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Life table analysis of the effectiveness of contraceptive methods using an APL computer program
LIFE TABLE ANALYSIS OF THE EFFECTIVENESS OF CONTRACEPTIVE METHODS USING AN APL COMPUTER PROGRAM
DONNAL. COOPER Depurtment
qf Obstetrics
and Gynecology. Los Ange/es,
University Calif;>rnia
of’Southern Calffornia 90033 (USA)
School
qf Medicine,
and JAMESWINTER Department
of Radiological
Sciences, Unirrrsirt of Califbmia Los Anples, Caljfbrnia 90024
Los Angeles
School
qf Medicine,
( USA)
(Received: 8 December. 1976)
SUMMARY
An APL computer program has been del:eloped to perform life table analysis without the tedium and error associated with manual computation. Life table analysis is proposed as the standard method of reporting and analysing the effectireness of contraceptive methods of all types.
SOMMAIRE
Unprogramme en APLpermet d’htablir les tables de mortalit& en Pvitant les erreurs inhirentes 6 la prockdure manuelle. La table de mortalit est propoke comme mPthode standard pour rapporter les constquences des mo_vens contraceptlfs.
INTRODUCTION
The use of the life table method of analysis has become the standard For reporting the effectiveness of contraceptive methods as expressed by net cumulative termination rates per 100 women per year. The method for calculating termination 1 M. J. Bio-Medical Computing (9) (1978)--,(y Applied Science Publishers Ltd. England, 1978 Printed in Great Britain
2
DONNA
L. COOPER, JAMES WINTER
rates for intra-uterine contraceptive devices has been described by Tietze and Lewit (1973). This method allows the investigator to analyse data by a series of small calculations. Unfortunately, the total number of arithmetic operations is quite large so that the actual calculation of the life table is a long, tedious, manual process even when a calculator is used. The chance for human error is great and correction of an error or updating with new data is prohibitively time consuming.
METHODS
An APL computer program has been developed that automatically calculates the life table analysis from the raw data according to the methods of Tietze and Lewit (1973). This computer program can be used by inexpensive telephone access of a remote typewriter terminal to a time-shared computer. The information necessary for the life table analysis is supplied through a dialogue with the computer. An example of the computer dialogue in a study of the TCU 300 is given below. The computer inquires NAME OF STUDY and the investigator types TCU-300 NULLIPAROUS The computer requests the START-UP DATE and January 1, 1973 is entered as 10173 Next the computer requests the CUT-OFF DATE and January 31, 1975 is entered as 13175 Dates are entered as month day year without punctuation or separation. The computer calculates 25 MONTH STUDY DURATION and then requests the NUMBER INSERTED DURING EACH CALENDAR MONTH (IN CHRONOLOGICAL ORDER) The investigator enters 3734465677536OOOOOOOOOOOOOOoOOOo for each of the twenty-five months. The computer then acknowledges 363 TOTAL INSERTIONS 25 MONTHS WERE ENTERED and then requests entry of the list of terminations FOR EACH PATIENT TERMINATED ENTER:
CONTRACEPTIVE
PATIENT
I 11002 11013
METHODS
STUDY NUMBER DATE OF INSERTION DATE OF TERMINATION CAUSE FOR TERMINATION
I 10273 10573
1 31874 40973
4 5 9
