1 Graphical Approaches to the Analysis of Safety Data from ...Graphical Approaches to the Analysis of Safety Data from Clinical Trials Richard M. Heiberger 2 I spent a research leave

1

Graphical Approaches to the Analysis ofSafety Data from Clinical Trials

Ohad Amit, Richard M. Heiberger, Peter W. Lane

Patient safety has always been a primary focus in the development of newpharmaceutical products.

Safety issues in clinical trials are usually reported in tables.

Formal analysis of safety data is much less developed than for efficacy data.

Safety data provides an ideal opportunity to use graphical methods

• Present concise summaries

• Communicate main messages

• Back up with tables as needed

Graphs can be used in

• an exploratory setting to help identify emerging safety signals.

• a confirmatory setting as a tool to elucidate known safety issues.

Graphical Approaches to the Analysis of Safety Data from Clinical Trials Richard M. Heiberger 2

I spent a research leave year at GSK where I joined a company-wide teaminvestigating graphical issues for display of clinical trial information.

We developed several graphical displays for routine safety data collected duringa clinical trial, covering a broad range of graphical techniques. Many of thedisplays we devised are now included in the GSK software library. Our results,coauthored with Ohad Amit and Peter W. Lane of GSK, appeared in 2008 inPharmaceutical Statistics.

The displays focus on key safety endpoints in clinical trials

• the QT interval from electrocardiograms

• laboratory measurements for detecting hepatotoxicity

• adverse events of special interest.

We discuss in detail the statistical and graphical principles underlying the pro-duction and interpretation of the displays.


We illustrate eleven specific graphical designs, many of which display the dataalong with statistics derived from them. Each will be discussed in detail.

• Two are simple, comparing distributions with boxplots or cumulative plots.

0

1

2

3

4

ALAT ASAT ALKPH BILTOT

Liver Function Test

Max

imum

LF

T (

ULN

)

Drug A (N=209) Drug B (N=405)

For ASAT, ALKPH, and ALAT, the Clinical Concern Level is >2 ULN;For BILTOT CCL is >1.5 ULN; where ULN is the Upper Level of Normal Range

• Five more display data and summaries over time, comparing informationfrom two groups in terms of distribution (with boxplots), cumulative inci-dence, hazard, or simply means with error bars.

0 50 100 150 200

0.0

0.05

0.10

0.15

0.20

0.25

Days on Study

Cum

ulat

ive

Pro

port

ion

with

Eve

nt

Drug ADrug B

Subjects at Risk_____________Drug ADrug B

218 201 190 176 162 0

447 339 305 278 264 2

Days since randomization

0 20 40 60 80 100 120 140 160 180 200

0.0

0.002

0.004

0.006

0.008

Drug ADrug B

Haz

ard

Rat

e

Average no. of subjects at risk during interval

Drug ADrug B 430 340 310 300 280 280 270 260 150 18

210 200 190 180 180 170 170 160 93 13

• The other four are multi-panel displays: one-dimensional and two-dimensionalarrays of scatterplots, a trellis of individual profiles, and a paired dotplotdisplaying risk together with relative risk.

0

1

2

3

4

0 1 2 3 4

ALAT

0 1 2 3 4

ALKPH

0 1 2 3 4

ASAT

0 1 2 3 4

BILTOT

Baseline (/ULN)

Max

imum

(/U

LN)

Drug A (N=209)Drug B (N=405)

For ASAT, ALKPH, and ALAT, the Clinical Concern Level is 2 ULN;For BILTOT, the CCL is 1.5 ULN;where ULN is the Upper Level of Normal Range

0 1 2 3

BILTOT (/ULN)

0 1 2 3

ALAT (/ULN)

0 1 2 3

0

1

2

3

ASAT (/ULN)

ALK

PH

(/U

LN)

0

1

2

3

BIL

TO

T (

/ULN

)

0

1

2

3

ALA

T (

/ULN

)


For ASAT, ALKPH, and ALAT, the Clinical Concern Level is 2 ULN;For BILTOT CCL is 1.5 ULN;where ULN is the Upper Level of Normal Range

