Correlation between miRseq expression and clinical features
Prostate Adenocarcinoma (Primary solid tumor)
02 April 2015  |  analyses__2015_04_02
Maintainer Information
Citation Information
doi:10.7908/C1SB44V1
Maintained by Juok Cho (Broad Institute)
Cite as Broad Institute TCGA Genome Data Analysis Center (2015): Correlation between miRseq expression and clinical features. Broad Institute of MIT and Harvard. doi:10.7908/C1SB44V1
Overview
Introduction

This pipeline uses various statistical tests to identify miRs whose log2 expression levels correlated to selected clinical features.

Summary

Testing the association between 469 miRs and 14 clinical features across 484 samples, statistically thresholded by P value < 0.05 and Q value < 0.3, 12 clinical features related to at least one miRs.

  • 30 miRs correlated to 'YEARS_TO_BIRTH'.

    • HSA-MIR-627 ,  HSA-MIR-425 ,  HSA-MIR-132 ,  HSA-MIR-34A ,  HSA-MIR-26B ,  ...

  • 30 miRs correlated to 'PATHOLOGY_T_STAGE'.

    • HSA-MIR-133A-1 ,  HSA-MIR-30A ,  HSA-MIR-3676 ,  HSA-MIR-222 ,  HSA-MIR-582 ,  ...

  • 30 miRs correlated to 'PATHOLOGY_N_STAGE'.

    • HSA-MIR-133A-2 ,  HSA-MIR-21 ,  HSA-MIR-133B ,  HSA-MIR-1-2 ,  HSA-MIR-217 ,  ...

  • 13 miRs correlated to 'HISTOLOGICAL_TYPE'.

    • HSA-MIR-423 ,  HSA-MIR-182 ,  HSA-MIR-152 ,  HSA-MIR-183 ,  HSA-MIR-326 ,  ...

  • 30 miRs correlated to 'COMPLETENESS_OF_RESECTION'.

    • HSA-MIR-425 ,  HSA-MIR-1274B ,  HSA-MIR-98 ,  HSA-MIR-891A ,  HSA-MIR-655 ,  ...

  • 30 miRs correlated to 'NUMBER_OF_LYMPH_NODES'.

    • HSA-MIR-133A-2 ,  HSA-MIR-21 ,  HSA-MIR-133B ,  HSA-MIR-1-2 ,  HSA-MIR-133A-1 ,  ...

  • 30 miRs correlated to 'GLEASON_SCORE_COMBINED'.

    • HSA-MIR-133B ,  HSA-MIR-217 ,  HSA-MIR-133A-2 ,  HSA-MIR-21 ,  HSA-MIR-133A-1 ,  ...

  • 30 miRs correlated to 'GLEASON_SCORE_PRIMARY'.

    • HSA-MIR-133B ,  HSA-MIR-217 ,  HSA-MIR-133A-2 ,  HSA-MIR-133A-1 ,  HSA-MIR-1-2 ,  ...

  • 30 miRs correlated to 'GLEASON_SCORE_SECONDARY'.

    • HSA-MIR-133B ,  HSA-MIR-592 ,  HSA-MIR-133A-2 ,  HSA-MIR-217 ,  HSA-MIR-21 ,  ...

  • 30 miRs correlated to 'GLEASON_SCORE'.

    • HSA-MIR-217 ,  HSA-MIR-133B ,  HSA-MIR-133A-2 ,  HSA-MIR-21 ,  HSA-MIR-1-2 ,  ...

  • 30 miRs correlated to 'PSA_RESULT_PREOP'.

    • HSA-MIR-145 ,  HSA-MIR-133A-1 ,  HSA-MIR-1-2 ,  HSA-MIR-222 ,  HSA-MIR-221 ,  ...

  • 30 miRs correlated to 'PSA_VALUE'.

    • HSA-MIR-135A-1 ,  HSA-MIR-582 ,  HSA-MIR-155 ,  HSA-MIR-330 ,  HSA-MIR-30A ,  ...

  • No miRs correlated to 'DAYS_TO_DEATH_OR_LAST_FUP', and 'RACE'.

Results
Overview of the results

Complete statistical result table is provided in Supplement Table 1

Table 1.  Get Full Table This table shows the clinical features, statistical methods used, and the number of miRs that are significantly associated with each clinical feature at P value < 0.05 and Q value < 0.3.