where the cause for termination is coded as follows: 1 PREGNANCY 2 EXPULSION @ 3 PAIN/BLEEDING 4 OTHER MEDICAL 5 PLAN PREGNANCY 6 OTHER PERSONAL 7 INVESTIGATORS CHOICE 8 RELEASE FROM STUDY 9 LOST TO FOLLOW-UP After all terminations are entered, the computer echoes back the terminations in order by patient study number, listing the insertion date, the termination date and the reason for termination in code number as well as in words to aid in checking the computer list against the original data (Table 1). TABLE TERMINATIONS
TCU300 Patient number
Insertion date
11002 11012 11013 11015 I1019 11034 11038 11039 11041 11046 11047 11051 11052 11053 11054 I1066
10273 10473 10573 10973 11073 11873 12373 12373 12373 12573 12673 12673 12973 12973 11273 20273
1 BY PATIENT
NULLIPAROUS
Termination date ______ 31874 92774 40973 10973 11073 10675 31573 73074 21974 51573 43073 20573 13173 30873 53073 80973
Reason for termination 5 2 9 9 9 5 3 4 3 3 9 2 2 3 9 5
Plan pregnancy Expulsion Lost to follow-up Lost to follow-up Lost to follow-up Plan pregnancy Pain/bleeding Other medical Pain/bleeding Pain/bleeding Lost to follow-up Expulsion Expulsion Pain/bleeding Lost to follow-up Plan pregnancy
4
DONNA
L. COOPER,
JAMES
WINTER
The life table analysis is then computed by ordinal month and the following six tables are printed out. TERMINATIONS CUMULATIVE TERMINATIONS WOMEN MONTHS OF USE NET CUMULATIVE TERMINATION 95 % CONFIDENCE UPPER LIMIT 95 % CONFIDENCE LOWER LIMIT
RATES PER 100 WOMEN
The first four of the above tables are illustrated (Tables 2-5). The 95 % confidence limits are printed in the same format as Table 5. The computer program was implemented on an IBM 360 Model 91 Computer using the APL*PLUS time-sharing system. The computer cost consisted of: (1) connect time (approximately $4 per hour)-the time the computer was con&ted to the typewriter terminal for entering the raw data, (2) computer (CPU) time (approximately $0.35/second) and (3) printing charges (approximately $0.50)---the use of a high speed line printer for printing the tables. Equivalent commercial computer rates are approximately triple those shown. A typical study of 300 patients with 100 terminations usually takes less than 1 hour connect time and less than 10 seconds CPU time to calculate the life table analysis for a total computer cost of approximately $8. Use of the computer in this way makes efficient use of staff time, yet allows freedom from calculation errors, and the ability to make later entries (additions or corrections) in a few minutes since both the program and the previously entered data are stored for later use. The life table analysis program calculates the duration of contraceptive use in ordinal months from the entered actual dates of insertion and termination. This feature allows combin.ation of studies done at the same or different times since it uses the ordinal month rather than the calendar month as a base line. In practice this means that termination rates for nulliparous and multiparous users may be expressed separately or combined, or that termination rates for users of a particular device in several different studies may be expressed separately or combined. The raw data for each study is entered once but the life table analysis may be run easily on any combination of studies.
RESULTS
The APL computer program was verified using the illustrative data utilised by Tietze and Lewit (1973) as an example for performing manual calculations of life table analysis and gave the same results. The program has been successfully used to perform the life table analysis for two comparative studies of intra-uterine devices
Pregnancy (1)
:
0 0 0
0
02 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0