DYSPNEACHRONIC OBSTRUCTIVE AIRWAY

CHEST PAINBRONCHITIS

RHINITISMELENA

MYALGIAURINARY TRACT INFECTION

COUGHINGUPPER RESP TRACT INFECTION

INFECTION VIRALSINUSITIS

HYPERKALEMIARASH

BACK PAINGASTROESOPHAGEAL REFLUX

INJURYHEADACHE

RESPIRATORY DISORDERABDOMINAL PAIN

DIZZINESSFLATULENCE

FATIGUEDIARRHEA

PAINWEIGHT DECREASE

DYSPEPSIAVOMITINGINSOMNIA

HEMATURIAANOREXIA

NAUSEAARTHRALGIA

0 10 20 30

Percent

•

.125 .5 1 2 4 8 1632

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

Relative Risk with 95% CI

•

Most Frequent On−Therapy Adverse Events Sorted by Relative Risk

TREATMENT A (N=216) TREATMENT B (N=431)


Graphical displays for safety data

We illustrate each of our graphs using real data from a drug development pro-gram: specifically, safety data from a large Phase III pivotal trial. This was atwo-arm randomized trial comparing a fixed dose of the test drug (Drug B be-low) to placebo (Drug A). Following a four-week placebo run-in, patients wererandomized to receive either placebo or test drug for 24 weeks. The safety datacollected in this trial is typical of the type of routine safety data collection thatis part of almost all Phase II and III trials of pharmaceutical products.

While the graphs were developed in the context of a randomized parallel-grouptrial we have provided commentary on their utility in other settings. Thisreal dataset has been used to demonstrate key concepts that we identified asimportant in the evaluation of safety, but the displays were not tailored to drawspecific conclusions regarding the safety profile of the test drug.


QT Interval

QTc measure of heart rhythm has become pivotal

Prolonged QTc interval is treated as a surrogate for serious arrhythmia

Change from baseline considered most relevant

Change associated with drug:

• > 30 msec → clinical concern

• > 60 msec → serious clinical concern

Entire distribution is of interest, as well as tail behaviour

We propose three graphs to help evaluate QTc.


Note: Increase <30msec ’Normal’, 30-60msec ’Concern’, >60msec ’High’


Cum

ulat

ive

Per

cent

0

10

20

30

40

50

60

70

80

90

100

Change in QTc interval (msec)

-30 -20 -10 0 10 20 30 40 50 60 70 80 90

Figure 1: Empirical distribution function for maximum change in QTc


The y-variable is the maximum change for each patient over the 24-week treat-ment period. Each point represents the percentage of patients on the y-axiswith a change in QTc less than or equal to the corresponding value on thex-axis. Reference lines have been provided at 30 and 60 msec as well as at 0msec to help the interpretation.

The distribution functions for the two treatment groups are drawn with fairlythin lines to allow assessment of small differences at the upper end; different line-styles are used as well as different colours for each treatment so that differencesare obvious when the graph is printed in black and white. As can easily beseen in the graph, in this particular dataset there is little difference in how thedistributions behave at the upper tail, though the distribution for the test drugis slightly less concentrated around the median than that for placebo. Theproportion of patients with a maximum change less than zero is about one-ninth, as expected in a trial with eight visits after baseline and no effect onQTc.


Figure 2: Boxplot of change from baseline in QTc by time and treatment


Figure 2 is a boxplot that displays the distribution of the changes in QTc ateach time-point during treatment. The distribution of the maximum changeover the entire treatment period is displayed in a “margin” at the right-handside of the graph. Alternative or additional information can be displayed inthe margin, such as derived variables like the last-observation-carried-forward(LOCF). In addition to providing a visual summary of variability and centraltendencies, this type of graphical display explicitly identifies the extreme valuesin the distribution. Reference lines are drawn as before at 30 and 60 msec toaid in the interpretation.

The concept of a graphical margin as used in Figure 2 is a powerful way toadd extra summary information in the context of a graph, just as a tabularmargin adds value to a table. It is of particular value in many graphs that showeffects over time to add a lower margin as here to show the number of subjectsinvolved in the summaries displayed at each time-point. Note that the numbersof subjects may differ among the graphs we present, because of different patternsof missing observations and different definitions of populations for the variablesinvolved.