Clinical feature Statistical test Significant miRs Associated with                 Associated with
DAYS_TO_DEATH_OR_LAST_FUP Cox regression test   N=0        
YEARS_TO_BIRTH Spearman correlation test N=30 older N=19 younger N=11
PATHOLOGY_T_STAGE Spearman correlation test N=30 higher stage N=7 lower stage N=23
PATHOLOGY_N_STAGE Wilcoxon test N=30 n1 N=30 n0 N=0
HISTOLOGICAL_TYPE Wilcoxon test N=13 prostate adenocarcinoma acinar type N=13 prostate adenocarcinoma other subtype N=0
COMPLETENESS_OF_RESECTION Kruskal-Wallis test N=30        
NUMBER_OF_LYMPH_NODES Spearman correlation test N=30 higher number_of_lymph_nodes N=12 lower number_of_lymph_nodes N=18
GLEASON_SCORE_COMBINED Spearman correlation test N=30 higher score N=13 lower score N=17
GLEASON_SCORE_PRIMARY Spearman correlation test N=30 higher score N=13 lower score N=17
GLEASON_SCORE_SECONDARY Spearman correlation test N=30 higher score N=17 lower score N=13
GLEASON_SCORE Spearman correlation test N=30 higher score N=12 lower score N=18
PSA_RESULT_PREOP Spearman correlation test N=30 higher psa_result_preop N=13 lower psa_result_preop N=17
PSA_VALUE Spearman correlation test N=30 higher psa_value N=9 lower psa_value N=21
RACE Kruskal-Wallis test   N=0        
Clinical variable #1: 'DAYS_TO_DEATH_OR_LAST_FUP'

No miR related to 'DAYS_TO_DEATH_OR_LAST_FUP'.

Table S1.  Basic characteristics of clinical feature: 'DAYS_TO_DEATH_OR_LAST_FUP'

DAYS_TO_DEATH_OR_LAST_FUP Duration (Months) 0.7-165.2 (median=26.4)
  censored N = 475
  death N = 8
     
  Significant markers N = 0
Clinical variable #2: 'YEARS_TO_BIRTH'

30 miRs related to 'YEARS_TO_BIRTH'.

Table S2.  Basic characteristics of clinical feature: 'YEARS_TO_BIRTH'

YEARS_TO_BIRTH Mean (SD) 60.93 (6.8)
  Significant markers N = 30
  pos. correlated 19
  neg. correlated 11
List of top 10 miRs differentially expressed by 'YEARS_TO_BIRTH'

Table S3.  Get Full Table List of top 10 miRs significantly correlated to 'YEARS_TO_BIRTH' by Spearman correlation test

SpearmanCorr corrP Q
HSA-MIR-627 0.1962 2.95e-05 0.0138
HSA-MIR-425 0.1542 0.0007682 0.109
HSA-MIR-132 -0.1536 0.0008059 0.109
HSA-MIR-34A 0.1518 0.0009275 0.109
HSA-MIR-26B 0.1467 0.001381 0.13
HSA-MIR-96 0.1428 0.001843 0.143
HSA-MIR-181D -0.1409 0.00213 0.143
HSA-MIR-335 0.1356 0.003129 0.183
HSA-MIR-339 0.1318 0.004089 0.213
HSA-MIR-590 0.1251 0.006444 0.229
Clinical variable #3: 'PATHOLOGY_T_STAGE'

30 miRs related to 'PATHOLOGY_T_STAGE'.

Table S4.  Basic characteristics of clinical feature: 'PATHOLOGY_T_STAGE'

PATHOLOGY_T_STAGE Mean (SD) 2.63 (0.52)
  N
  T2 188
  T3 284
  T4 9
     
  Significant markers N = 30
  pos. correlated 7
  neg. correlated 23
List of top 10 miRs differentially expressed by 'PATHOLOGY_T_STAGE'

Table S5.  Get Full Table List of top 10 miRs significantly correlated to 'PATHOLOGY_T_STAGE' by Spearman correlation test

