts of NCEIND filings to determine whether success rates
may be changing with time, involves a statistical model of the U. S. drug development process to estimate eventual success rates based on
past trends in IND research abandonment and
NDA approval, and examines the effects of
previous foreign clinical study on IND success
rates. Success rates of compounds in clinical
research under an IND have been increasing
over time, from 9.4% after 17 yr for the 196971 cohort to 13.7% after just 12 yr for the
1969-71 IND cohort. The success rate for the
1972-74 IND cohort surpasses that of the
1969-71 cohort after 8 yr of IND study. This
indicates a trend towards higher IND success
rates.
The mathematical model we used produced
estimated success rates that were in good
agreement with observed data for INDs in the
cohorts compared and predicts that success rates
will continue to rise for INDs filed after 1974.
Eventual success rate is projected at about 10%
for the 1963-65 cohort, increasing to 16% for
the 1972-74 cohort. For INDs filed between
1975 and 1979, eventual success rates are estimated at about 20%. These projections are for
INDs only and assume that current trends will
continue. Although the model allows us to predict future success rates for INDs, we emphasize its simplicity and warn that factors that may
influence the rate at which an IND moves
through the drug development system have not
been incorporated into the model.
One such factor that has been shown to affect
the success rates of INDs is the impact of the
increasing trend in initial foreign clinical study.
For the last cohort, a substantial portion of the
NDA approvals were first studied abroad before
582 Sheck et al.
I N D filing. INDs with initial foreign testing had
much higher success rates than those first tested
in man in the United States, and the proportion
of NCEs first tested abroad and having no I N D
has increased over time. These findings indicate
that foreign screening of compounds may be
responsible for much of the rise in IND success
rates, and that exclusion of these NCEs studied
abroad that as yet have no I N D leads to an overestimate of actual clinical success rates.
The relatively simple questions of what the
success rate of drugs in clinical development is,
and whether o r not it is changing, are not simple
to answer. The increasing trend toward initial
foreign clinical testing should make us cautious
in interpreting I N D trends. Foreign testing may
reduce the number of INDs, but will be offset at
least in part by an increase in the probability of
success for those NCEs selected for further testing in the United States. Thus the declining IND
filing rate during the late 1970s overstates the
reduction in clinical testing, but the I N D success rate overstates the success rate for all NCEs
clinically tested. In a future study w e plan to
incorporate data for foreign study into our calculations of success rates and into our mathematical model.
Appendix: Statistics
Srrccess rate cind residence time for cliniccrllg
inrestigrted NCE-INDs. A model for IND success
rates must consider the reciprocal relationship between success rate and residence time for NCEs in
clinical investigation. The success rate of a class of
NCEs depends on the amount of time elapsed since
testing began (residence time) and marketing approval is received (point of success). For example,
the success rate for a group of NCEs under observation for 10 yr might be lo%, while after 15 yr the
success rate might rise to 15%. These hypothetic success rates illustrate the dependence of success rate on
residence time, i.e., there is a different success rate
associated with each interval of time since testing
began.
Some general features of the dependence of success rate on elapsed time can be seen from the above
example. First, the success rate associated with zero
time is zero. Second, as time increases, the success
rate either increases or stays constant for a time.
Third, the success rate will eventually reach a plateau
and the ultimate level of this plateau is clearly much
less than 100% (it is currently of the order of 10% to
15%), since most INDs are terminated by research
abandonment and hence are not available for NDA
approval.
Clin. Pharmacol. Ther.
November I984
To construct a mathematical model for success
rates, we need to model the dependence of success
rate on time. To do this, we interpret a success rate as
a probability. That is, we assume that a success rate
of 9% during the initial 10-yr period of observation
represents a probability of success of 0.09 for an
individual NCE during its first 10 yr under observation. NCEs of a common type being modeled are
assumed to act randomly and independently according to the dictates (in the sense of dictating averages
over a great many individual NCEs) of the same distribution (over time) of success rates (probabilities).
Rather than having a random sample from some
population, however, we have data on the entire
population. Second, we are really modeling a subdistribution; i.e., the total probability (ultimate success rate) is less than one.
In the fields of industrial reliability testing and
epidemiology, the distribution of success rates is
often called the "survival distribution." A common
feature of survivorship data is that at any particular
observation point there will always be NCEs on
which research is still proceeding and whose fate is,
therefore, unknown. One of the advantages of our
statistical approach to modeling is that such "censored" observations can be used in construction of
the model.
From the point of view of statistical modeling,
perhaps the most important feature of the IND-NDA
process is the existence of two distinct endpoints:
research abandonment or NDA approval. A statistical
model can use the extra information on abandonment
to gain more knowledge of the process than can be
obtained from the observed success rates alone. Our
approach to this two-stage process was a two-stage
model. We make the assumption that every IND will
eventually terminate in either research abandonment
or NDA approval, and we define residence time as
the time until such termination occurs. The distribution of residence times now becomes a genuine probability distribution that can be modeled with the
techniques of survivorship analysis. As discussed below, we chose a model that would permit the distribution of residence times to depend on the year of
IND filing. The second stage of the model is designed
to separate the two endpoints by modeling the probability of NDA approval as a function of length of
residence time and year of IND filing. Total probability is allowed to be less than one, reflecting the
fact that some terminations are research abandonments. As described below, this total probability is
represented by a parameter of the model and is, therefore, estimated from the data. The two different
models can then be combined into a single model to
estimate success rates for the entire process.