Note: Vertical lines are 95% confidence limit ranges, LOCF is last observation carried forward

Subjects at Visit_____________Drug ADrug B

216431

210423

206384

199362

191337

184315

176311

169299

164293

214429

Drug A Drug B

Mea

n C

hang

e (m

sec)

-6

-5

-4

-3

-2

-1

0

1

2

3

Week

0 2 4 8 12 16 20 24 LOCF

Figure 3: Mean (95% CI) change from baseline in QTc by time and treatment


Recent ICH guidance (ICH, 2005) on evaluation of QT prolongation has recom-mended the use of means and confidence intervals in summarizing QTc data; wepropose Figure 3 to address those recommendations. Figure 3 displays meansand associated 95% confidence intervals for change in QTc by time. The LOCFvalue is displayed in a margin; but, as in Figure 2, alternative values, suchas the maximum change over the treatment period, can be displayed instead.Within-group mean changes with 95% confidence intervals are displayed as barsaround a point.

In a thorough QT study (see ICH, 2005) the focus is on the mean differencefrom placebo along with a 90% confidence interval. Mean differences fromplacebo and the relevant measure of variability could also be displayed usingthe graphical display in Figure 3.


Liver Function Tests (LFTs)

Evaluation of hepatotoxicity has become a central part of many pharmaceuticaldevelopment programs. Hepatotoxicity is evaluated through the collection ofkey laboratory variables, including aspartate aminotransferase (ASAT), alanineaminotransferase (ALAT), alkaline phosphatase (ALKPH) and total bilirubin(BILTOT).

We have created graphics that summarize these variables individually and col-lectively. We recognize that summary statistics may be of little value in theevaluation of hepatotoxicity, so we propose graphics that aid in describing prop-erties of the distribution and provide greater insight where it is needed: at theindividual patient level.

Unlike with the QT interval, where changes over the baseline are deemed im-portant, with liver function it is the result itself, relative to the “upper limit ofnormal” (ULN), which represents the clinically meaningful metric. The ULNis a value routinely specified for each variable by each laboratory, and allowsthe standardization of results coming from different labs with different normalranges.


Figure 4: Distribution of ASAT by time and treatment


Boxplots as a function of time

We propose boxplots for each LFT measurement as a function of time (Figure4). The maximum value over the entire treatment period is displayed in a mar-gin at the right-hand side of the graph, and alternatives should be considered asappropriate. To better facilitate a comparison and to highlight true elevations,patients who were above the upper limit of normal at baseline are excluded fromthis graph. We have reduced the vertical spread of the graph by summarizingall values above twice the ULN as counts in an upper margin of the graph.


0

1

2

3

4

ALAT ASAT ALKPH BILTOT

Liver Function Test

Max

imum

LF

T (

ULN

)

Drug A (N=209) Drug B (N=405)

For ASAT, ALKPH, and ALAT, the Clinical Concern Level is >2 ULN;For BILTOT CCL is >1.5 ULN; where ULN is the Upper Level of Normal Range

Figure 5: Distribution of maximum liver function test values by treatment


Parallel boxplots of the maximum elevation

We propose a set of boxplots displaying the maximum elevation in each LFTover the treatment interval, side-by-side (Figure 5). This type of display allowsclinicians to evaluate elevations simultaneously across LFT measurements.

Reference lines are provided at selected levels relative to the upper limit ofnormal. These are intended to help highlight subjects with elevations exceedingthese levels and can be modified as appropriate for the disease or populationunder study.

An additional issue to consider when displaying multiple LFT measurementswithin the same plot is how to define the maximum. In Figure 5, we chose themaximum for each patient on each measurement individually. With this ap-proach a patient’s maximum value may occur at different time-points dependingon the measurement.


0

1

2

3

4

0 1 2 3 4

ALAT

0 1 2 3 4

ALKPH

0 1 2 3 4

ASAT

0 1 2 3 4

BILTOT

Baseline (/ULN)

Max

imum

(/U

LN)


For ASAT, ALKPH, and ALAT, the Clinical Concern Level is 2 ULN;For BILTOT, the CCL is 1.5 ULN;where ULN is the Upper Level of Normal Range

Figure 6: Empirical distribution function for maximum change in QTc


Scatterplots of LFT maximum values against baseline

To help explain what is happening at the individual patient level, we proposetwo multiple-panel displays. Figure 6 is a set of scatterplots of the maximumvalue against baseline over the treatment period with a panel for each LFTmeasurement and a symbol for each treatment group. It is important to useidentical scaling on the x- and y-axes. This display can be considered thegraphical analogue to laboratory shift tables. Specifically, focusing on the upperleft-hand quadrant of the graph allows you to note patients who were normalat baseline and have had subsequent elevations during the treatment period.