SpearmanCorr corrP Q
HSA-MIR-133A-1 -0.2991 2.136e-11 1e-08
HSA-MIR-30A -0.2917 6.865e-11 1.61e-08
HSA-MIR-3676 -0.2683 3.177e-09 4.27e-07
HSA-MIR-222 -0.2649 3.64e-09 4.27e-07
HSA-MIR-582 -0.2416 8.161e-08 6.63e-06
HSA-MIR-221 -0.2406 9.262e-08 6.63e-06
HSA-MIR-217 0.24 9.894e-08 6.63e-06
HSA-MIR-133B -0.2386 1.261e-07 7.39e-06
HSA-MIR-574 -0.2282 4.207e-07 2.19e-05
HSA-MIR-378C -0.2254 5.855e-07 2.69e-05
Clinical variable #4: 'PATHOLOGY_N_STAGE'

30 miRs related to 'PATHOLOGY_N_STAGE'.

Table S6.  Basic characteristics of clinical feature: 'PATHOLOGY_N_STAGE'

PATHOLOGY_N_STAGE Labels N
  N0 339
  N1 76
     
  Significant markers N = 30
  Higher in N1 30
  Higher in N0 0
List of top 10 miRs differentially expressed by 'PATHOLOGY_N_STAGE'

Table S7.  Get Full Table List of top 10 miRs differentially expressed by 'PATHOLOGY_N_STAGE'

W(pos if higher in 'N1') wilcoxontestP Q AUC
HSA-MIR-133A-2 7976 5.647e-07 0.000221 0.6839
HSA-MIR-21 17461 1.268e-06 0.000221 0.6777
HSA-MIR-133B 8346 1.827e-06 0.000221 0.6751
HSA-MIR-1-2 8378 1.886e-06 0.000221 0.6748
HSA-MIR-217 17102 8.016e-06 0.000752 0.6638
HSA-MIR-133A-1 8761 1.301e-05 0.00102 0.66
HSA-MIR-184 5217 2.079e-05 0.00124 0.6776
HSA-MIR-139 8879 2.284e-05 0.00124 0.6554
HSA-MIR-3676 8588 2.379e-05 0.00124 0.6561
HSA-MIR-221 9092 6.078e-05 0.00285 0.6471
Clinical variable #5: 'HISTOLOGICAL_TYPE'

13 miRs related to 'HISTOLOGICAL_TYPE'.

Table S8.  Basic characteristics of clinical feature: 'HISTOLOGICAL_TYPE'

HISTOLOGICAL_TYPE Labels N
  PROSTATE ADENOCARCINOMA OTHER SUBTYPE 15
  PROSTATE ADENOCARCINOMA ACINAR TYPE 469
     
  Significant markers N = 13
  Higher in PROSTATE ADENOCARCINOMA ACINAR TYPE 13
  Higher in PROSTATE ADENOCARCINOMA OTHER SUBTYPE 0
List of top 10 miRs differentially expressed by 'HISTOLOGICAL_TYPE'

Clinical variable #6: 'COMPLETENESS_OF_RESECTION'

30 miRs related to 'COMPLETENESS_OF_RESECTION'.

Table S10.  Basic characteristics of clinical feature: 'COMPLETENESS_OF_RESECTION'

COMPLETENESS_OF_RESECTION Labels N
  R0 310
  R1 140
  R2 5
  RX 15
     
  Significant markers N = 30
List of top 10 miRs differentially expressed by 'COMPLETENESS_OF_RESECTION'

Table S11.  Get Full Table List of top 10 miRs differentially expressed by 'COMPLETENESS_OF_RESECTION'

kruskal_wallis_P Q
HSA-MIR-425 6.234e-05 0.0292
HSA-MIR-1274B 0.0003633 0.0645
HSA-MIR-98 0.0004124 0.0645
HSA-MIR-891A 0.0006739 0.079
HSA-MIR-655 0.001418 0.101
HSA-MIR-653 0.001529 0.101
HSA-MIR-96 0.002052 0.101
HSA-MIR-301A 0.00213 0.101
HSA-MIR-16-2 0.002255 0.101
HSA-MIR-3676 0.002593 0.101
Clinical variable #7: 'NUMBER_OF_LYMPH_NODES'

30 miRs related to 'NUMBER_OF_LYMPH_NODES'.