The form of our mathematical model was suggested by two preliminary analyses of the data. First
we used the methodology of nonparametric survival
analysis, specifically the Kaplan-Meier product limit
estimate^,^ to examine residence times. (This re-
Volume 36
Number 5
Success rates in U . S. drug development
quires the assumption that the residence times of the
various NCEs are independent.) Since previous
analyses have suggested that residence time might
change through the years, it would have been desirable to perform individual Kaplan-Meier analyses for
each year; however, there were too few NCEs having
INDs filed in any given year for this to be practical.
Thus we grouped the NCEs over 3-year intervals for
the Kaplan-Meier analysis.
Second, we examined fate as a function of residence time by logistic regression.' An additional
multiplicative parameter was added to the logistic
model to allow the total proportion of NDA approvals
to be less than 100%.
Constrrrction of the nctrral model. We let G(t)
denote the subdistribution for the NDA approval process and g(t) its density. In the construction of G(t),
we use two functions corresponding to the two aspects of the IND phase under consideration: ( I ) F(t),
the residence time distribution function with density
f(t), and (2) Pit), the probability of NDA approval
given termination of the IND phase at time t. In this
case, g(t) = f(t)P(t), and
ified logistic and the multiplicative parameter 0 <
y 5 1 is the limit of P(t) as t increases. As shown,
G(t) =
y,, f(u)P(u) du.
Examination of Kaplan-Meier curves for residence
times analyses indicated that, for each year of IND
filing, the distribution function F(t) was well approximated by an exponential distribution. Therefore, if
we assume that F(t) is an exponential distribution for
every year of IND filing, we have
f(t) = ( I /A)exp(- At) for t > 0
where the parameter A > 0 controls mean residence
time and is allowed to depend in a log-linear manner
on the year of IND filing. The method of maximum
likelihood was used to estimate parameters of the
model. A likelihood ratio test was used to examine
the questions of dependency of the parameter A on
the year of IND filing. As shown in Fig. 2, the predicted curves gave a good fit to the observed rates of
abandonmentlapproval.
Observed data indicated that P(t) should be a
monotone increasing function of t whose range was
the interval (0,l). One of the most useful such functions in statistical modeling is the logistic function.
For modeling P(t), we chose to modify the usual
logistic function by incorporating a multiplicative
factor y that would allow the total probability of
NDA approval to be less than one. Specifically, we
assumed that P(t) had the form
where a and /3 are the usual parameters of the unmod-
583
this model provided an adequate fit to the data. The
parameter a has an interesting interpretation in our
model; specifically, yl[l + exp(-a)] is the approximate probability of NDA approval for NCEs whose
residence times are short. The value of y was approximately 36% for both processes. This can be seen in
Fig. 2, in which the curve levels off at approximately
100 mo.
References
Cox DR: Analysis of binary data. London, 1970,
Methuen.
Faust RE, Harris MR, Lee KI: Factors which can
harm the patient: Economic restraints on research
and development in the pharmaceutical industry,
in L'Etang H, editor: Regulation and restraint in
contemporary medicine in the U. K. and U. S. A.
London, 1983, London Royal Society of Medicine and MacMillian Press Ltd.
Hansen RW: The pharmaceutical development
process: Estimates of current development costs
and times and the effects of proposed regulatory
changes, in Chien RI, editor: Issues in pharmaceutical economics. Lexington, Mass., 1979,
D. C. Heath and Co.
James B: The future of the multinational pharmaceutical industry to 1990. London, 1977, Associated Business Programmes Ltd.
Kaplan EL, Meier P: Nonparametric estimation
from incomplete observations. J Am Stat Assoc
53:457-481, 1958.
Wardell WM, DiRaddo J, Trimble AG: Development of new drugs originated and acquired
by United States-owned pharmaceutical firms,
1963-76. CLIN PHARMACOL
THER28:270-277,
1980.
Wardell WM, Hassar M, Anavekar SN, Lasagna
L: The rate of development of new drugs in the
United States, 1963-75. CLINPHARMACOL
THER
24:133-145, 1978.
Wardell WM, May MS, Trimble AG: New drug
development by U. S. pharmaceutical firms with
analyses of trends in the acquisition and origin of
drug candidates, 1963-79. CLIN PHARMACOI.
THER32:407-417, 1982.
Wardell WM, Sheck LE: Is pharmaceutical innovation declining? Interpreting measures of pharmaceutical innovation and regulatory impact in
the U. S. A . , 1950-80. Arne Ryde Symposium on
Pharmaceutical Economics, Helsingborg, Sweden, September 1982. (In press.)