Ordinal month
:
3 4 5
61
; 10 11 12 13 14 15 16
11 18 19 20 21 22 23 24 25
0 0 0
0 0 0 :, :, 0 0 0 0 0
02
3 1 0 0
1
0 0 2
42 3 4
0 4
3 3 3
:,
Pain or bleeding (3)
0 2 0”
0
4 0 0
41
Expulsion (2)
0 0 0 0 0 0
1
1
2 0 0 3 1 0 0 1 0
1
x 0 0
i 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 1 0 0 0 0 0 0 0 0 0 0
; 0 1 1
: 1 1 1 2 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0
8 0
0 0 0 0 0 0 0 0 0 0
1 0 2 0 0 2 0 8 0 0 0
0 0
(8)
0 0 0 0 2 0 2
Released
Investigator’s cho-ice (7)
Other personal (6)
NULLIPAROUS
Plan pregnancy (5)
TCU300 Other medical (4) 0
TABLE 2 TERMINATIONS
13 1 1 7 4 2 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0
Lost to follow-up (9)
: 0 2 0 0 1 0
: 4 3 4
t
i 9 7
21 8 10 10 9 5
All causes
:: 22 23 24 25
1 2 3 4 5 6 I 8 9 10 11 12 13 14 15 16 17 18 19
month
: 3
: 3
z
: 3 3 3
0 2 3 3 3
Pregnancy (1)
; 9 9 11 11 11 12 12 12 14 14 14 14 14 15 14 15 15 15
4 5 9 9 9
Expulsion (2)
2 40 40 40 40
3 9 12 15 18 18 22 26 28 31 31 33 36 37 37 37 39 39 40
Pain or bleeding (3)
8 0 1 2 4 4 4 7 8 8 8 9 9 10 11 12 12 12 12 12 12 12
0 0
Other medical (4) 0 0 0 0 2 2 4 5 7 8 9 10 12 12 13 14 15 15 16 16 16 16 16 17 17 :: 12 12 12 12
1 1 3 3 3 5 5 5 7 I 8 9 10 11 11 11 11 11 11
Other personal (6)
NULLIPAROUS
Plan pregnancy (5)
TCU300
3
TERMINATIONS
TABLE CUMULATIVE
1
0 1 1
0
0 0 0 0 0
0 0
8 0
0 0
Investigator’s choice (7)
0 0 0
0 0
: 0 0 0 0
0 0 0 0 0
0 0 0
0 0 0 0 0
0
Released (8)
29 30 31 31 32 33 33 33 34 34 34 34 34 34 34 34 34 34 34
:i
13 14 15 22
Lost ro follow-up (9)
21 29 39 49 58 63 71 79 88 95 101 107 114 116 120 123 127 128 131 131 133 133 133 134 134
All causes
CONTRACEPTIVE
7
METHODS
TABLE 4 WOMEN
MONTHS
TCU300
OF USE
NULLIPAROUS
Ordinal
Active
Women months
Total women
month
users
of use
months
9 IO I1 12 13 14 15 16 17 18 19 20 21 22 23 24 25
342 334 324 314 305 300 292 284 275 268 262 256 249 247 243 240 236 235 232 232 230 230 230 229 229
352.5 338.0 329.0 319.0 309.5 302.5 296.0 288.0 279.5 271.5 265.0 259.0 252.5 248.0 245.0 241.5 238.0 235.5 212.5 170.5 126.0 84.0 55.0 32.5 11.0
352.5 690.5 1019.5 1338.5 1648.0 1950.5 2246.5 2534.5 2814.0 3085.5 3350.5 3609.5 3862.0 4110.0 4355.0 4596.5 4834.5 5070.0 5282.5 5453.0 5579.0 5663.0 5718.0 5750.5 5161.5
(Cooper et al., 1975; Cooper et al., 1976) as well as to provide updated analyses for subsequent monitoring of the progress of these and more recent studies.
DISCUSSION
In his survey of the literature, Faundes (1975) found that 33 of 53 studies of intrauterine devices used the life table method of analysis but only 7 of 100 clinical studies of other contraceptive methods did so. We agree with Faundes’ recommendation that life table analysis be used to analyse data from all clinical studies of new contraceptive methods. However, a major disincentive for using life table analysis has been the tedium of the calculations. The automated approach described here relieves the tedium of manually calculating life table analysis and makes the use of life table analysis easily performed for all clinical contraceptive studies. An appropriate standardised classification of causes of termination (use and non-use related) is needed for each type of contraceptive method analogous to the classification of terminations currently in use for intra-uterine devices. Faundes recommends the classification: pregnancy, termination for medical reasons and
DONNA L. COOPER,
8
JAMES WINTER
TABLE 5 NET CUMULATIVE
TERMINATION
TCU300 Ordinal
month
Pregnancy (1)
: 3 4 5 6 I 8 9 10 11 12 13 14 15 16 11 18 19 20 21 ;: 24 25
PER 100 WOMEN