Table S12.  Basic characteristics of clinical feature: 'NUMBER_OF_LYMPH_NODES'

NUMBER_OF_LYMPH_NODES Mean (SD) 0.45 (1.4)
  Significant markers N = 30
  pos. correlated 12
  neg. correlated 18
List of top 10 miRs differentially expressed by 'NUMBER_OF_LYMPH_NODES'

Table S13.  Get Full Table List of top 10 miRs significantly correlated to 'NUMBER_OF_LYMPH_NODES' by Spearman correlation test

SpearmanCorr corrP Q
HSA-MIR-133A-2 -0.2699 6.135e-08 2.59e-05
HSA-MIR-21 0.2626 1.103e-07 2.59e-05
HSA-MIR-133B -0.2574 2.059e-07 3.22e-05
HSA-MIR-1-2 -0.2481 5.527e-07 6.48e-05
HSA-MIR-133A-1 -0.2344 2.329e-06 0.000218
HSA-MIR-217 0.2315 3.139e-06 0.000245
HSA-MIR-139 -0.2258 5.549e-06 0.000372
HSA-MIR-221 -0.224 6.614e-06 0.000388
HSA-MIR-184 -0.2402 1.319e-05 0.000688
HSA-MIR-3676 -0.215 1.845e-05 0.000865
Clinical variable #8: 'GLEASON_SCORE_COMBINED'

30 miRs related to 'GLEASON_SCORE_COMBINED'.

Table S14.  Basic characteristics of clinical feature: 'GLEASON_SCORE_COMBINED'

GLEASON_SCORE_COMBINED Mean (SD) 7.55 (1)
  Significant markers N = 30
  pos. correlated 13
  neg. correlated 17
List of top 10 miRs differentially expressed by 'GLEASON_SCORE_COMBINED'

Table S15.  Get Full Table List of top 10 miRs significantly correlated to 'GLEASON_SCORE_COMBINED' by Spearman correlation test

SpearmanCorr corrP Q
HSA-MIR-133B -0.4073 1.099e-20 5.16e-18
HSA-MIR-217 0.4002 4.863e-20 1.14e-17
HSA-MIR-133A-2 -0.3957 2.693e-19 4.21e-17
HSA-MIR-21 0.3649 1.078e-16 1.11e-14
HSA-MIR-133A-1 -0.3645 1.178e-16 1.11e-14
HSA-MIR-1-2 -0.3532 1.145e-15 8.95e-14
HSA-MIR-592 0.3544 7.616e-14 5.1e-12
HSA-MIR-221 -0.3155 1.195e-12 7.01e-11
HSA-MIR-3676 -0.3161 1.746e-12 9.1e-11
HSA-MIR-708 0.3095 3.32e-12 1.56e-10
Clinical variable #9: 'GLEASON_SCORE_PRIMARY'

30 miRs related to 'GLEASON_SCORE_PRIMARY'.

Table S16.  Basic characteristics of clinical feature: 'GLEASON_SCORE_PRIMARY'

GLEASON_SCORE_PRIMARY Mean (SD) 3.69 (0.68)
  Score N
  2 1
  3 205
  4 220
  5 58
     
  Significant markers N = 30
  pos. correlated 13
  neg. correlated 17
List of top 10 miRs differentially expressed by 'GLEASON_SCORE_PRIMARY'

Table S17.  Get Full Table List of top 10 miRs significantly correlated to 'GLEASON_SCORE_PRIMARY' by Spearman correlation test

SpearmanCorr corrP Q
HSA-MIR-133B -0.3677 7.004e-17 3.28e-14
HSA-MIR-217 0.3533 1.135e-15 2.66e-13
HSA-MIR-133A-2 -0.3533 1.936e-15 3.03e-13
HSA-MIR-133A-1 -0.3425 9.088e-15 9.97e-13
HSA-MIR-1-2 -0.3417 1.063e-14 9.97e-13
HSA-MIR-3676 -0.3318 1.149e-13 8.98e-12
HSA-MIR-221 -0.3218 3.99e-13 2.67e-11
HSA-MIR-21 0.3098 3.141e-12 1.84e-10
HSA-MIR-222 -0.3029 9.975e-12 5.2e-10
HSA-MIR-425 0.2982 2.153e-11 1.01e-09
Clinical variable #10: 'GLEASON_SCORE_SECONDARY'

30 miRs related to 'GLEASON_SCORE_SECONDARY'.