These are intended to help highlight patients with elevations exceeding levelsof clinical concern. While individual points are not labelled, it may be usefulto add labels (such as subject ID) for those observations above one of the levelsof concern in one or both dimensions. Note that this type of graphical displayis useful across a wide range of clinical trial designs.


0 1 2 3

BILTOT (/ULN)

0 1 2 3

ALAT (/ULN)

0 1 2 3

0

1

2

3

ASAT (/ULN)

ALK

PH

(/U

LN)

0

1

2

3

BIL

TO

T (

/ULN

)

0

1

2

3A

LAT

(/U

LN)


For ASAT, ALKPH, and ALAT, the Clinical Concern Level is 2 ULN;For BILTOT CCL is 1.5 ULN;where ULN is the Upper Level of Normal Range

Figure 7: Matrix Display of Maximum LFT Values


Scatterplot matrix of maximum LFT values

A second multiple-panel display (Figure 7) represents the lower triangle of afour-by-four matrix of scatterplots of all possible combinations of the four LFTmeasurements. This type of display is helpful in visually identifying patientswith simultaneous elevations in two liver function tests. For this graph, themaximum value for each patient on each measurement over the treatment in-terval is used, and reference lines are provided at selected levels relative to theupper limit of normal.

One feature that is disconcerting at first sight is the overlaying of points fromone treatment by those of another. However, this can be used to advantage: bychoosing to draw the Placebo points last (Drug A), the effect is to highlight anydifference in distribution of the test drug compared to this standard distribution.In this application, there is little difference to see apart from the four patientson Drug A with high ASAT values.


Patient: 5152 Drug: A White Male Age: 48

LFT(

ULN)

0.00.51.01.52.02.53.03.54.04.55.0

-50 -25 0 25 50 75 100 125 150 175 200


LFT(

ULN)

0.00.51.01.52.02.53.03.54.04.55.0

-50 -25 0 25 50 75 100 125 150 175 200


LFT(

ULN)

0.00.51.01.52.02.53.03.54.04.55.0

-50 -25 0 25 50 75 100 125 150 175 200

Patient: 5269 Drug: B White Female Age: 48

LFT(

ULN)

0.00.51.01.52.02.53.03.54.04.55.0

-50 -25 0 25 50 75 100 125 150 175 200

Note: Clinical concern level for ALAT, ASAT and ALKPH is 2xULN, for BILTOT is 1.5xULN

ALAT ASAT ALKPH BILTOT_

Study Days

Figure 8: LFT patient profiles


Patient profiles of LFT values

Patient profiles of LFT values can be shown in a trellis display with severalpanels on a page and potentially many pages, each panel representing one pa-tient’s data for the LFT measurements of interest. The display may usefully berestricted to just those patients whose values give cause for concern. Referencelines are provided as before. Also note that the treatment period is displayedas a thick red line at the bottom of each panel. At the individual patient levelthis allows the observer to see which measurements are causing concern and towhat extent, to assess their temporal relationship to treatment, and to evaluatethe onset and duration of the elevation.

Note that care needs to be taken when constructing multiple-panel displays toensure that text is not made unreadable for the intended medium, as a result ofpacking several panels onto a page: default settings suitable for single displaysusually need to be changed.


Adverse experience data

Evaluation of adverse experience data is a critical aspect of all clinical trials.We propose graphics for exploratory data analysis or signal identification, andfor adverse experiences (AEs, also read as adverse events) that may result froma compound’s mechanism of action or events that are of special interest toregulators.