Expulsion (2)
Pain or bleeding (3)
Other medical (4)
Plan pregnancy (5)
1,122 1,408 2,557 2.557 2.557 2.551 2.551 2.551 2.557 3.162 3.162 3.162 3468 3.468 3.468 4,083 4.083 4.083 4.083 4.083 4.644 4.644 4.644 4.644 4644
0,842 2,559 3,420 4,292 5.180 5.180 6.381 7.586 8.191 9.099 9.099 9,708 10.624 10.929 10.929 10,929 11.545 11.545 11.883 11.883 11.883 11.883 11.883 11.883 11.883
0.000 0.000 0.000 0~000 0.000 0.299 0.599
0.000 0.000 0.000 0.000
0.000 0.000 0~000 0~000 0~000 0~000 0~000 0~000 0.605 0.908 0.908 0.908 0.908 0.908 0.908 0.908 0.908 0,908 0,908 0,908 0,908 0.908 0.908 0.908 0.908
RATES
NULLIPAROUS
1.202 1.202 1.202 2.112 2.416 2,416 2,416 2.123 2.123 3.031 3.338 3.67’6 3.676 3.616 3.676 3,676 3.676 3.676
0.592 0.592 1,192 I.493 2,098 2.401 2.704 3.009 3.619 3.619 3.926 4.234 4,541 4,541 4,879 4.879 4.879 4.879 4.879 7.006 7.006
Other personal (6)
0.281 0.281 0.855 0,855 0,855 1,452 1.452 1.452 2,057 2.057 2.360 2.665 2.970 3.215 3.275 3,215 3,215 3,215 3.215 3.215 3.837 3.837 3.837 3.837 3.831
All causes
2.244 4.248 6.832 7.704 9.183 10.079 12.181 14.290 16.708 18.829 20,346 21,869 24,005 24.616 25.228 26.152 27.382 27.690 28.704 28.704 29,827 29.827 29.821 31.953 31.953
termination for personal reasons as use related terminations and termination at investigator’s choice, release from study and lost to follow up as non-use related terminations, with additional sub-categories as needed. The computer program described here can be used for such studies with only minor modifications to accommodate the differences in column titles in the computer print out. The rapid development of contraceptive methods requires accurate and rapid reporting of their effectiveness both before and after their release for widespread use. It is hoped that the development of this APL computer program for life table analysis will hasten and expand that reporting especially among investigators not already using a computer system.
APPENDIX
The portion of the APL program that performs the actual life table analysis is illustrated below. Information concerning the availability of the complete program can be obtained from the authors.
CONTRACEPTIVE
5;;
V LTl : LLH
InEU AlldItWS COPIRIGBT
c33
n
141 CSI
n c n F
:t: [El
n i
C93
n
Cl01 n Cl11 n ii;;
,”
Cl41
n
Cl51 cl63 Cl71
METHODS
tC) 1976 BY J.
WINTER. M.D.
= NUMBER CONTINUIIOG = TOTAL RONwUSE RELATED TERMINATIORS USE RELATED TBRMIRATIORS BY CAUSE HORTES OF USE ” = VOMAN :: : NUMBER ENTERING 3 = CORRECTED MIDMONTR N D = RUMEER OF USE RELATED TERHIRATIONS P = MORTRLY CUMULATIVE CORTIRUATIOR RATE DISCORTIRUATIOR/lOO gaP = PERCERT CUMULATIVB QQ BY CAUSE
PATIENTS
=
~~+lOO~l~P+~\l-Dt~~(~~+\(1t~),-1+~F+C+D~+~~~-(~+F)t2 WN-(C+D+F)tP ~+l00~+\A~~pA)p(l,-l+P~t~ V
ACKNOWLEDGEMENTS
Computing assistance was obtained from the Campus Computing Network, University of California, Los Angeles. Dr Winter was supported by the James Picker Foundation.
REFERENCES
COOPER,D. L., ISRAEL,R. and MISHELL,D. R. JR., Randomized comparative study ofthe Copper T 300, Dalkon Shield and Shell Loop in parous women. Obsfet. Gynec., 45 (1975) pp. 569-73. COOPER,D. L., MILLEN,A. K.‘and MISHELL,D. R. JR., The Copper T 220C: A new long-acting copper intrauterine contraceptive device, Amer. 1. Obsret. Gynec., 124(1976) pp. 121-4. FAUNDES,A., Assessment of clinical testing methodology, Contraceprion, 11(1975) pp. 363-94. TIETZE, C. and LEWIT, S., Recommended procedures for the statistical evaluation of intrauterine contraception, Studies in Family Planning, 4 (1973) pp. 35-42.