Table S18.  Basic characteristics of clinical feature: 'GLEASON_SCORE_SECONDARY'

GLEASON_SCORE_SECONDARY Mean (SD) 3.86 (0.68)
  Score N
  3 150
  4 251
  5 83
     
  Significant markers N = 30
  pos. correlated 17
  neg. correlated 13
List of top 10 miRs differentially expressed by 'GLEASON_SCORE_SECONDARY'

Table S19.  Get Full Table List of top 10 miRs significantly correlated to 'GLEASON_SCORE_SECONDARY' by Spearman correlation test

SpearmanCorr corrP Q
HSA-MIR-133B -0.2295 3.521e-07 7.18e-05
HSA-MIR-592 0.2424 5.118e-07 7.18e-05
HSA-MIR-133A-2 -0.2272 5.461e-07 7.18e-05
HSA-MIR-217 0.2244 6.127e-07 7.18e-05
HSA-MIR-21 0.2082 3.836e-06 0.00036
HSA-MIR-133A-1 -0.191 2.336e-05 0.00183
HSA-MIR-1-2 -0.1708 0.00016 0.0107
HSA-MIR-708 0.1633 0.0003097 0.0163
HSA-MIR-135A-2 -0.1642 0.0003126 0.0163
HSA-MIR-103-1 0.1539 0.0006801 0.0319
Clinical variable #11: 'GLEASON_SCORE'

30 miRs related to 'GLEASON_SCORE'.

Table S20.  Basic characteristics of clinical feature: 'GLEASON_SCORE'

GLEASON_SCORE Mean (SD) 7.58 (1)
  Score N
  6 45
  7 245
  8 62
  9 130
  10 2
     
  Significant markers N = 30
  pos. correlated 12
  neg. correlated 18
List of top 10 miRs differentially expressed by 'GLEASON_SCORE'

Table S21.  Get Full Table List of top 10 miRs significantly correlated to 'GLEASON_SCORE' by Spearman correlation test

SpearmanCorr corrP Q
HSA-MIR-217 0.3954 1.459e-19 6.84e-17
HSA-MIR-133B -0.3775 9.037e-18 2.12e-15
HSA-MIR-133A-2 -0.3719 4.671e-17 7.3e-15
HSA-MIR-21 0.3564 6.069e-16 7.12e-14
HSA-MIR-1-2 -0.353 1.206e-15 1.13e-13
HSA-MIR-133A-1 -0.3483 2.966e-15 2.32e-13
HSA-MIR-221 -0.3254 2.114e-13 1.42e-11
HSA-MIR-592 0.3444 4.112e-13 2.41e-11
HSA-MIR-222 -0.3169 9.459e-13 4.93e-11
HSA-MIR-708 0.3137 1.635e-12 7.67e-11
Clinical variable #12: 'PSA_RESULT_PREOP'

30 miRs related to 'PSA_RESULT_PREOP'.

Table S22.  Basic characteristics of clinical feature: 'PSA_RESULT_PREOP'

PSA_RESULT_PREOP Mean (SD) 10.85 (12)
  Significant markers N = 30
  pos. correlated 13
  neg. correlated 17
List of top 10 miRs differentially expressed by 'PSA_RESULT_PREOP'

Table S23.  Get Full Table List of top 10 miRs significantly correlated to 'PSA_RESULT_PREOP' by Spearman correlation test

SpearmanCorr corrP Q
HSA-MIR-145 -0.2054 5.61e-06 0.00263
HSA-MIR-133A-1 -0.1839 4.971e-05 0.00731
HSA-MIR-1-2 -0.1838 5.028e-05 0.00731
HSA-MIR-222 -0.1815 6.239e-05 0.00731
HSA-MIR-221 -0.1694 0.0001892 0.0177
HSA-MIR-15B 0.167 0.0002349 0.0184
HSA-MIR-424 0.1625 0.0003461 0.0232
HSA-MIR-100 -0.1583 0.0004909 0.0275
HSA-MIR-205 -0.1567 0.0005705 0.0275
HSA-MIR-7-3 0.2007 0.0005857 0.0275
Clinical variable #13: 'PSA_VALUE'

30 miRs related to 'PSA_VALUE'.