DYSPNEACHRONIC OBSTRUCTIVE AIRWAY

CHEST PAINBRONCHITIS

RHINITISMELENA

MYALGIAURINARY TRACT INFECTION

COUGHINGUPPER RESP TRACT INFECTION

INFECTION VIRALSINUSITIS

HYPERKALEMIARASH

BACK PAINGASTROESOPHAGEAL REFLUX

INJURYHEADACHE

RESPIRATORY DISORDERABDOMINAL PAIN

DIZZINESSFLATULENCE

FATIGUEDIARRHEA

PAINWEIGHT DECREASE

DYSPEPSIAVOMITINGINSOMNIA

HEMATURIAANOREXIA

NAUSEAARTHRALGIA

0 10 20 30

Percent

•

.125 .5 1 2 4 8 1632

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

((

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

))

Relative Risk with 95% CI

•

Most Frequent On−Therapy Adverse Events Sorted by Relative Risk

TREATMENT A (N=216) TREATMENT B (N=431)

Figure 9: Most frequent on-therapy adverse events sorted by relative risk


AE dotplot of incidence and relative risk

Figure 9 is a two-panel display of the most frequently occurring AEs in theactive arm of the study. The first panel displays their incidence by treatmentgroup, with different symbols for each group. The second panel displays therelative risk of an event on the active arm relative to the placebo arm, with95% confidence intervals as defined by Agresti (2004) for a 2×2 table.

If confidence intervals are presented, multiple comparison issues should be givenconsideration, particularly if there is interest in assessing the statistical signif-icance of differences of the relative risk for so many types of events. However,the primary goal of this display is to highlight potential signals by providingan estimate of treatment effect and the precision of that estimate. S-Plus codefor the construction of this plot is available in the online files that accompanyHeiberger and Holland (2004).

The AEs are ordered by relative risk so that events with the largest increasesin risk for the active treatment are prominent at the top of the display. We donot recommend ordering alphabetically by preferred term, which is the likelydefault with routine programming, because that makes it more difficult to seethe crucial information of relative importance of the AEs.


AE dotplot from Excel with the RExcel interface

Recently I have been working on the RExcel interface with Erich Neuwirth.Our book R through Excel will be available from Springer this summer. Oneof the examples shows control of the AEdotplot from Excel.


Figure 10: Data on adverse events in an Excel spreadsheet.


Figure 11: Most frequent on-therapy adverse events sorted by relative risk


Figure 12: Double-click the spreadsheet on a column title, in this case alphabetical by event name

(silly, yes, but the data may have been given to you in that sort order).


Figure 13: The graph immediately sorts itself to match.


Time-to-event plots for AEs

Of particular interest in AE data is the onset date of each event relative tothe start of treatment. Specifically, we may want to summarize how the riskfor an event is changing over time. It is both convenient and appropriate totreat AEs as time-to-event data. Unlike simple incidence rates, this approachallows evaluation of the risk as a function of time. In fact, it can be arguedthat the most appropriate and unbiased approach to estimating the risk ofan event is through the use of statistical methodology for time-to-event data.This approach to analyses of AE data has been advocated in several regulatoryguidance documents including the Statistical Principles for Clinical Trials E9(ICH, 1998) and the ICH Structure and Content of Clinical Study ReportsE3 (ICH, 1995). Several authors have also advocated the approach includingO’Neill (1998), Gait et al (2000) and Ioannidis and Lau (2002), and severalreal-life examples have demonstrated its value.

We propose two graphical displays based on non-parametric survival methods.As there can typically be dozens of events reported in any clinical trial, werecommend that these displays be tailored around events that are of particularinterest to a given compound. In our example, the particular events of interestare gastrointestinal (GI) AEs of concern.


0 50 100 150 200

0.0

0.05

0.10

0.15

0.20

0.25

Days on Study

Cum

ulat

ive

Pro

port

ion

with

Eve

nt

Drug ADrug B

Subjects at Risk_____________Drug ADrug B

218 201 190 176 162 0

447 339 305 278 264 2

Figure 14: Cumulative distribution (with SEs) of time to first AE of special interest


Figure 10 is a Kaplan-Meier plot by treatment group of the cumulative incidenceof GI adverse events of concern by time. We adhered to the principles laid outby Pocock et al (2002) for display of censored survival data. Standard errorbars for the cumulative incidence at selected time-points on the x-axis have alsobeen included. Simultaneous confidence bands may be displayed instead.

The readability and clarity of the graph should be a factor in consideringwhether or not to display standard error bars or confidence bands. For ex-ample, if the estimated curves are close together, the use of confidence bandsmay make it difficult to distinguish between the curves or between the estimatedcurve and the confidence bands. The graph provides a clear indication of theevolving incidence of these events as a function of time making the appropriateadjustments to the risk set as patients withdraw from the trial.