DONNAL. COOPER Depurtment
qf Obstetrics
and Gynecology. Los Ange/es,
University Calif;>rnia
of’Southern Calffornia 90033 (USA)
School
qf Medicine,
and JAMESWINTER Department
of Radiological
Sciences, Unirrrsirt of Califbmia Los Anples, Caljfbrnia 90024
Los Angeles
School
qf Medicine,
( USA)
(Received: 8 December. 1976)
SUMMARY
An APL computer program has been del:eloped to perform life table analysis without the tedium and error associated with manual computation. Life table analysis is proposed as the standard method of reporting and analysing the effectireness of contraceptive methods of all types.
SOMMAIRE
Unprogramme en APLpermet d’htablir les tables de mortalit& en Pvitant les erreurs inhirentes 6 la prockdure manuelle. La table de mortalit est propoke comme mPthode standard pour rapporter les constquences des mo_vens contraceptlfs.
INTRODUCTION
The use of the life table method of analysis has become the standard For reporting the effectiveness of contraceptive methods as expressed by net cumulative termination rates per 100 women per year. The method for calculating termination 1 M. J. Bio-Medical Computing (9) (1978)--,(y Applied Science Publishers Ltd. England, 1978 Printed in Great Britain
2
DONNA
L. COOPER, JAMES WINTER
rates for intra-uterine contraceptive devices has been described by Tietze and Lewit (1973). This method allows the investigator to analyse data by a series of small calculations. Unfortunately, the total number of arithmetic operations is quite large so that the actual calculation of the life table is a long, tedious, manual process even when a calculator is used. The chance for human error is great and correction of an error or updating with new data is prohibitively time consuming.
METHODS
An APL computer program has been developed that automatically calculates the life table analysis from the raw data according to the methods of Tietze and Lewit (1973). This computer program can be used by inexpensive telephone access of a remote typewriter terminal to a time-shared computer. The information necessary for the life table analysis is supplied through a dialogue with the computer. An example of the computer dialogue in a study of the TCU 300 is given below. The computer inquires NAME OF STUDY and the investigator types TCU-300 NULLIPAROUS The computer requests the START-UP DATE and January 1, 1973 is entered as 10173 Next the computer requests the CUT-OFF DATE and January 31, 1975 is entered as 13175 Dates are entered as month day year without punctuation or separation. The computer calculates 25 MONTH STUDY DURATION and then requests the NUMBER INSERTED DURING EACH CALENDAR MONTH (IN CHRONOLOGICAL ORDER) The investigator enters 3734465677536OOOOOOOOOOOOOOoOOOo for each of the twenty-five months. The computer then acknowledges 363 TOTAL INSERTIONS 25 MONTHS WERE ENTERED and then requests entry of the list of terminations FOR EACH PATIENT TERMINATED ENTER:
CONTRACEPTIVE
PATIENT
I 11002 11013
METHODS
STUDY NUMBER DATE OF INSERTION DATE OF TERMINATION CAUSE FOR TERMINATION
I 10273 10573
1 31874 40973
4 5 9
where the cause for termination is coded as follows: 1 PREGNANCY 2 EXPULSION @ 3 PAIN/BLEEDING 4 OTHER MEDICAL 5 PLAN PREGNANCY 6 OTHER PERSONAL 7 INVESTIGATORS CHOICE 8 RELEASE FROM STUDY 9 LOST TO FOLLOW-UP After all terminations are entered, the computer echoes back the terminations in order by patient study number, listing the insertion date, the termination date and the reason for termination in code number as well as in words to aid in checking the computer list against the original data (Table 1). TABLE TERMINATIONS