Table S24.  Basic characteristics of clinical feature: 'PSA_VALUE'

PSA_VALUE Mean (SD) 1.08 (4.1)
  Significant markers N = 30
  pos. correlated 9
  neg. correlated 21
List of top 10 miRs differentially expressed by 'PSA_VALUE'

Table S25.  Get Full Table List of top 10 miRs significantly correlated to 'PSA_VALUE' by Spearman correlation test

SpearmanCorr corrP Q
HSA-MIR-135A-1 -0.2011 2.667e-05 0.0125
HSA-MIR-582 -0.172 0.0003407 0.072
HSA-MIR-155 0.1682 0.0004608 0.072
HSA-MIR-330 0.1583 0.0009851 0.0863
HSA-MIR-30A -0.1561 0.00116 0.0863
HSA-MIR-133A-1 -0.1544 0.001316 0.0863
HSA-MIR-148A -0.1542 0.001343 0.0863
HSA-MIR-150 0.1529 0.001472 0.0863
HSA-MIR-141 -0.1477 0.002132 0.111
HSA-MIR-145 -0.1425 0.003069 0.144
Clinical variable #14: 'RACE'

No miR related to 'RACE'.

Table S26.  Basic characteristics of clinical feature: 'RACE'

RACE Labels N
  ASIAN 2
  BLACK OR AFRICAN AMERICAN 7
  WHITE 146
     
  Significant markers N = 0
Methods & Data
Input

  • Expresson data file = PRAD-TP.miRseq_RPKM_log2.txt

  • Clinical data file = PRAD-TP.merged_data.txt

  • Number of patients = 484

  • Number of miRs = 469

  • Number of clinical features = 14

Selected clinical features

  • For clinical features selected for this analysis and their value conozzle.versions, please find a documentation on selected CDEs .

  • Survival time data

    • Survival time data is a combined value of days_to_death and days_to_last_followup. For each patient, it creates a combined value 'days_to_death_or_last_fup' using conversion process below.

      • if 'vital_status'==1(dead), 'days_to_last_followup' is always NA. Thus, uses 'days_to_death' value for 'days_to_death_or_fup'

      • if 'vital_status'==0(alive),

        • if 'days_to_death'==NA & 'days_to_last_followup'!=NA, uses 'days_to_last_followup' value for 'days_to_death_or_fup'

        • if 'days_to_death'!=NA, excludes this case in survival analysis and report the case.

      • if 'vital_status'==NA,excludes this case in survival analysis and report the case.

    • cf. In certain diesase types such as SKCM, days_to_death parameter is replaced with time_from_specimen_dx or time_from_specimen_procurement_to_death .

  • This analysis excluded clinical variables that has only NA values.

Survival analysis

For survival clinical features, Wald's test in univariate Cox regression analysis with proportional hazards model (Andersen and Gill 1982) was used to estimate the P values using the 'coxph' function in R. Kaplan-Meier survival curves were plot using the four quartile subgroups of patients based on expression levels

Correlation analysis

For continuous numerical clinical features, Spearman's rank correlation coefficients (Spearman 1904) and two-tailed P values were estimated using 'cor.test' function in R

Wilcoxon rank sum test (Mann-Whitney U test)

For two groups (mutant or wild-type) of continuous type of clinical data, wilcoxon rank sum test (Mann and Whitney, 1947) was applied to compare their mean difference using 'wilcox.test(continuous.clinical ~ as.factor(group), exact=FALSE)' function in R. This test is equivalent to the Mann-Whitney test.

Q value calculation

For multiple hypothesis correction, Q value is the False Discovery Rate (FDR) analogue of the P value (Benjamini and Hochberg 1995), defined as the minimum FDR at which the test may be called significant. We used the 'Benjamini and Hochberg' method of 'p.adjust' function in R to convert P values into Q values.

Download Results

In addition to the links below, the full results of the analysis summarized in this report can also be downloaded programmatically using firehose_get, or interactively from either the Broad GDAC website or TCGA Data Coordination Center Portal.

References
[1] Andersen and Gill, Cox's regression model for counting processes, a large sample study, Annals of Statistics 10(4):1100-1120 (1982)
[2] Spearman, C, The proof and measurement of association between two things, Amer. J. Psychol 15:72-101 (1904)
[3] Mann and Whitney, On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other, Annals of Mathematical Statistics 18 (1), 50-60 (1947)
[4] Benjamini and Hochberg, Controlling the false discovery rate: a practical and powerful approach to multiple testing, Journal of the Royal Statistical Society Series B 59:289-300 (1995)
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