This graph is useful in many settings where there is a sufficiently long follow-upperiod. It can be applied across a wide range of clinical trial designs.

We have included “rug-plots” along each stepped line to characterize the distri-bution of censored events in each treatments, i.e. the times at which individualswithdraw from the trial. In conjunction with the steps, which represent indi-vidual adverse events, the graph therefore displays all the relevant data alongwith the statistical summary of cumulative incidence.


Days since randomization

0 20 40 60 80 100 120 140 160 180 200

0.0

0.002

0.004

0.006

0.008

Drug ADrug B

Haz

ard

Rat

e

Average no. of subjects at risk during interval

Drug ADrug B 430 340 310 300 280 280 270 260 150 18

210 200 190 180 180 170 170 160 93 13

Figure 15: Hazard function for AEs of special interes


A complementary display to the cumulative incidence plot is a graphical displayof the hazard for each treatment group as a function of time (Figure 11). Life-table estimates of the hazard function for each treatment group were generatedand then displayed graphically along with their standard errors. The life-tableanalysis was based here on 10-day intervals, and the hazard displayed at themidpoint of each interval. This display is intended to provide a more directassessment of the risk of an event occurring at any given time during the follow-up period.

The values provided in the lower margin give the context of the estimatedhazard rates above, as seen in the earlier graphs. However, these values are notnecessarily integral (unless rounded, as here), as a fundamental assumption ofthe life-table method is that all censoring occurs at the midpoint of an interval.Therefore, the number of censored patients, who are assumed to be at risk foronly half the interval, is multiplied by 0.5.


Discussion

The eleven graphs described above represent our key areas of focus. Thereare several additional pieces of safety data that might be displayed graphicallyand there are several additional graphical approaches that could be consid-ered for the endpoints discussed above. Other common safety measurements,in addition to those discussed above, consist of vital signs, additional ECGmeasurements, and additional clinical laboratory measurements. Although thegraphics described above were not developed with these in mind, several arestill applicable. We give here a brief description of how these graphics may beapplied to these additional safety endpoints, and


Conclusions—Tools

The production of graphs has always been a time-consuming process. Withthe pressure of deadlines in a development project, it is essential to providetools that take care of the details of graph construction in whatever softwareis used, and allow people to concentrate on selecting the right information topresent. In GlaxoSmithKline we are developing standard tools for producinggood-quality graphical displays. These include

• validated scripts to allow straightforward production of standard graphs likethose presented here. We estimate that these will provide for only abouthalf the graphs that are needed, on average.

• a graphical environment in which it is easier to construct ad hoc displays,and export scripts that capture the process into the standard productionenvironment.


Conclusions—Context

The graphical displays described above should be given prime consideration inthe analysis of safety data arising from clinical trials. They allow the analysta broad range of options to evaluate safety data. While tabular summaries ofsafety data can be voluminous and difficult to interpret, graphical summariesdisplay information in a clear and concise manner. Many of these graphs displaynot only the summary statistics derived from analysis, but also some or all ofthe original data, putting the statistics into context and highlighting individualobservations that are of particular concern in safety analysis.


Acknowledgements

We are indebted to the other members of the Graphics Team in the Biomedicaland Data Sciences Division of GlaxoSmithKline: Susan P. Duke, Daniel C.Park, Mike Colopy, Nada X. Boudiaf, Randall R. Austin, and Shi-Tao Yeh(who programmed the SAS versions of most of the graphs). We also thankMichael Durante for programming the S-Plus version of two of the graphs.

This talk is based on the paper:

Ohad Amit, Richard M. Heiberger, and Peter W. Lane. (2008) “Graphical Ap-proaches to the Analysis of Safety Data from Clinical Trials”. PharmaceuticalStatistics, 7, 1, 20-35.http://www3.interscience.wiley.com/journal/114129388/abstract

The S-Plus/R function for the AEdotplot is included in the HH package avail-able for S-Plus on CSAN and for R on CRAN. The RExcel example for theAEdotplot is included with the R package for R through Excel by Richard M.Heiberger and Erich Neuwirth to be published by Springer in August 2009.

Documents

1 Graphical Approaches to the Analysis of Safety Data from ...Graphical Approaches to the Analysis of Safety Data from Clinical Trials Richard M. Heiberger 2 I spent a research leave