TCU300 Patient number
Insertion date
11002 11012 11013 11015 I1019 11034 11038 11039 11041 11046 11047 11051 11052 11053 11054 I1066
10273 10473 10573 10973 11073 11873 12373 12373 12373 12573 12673 12673 12973 12973 11273 20273
1 BY PATIENT
NULLIPAROUS
Termination date ______ 31874 92774 40973 10973 11073 10675 31573 73074 21974 51573 43073 20573 13173 30873 53073 80973
Reason for termination 5 2 9 9 9 5 3 4 3 3 9 2 2 3 9 5
Plan pregnancy Expulsion Lost to follow-up Lost to follow-up Lost to follow-up Plan pregnancy Pain/bleeding Other medical Pain/bleeding Pain/bleeding Lost to follow-up Expulsion Expulsion Pain/bleeding Lost to follow-up Plan pregnancy
4
DONNA
L. COOPER,
JAMES
WINTER
The life table analysis is then computed by ordinal month and the following six tables are printed out. TERMINATIONS CUMULATIVE TERMINATIONS WOMEN MONTHS OF USE NET CUMULATIVE TERMINATION 95 % CONFIDENCE UPPER LIMIT 95 % CONFIDENCE LOWER LIMIT
RATES PER 100 WOMEN
The first four of the above tables are illustrated (Tables 2-5). The 95 % confidence limits are printed in the same format as Table 5. The computer program was implemented on an IBM 360 Model 91 Computer using the APL*PLUS time-sharing system. The computer cost consisted of: (1) connect time (approximately $4 per hour)-the time the computer was con&ted to the typewriter terminal for entering the raw data, (2) computer (CPU) time (approximately $0.35/second) and (3) printing charges (approximately $0.50)---the use of a high speed line printer for printing the tables. Equivalent commercial computer rates are approximately triple those shown. A typical study of 300 patients with 100 terminations usually takes less than 1 hour connect time and less than 10 seconds CPU time to calculate the life table analysis for a total computer cost of approximately $8. Use of the computer in this way makes efficient use of staff time, yet allows freedom from calculation errors, and the ability to make later entries (additions or corrections) in a few minutes since both the program and the previously entered data are stored for later use. The life table analysis program calculates the duration of contraceptive use in ordinal months from the entered actual dates of insertion and termination. This feature allows combin.ation of studies done at the same or different times since it uses the ordinal month rather than the calendar month as a base line. In practice this means that termination rates for nulliparous and multiparous users may be expressed separately or combined, or that termination rates for users of a particular device in several different studies may be expressed separately or combined. The raw data for each study is entered once but the life table analysis may be run easily on any combination of studies.
RESULTS
The APL computer program was verified using the illustrative data utilised by Tietze and Lewit (1973) as an example for performing manual calculations of life table analysis and gave the same results. The program has been successfully used to perform the life table analysis for two comparative studies of intra-uterine devices
Pregnancy (1)
:
0 0 0
0
02 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0
Ordinal month
:
3 4 5
61
; 10 11 12 13 14 15 16
11 18 19 20 21 22 23 24 25
0 0 0
0 0 0 :, :, 0 0 0 0 0
02
3 1 0 0
1
0 0 2
42 3 4
0 4
3 3 3
:,
Pain or bleeding (3)
0 2 0”
0
4 0 0
41
Expulsion (2)
0 0 0 0 0 0
1
1
2 0 0 3 1 0 0 1 0
1
x 0 0
i 0 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 1 0 0 0 0 0 0 0 0 0 0
; 0 1 1
: 1 1 1 2 0 1 1 1 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0
8 0
0 0 0 0 0 0 0 0 0 0
1 0 2 0 0 2 0 8 0 0 0
0 0
(8)
0 0 0 0 2 0 2
Released
Investigator’s cho-ice (7)
Other personal (6)
NULLIPAROUS
Plan pregnancy (5)
TCU300 Other medical (4) 0
TABLE 2 TERMINATIONS
13 1 1 7 4 2 1 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0
Lost to follow-up (9)
: 0 2 0 0 1 0
: 4 3 4
t
i 9 7
21 8 10 10 9 5
All causes
:: 22 23 24 25
1 2 3 4 5 6 I 8 9 10 11 12 13 14 15 16 17 18 19
month
: 3
: 3
z
: 3 3 3
0 2 3 3 3
Pregnancy (1)
; 9 9 11 11 11 12 12 12 14 14 14 14 14 15 14 15 15 15
4 5 9 9 9
Expulsion (2)
2 40 40 40 40
3 9 12 15 18 18 22 26 28 31 31 33 36 37 37 37 39 39 40
Pain or bleeding (3)
8 0 1 2 4 4 4 7 8 8 8 9 9 10 11 12 12 12 12 12 12 12
0 0
Other medical (4) 0 0 0 0 2 2 4 5 7 8 9 10 12 12 13 14 15 15 16 16 16 16 16 17 17 :: 12 12 12 12
1 1 3 3 3 5 5 5 7 I 8 9 10 11 11 11 11 11 11
Other personal (6)
NULLIPAROUS
Plan pregnancy (5)
TCU300
3
TERMINATIONS
TABLE CUMULATIVE
1
0 1 1
0
0 0 0 0 0
0 0
8 0
0 0
Investigator’s choice (7)
0 0 0
0 0
: 0 0 0 0
0 0 0 0 0
0 0 0
0 0 0 0 0
0
Released (8)
29 30 31 31 32 33 33 33 34 34 34 34 34 34 34 34 34 34 34
:i
13 14 15 22
Lost ro follow-up (9)
21 29 39 49 58 63 71 79 88 95 101 107 114 116 120 123 127 128 131 131 133 133 133 134 134
All causes
CONTRACEPTIVE
7
METHODS
TABLE 4 WOMEN
MONTHS
TCU300
OF USE
NULLIPAROUS
Ordinal
Active
Women months
Total women
month
users
of use
months
9 IO I1 12 13 14 15 16 17 18 19 20 21 22 23 24 25
342 334 324 314 305 300 292 284 275 268 262 256 249 247 243 240 236 235 232 232 230 230 230 229 229
352.5 338.0 329.0 319.0 309.5 302.5 296.0 288.0 279.5 271.5 265.0 259.0 252.5 248.0 245.0 241.5 238.0 235.5 212.5 170.5 126.0 84.0 55.0 32.5 11.0
352.5 690.5 1019.5 1338.5 1648.0 1950.5 2246.5 2534.5 2814.0 3085.5 3350.5 3609.5 3862.0 4110.0 4355.0 4596.5 4834.5 5070.0 5282.5 5453.0 5579.0 5663.0 5718.0 5750.5 5161.5
(Cooper et al., 1975; Cooper et al., 1976) as well as to provide updated analyses for subsequent monitoring of the progress of these and more recent studies.
DISCUSSION
In his survey of the literature, Faundes (1975) found that 33 of 53 studies of intrauterine devices used the life table method of analysis but only 7 of 100 clinical studies of other contraceptive methods did so. We agree with Faundes’ recommendation that life table analysis be used to analyse data from all clinical studies of new contraceptive methods. However, a major disincentive for using life table analysis has been the tedium of the calculations. The automated approach described here relieves the tedium of manually calculating life table analysis and makes the use of life table analysis easily performed for all clinical contraceptive studies. An appropriate standardised classification of causes of termination (use and non-use related) is needed for each type of contraceptive method analogous to the classification of terminations currently in use for intra-uterine devices. Faundes recommends the classification: pregnancy, termination for medical reasons and
DONNA L. COOPER,
8
JAMES WINTER
TABLE 5 NET CUMULATIVE
TERMINATION
TCU300 Ordinal
month
Pregnancy (1)
: 3 4 5 6 I 8 9 10 11 12 13 14 15 16 11 18 19 20 21 ;: 24 25
PER 100 WOMEN
Expulsion (2)
Pain or bleeding (3)
Other medical (4)
Plan pregnancy (5)
1,122 1,408 2,557 2.557 2.557 2.551 2.551 2.551 2.557 3.162 3.162 3.162 3468 3.468 3.468 4,083 4.083 4.083 4.083 4.083 4.644 4.644 4.644 4.644 4644
0,842 2,559 3,420 4,292 5.180 5.180 6.381 7.586 8.191 9.099 9.099 9,708 10.624 10.929 10.929 10,929 11.545 11.545 11.883 11.883 11.883 11.883 11.883 11.883 11.883
0.000 0.000 0.000 0~000 0.000 0.299 0.599
0.000 0.000 0.000 0.000
0.000 0.000 0~000 0~000 0~000 0~000 0~000 0~000 0.605 0.908 0.908 0.908 0.908 0.908 0.908 0.908 0.908 0,908 0,908 0,908 0,908 0.908 0.908 0.908 0.908
RATES
NULLIPAROUS
1.202 1.202 1.202 2.112 2.416 2,416 2,416 2.123 2.123 3.031 3.338 3.67’6 3.676 3.616 3.676 3,676 3.676 3.676
0.592 0.592 1,192 I.493 2,098 2.401 2.704 3.009 3.619 3.619 3.926 4.234 4,541 4,541 4,879 4.879 4.879 4.879 4.879 7.006 7.006
Other personal (6)
0.281 0.281 0.855 0,855 0,855 1,452 1.452 1.452 2,057 2.057 2.360 2.665 2.970 3.215 3.275 3,215 3,215 3,215 3.215 3.215 3.837 3.837 3.837 3.837 3.831
All causes
2.244 4.248 6.832 7.704 9.183 10.079 12.181 14.290 16.708 18.829 20,346 21,869 24,005 24.616 25.228 26.152 27.382 27.690 28.704 28.704 29,827 29.827 29.821 31.953 31.953
termination for personal reasons as use related terminations and termination at investigator’s choice, release from study and lost to follow up as non-use related terminations, with additional sub-categories as needed. The computer program described here can be used for such studies with only minor modifications to accommodate the differences in column titles in the computer print out. The rapid development of contraceptive methods requires accurate and rapid reporting of their effectiveness both before and after their release for widespread use. It is hoped that the development of this APL computer program for life table analysis will hasten and expand that reporting especially among investigators not already using a computer system.
APPENDIX
The portion of the APL program that performs the actual life table analysis is illustrated below. Information concerning the availability of the complete program can be obtained from the authors.
CONTRACEPTIVE
5;;
V LTl : LLH
InEU AlldItWS COPIRIGBT
c33
n
141 CSI
n c n F
:t: [El
n i
C93
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,”
Cl41
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METHODS
tC) 1976 BY J.
WINTER. M.D.
= NUMBER CONTINUIIOG = TOTAL RONwUSE RELATED TERMINATIORS USE RELATED TBRMIRATIORS BY CAUSE HORTES OF USE ” = VOMAN :: : NUMBER ENTERING 3 = CORRECTED MIDMONTR N D = RUMEER OF USE RELATED TERHIRATIONS P = MORTRLY CUMULATIVE CORTIRUATIOR RATE DISCORTIRUATIOR/lOO gaP = PERCERT CUMULATIVB QQ BY CAUSE
PATIENTS
=
~~+lOO~l~P+~\l-Dt~~(~~+\(1t~),-1+~F+C+D~+~~~-(~+F)t2 WN-(C+D+F)tP ~+l00~+\A~~pA)p(l,-l+P~t~ V
ACKNOWLEDGEMENTS
Computing assistance was obtained from the Campus Computing Network, University of California, Los Angeles. Dr Winter was supported by the James Picker Foundation.
REFERENCES
COOPER,D. L., ISRAEL,R. and MISHELL,D. R. JR., Randomized comparative study ofthe Copper T 300, Dalkon Shield and Shell Loop in parous women. Obsfet. Gynec., 45 (1975) pp. 569-73. COOPER,D. L., MILLEN,A. K.‘and MISHELL,D. R. JR., The Copper T 220C: A new long-acting copper intrauterine contraceptive device, Amer. 1. Obsret. Gynec., 124(1976) pp. 121-4. FAUNDES,A., Assessment of clinical testing methodology, Contraceprion, 11(1975) pp. 363-94. TIETZE, C. and LEWIT, S., Recommended procedures for the statistical evaluation of intrauterine contraception, Studies in Family Planning, 4 (1973) pp. 35-42.