Results II: Including transferred infants
7.4 Results for analysis of neonatal data
7.4.2 Weight distribution
Table 7.4 compares how the total weight across all infants is allocated to the different NNU levels, shown for the whole cohort and by survival status. More care was attributed
to higher level NNU, similarly to the analysis in section 2.3.2. In particular, infants that died were mostly allocated to neonatal intensive care units (NICUs) (consistent with section 2.3.4) but the differences were less strong for the First weighting. Otherwise, deaths were distributed fairly similarly across NNU levels for weightings, though there was slightly less care allocated to NICUs under Equal weighting. The WLOS weighting allocated the lowest proportion of survivors to NICUs compared with other weights and, correspondingly, the highest proportion for special care baby units (SCBUs) and local neonatal units (LNUs). The Beta3 weighting allocated the highest proportion of survivors to NICUs compared with other weights. There was no consistent pattern to the weights as more weight was placed at the beginning of stay (comparing Beta2, Beta3 and First ).
To show how the weight was distributed over the course of stay, table 7.5 compares how the total weight across all transferred infants is allocated to the first NNU, interim NNU(s) and last NNU they are treated in (infants only transferred once they will only have a first and last NNU). The LOS weighting places the most weight with the final NNU treating the infant. After the First weighting, the Beta3 and Beta2 weightings place the most weight on the first NNU, but the differences compared with the other weights are not large. Comparison of the LOS and WLOS weightings shows a difference for survivors, with the end of stay downweighted for the latter.
7.4.3 Model checking
Convergence Model details were described in section 5.4. All models were run with a burn-in of 20,000 iterations and a subsequent posterior sample of 200,000 iterations.
Similar to the analysis presented in chapter 6, autocorrelation was high for some pa-rameters so a large number of posterior samples were required to obtain the required effective sample size. Convergence assessment was described in section 5.4; the Monte Carlo standard error and effective sample size are provided in appendix F.
Model fit Table 7.6 shows the DIC, deviance and effective number of parameters for the difference MM models. There were substantial differences in DIC across models (minimum difference of 20), with the LOS weighting giving the lowest DIC and the First weighting the highest DIC. Here the models differ only in the NNU effects, so a higher effective number of parameters indicates larger difference between the NNU effects (i.e. a higher between-NNU variance, as will be discussed in section 7.4.5).
SCBU LNU NICU All infants
Equal 9.4 40.0 50.7
LOS 9.4 40.2 50.4
Beta2 7.5 38.8 53.7
Beta3 6.5 38.1 55.4
WLOS 7.9 38.8 53.3
First 8.1 40.1 51.8
Survivors
Equal 9.9 41.8 48.3
LOS 10.1 42.4 47.5
Beta2 8.0 40.9 51.0
Beta3 6.9 40.0 53.1
WLOS 8.5 40.9 50.6
First 8.2 41.0 50.8
Deaths
Equal 4.5 23.8 71.6
LOS 3.0 20.4 76.6
Beta2 2.8 20.3 76.9
Beta3 3.0 20.8 76.2
WLOS 3.0 20.2 76.9
First 7.1 31.5 61.4
Table 7.4: Distribution of multiple membership weight across NNU levels 7.4.4 Infant and provider characteristics
Table 7.7 shows the posterior mean odds ratios (OR) and 95% credible intervals (95%
CrI) for the infant characteristics. Results were fairly similar across all six weights, though different to those estimated for inborn infants alone in table 6.3. The odds ratios for male sex and antenatal steroids were both lower than that for non-transferred infants, but more similar to those in the single level model developed in chapter 3 (see table 3.5).
The ORs comparing mortality in SCBUs and NICUs with LNUs varied considerably across the six weights, with all results different from those for non-transferred infants, where both SCBUs and NICUs had higher mortality than LNUs. The LOS weighting gave the largest differences with the odds of mortality in SCBUs being half those in LNUs (OR 0.46 95% CI (0.28,0.75)), while the OR for NICUs was 2.68 (2.18,3.30). The Equal and WLOS weightings produced similar but less extreme results: Equal SCBU OR 0.62 (0.40,0.93) NICU 2.22 (1.82,2.73); WLOS SCBU 0.64 (0.38,1.04) NICU 2.01 (1.62,2.47). There was a pattern of decreasing mortality in NICUs as more weight was assigned to the early part of stay: Beta2 1.79 (1.48,2.18); Beta3 : 1.33 (1.10,1.60); First :
First Interim Last All transferred infants
Equal 40.3 19.4 40.3
LOS 26.6 18.7 54.6
Beta2 37.7 23.4 38.9
Beta3 45.1 25.3 29.6
WLOS 35.2 22.4 42.4
First 100.0 0.0 0.0
Survivors
Equal 39.8 20.5 39.7
LOS 26.5 19.7 53.8
Beta2 38.2 24.7 37.1
Beta3 45.7 26.8 27.5
WLOS 35.8 23.7 40.4
First 100.0 0.0 0.0
Deaths
Equal 45.9 8.0 46.1
LOS 28.6 8.1 63.3
Beta2 32.6 9.0 58.4
Beta3 38.2 9.1 52.7
WLOS 28.7 7.9 63.3
First 100.0 0.0 0.0
Table 7.5: Distribution of multiple membership weight across episodes, transferred in-fants only
DIC Deviance Effective parameters
Equal 7644.00 7589.00 55.08
LOS 7572.00 7513.00 59.21
Beta2 7712.00 7663.00 48.72
Beta3 7758.00 7713.00 44.94
WLOS 7686.00 7633.00 53.06
First 7778.00 7736.00 42.23
Table 7.6: Model performance
0.93 (0.80,1.08).
Table7.7:Posteriormeanoddsratiosand95%credibleintervalsforinfantandprovidercharacteristicsformultiplemembershipmodels EqualLOSBeta2Beta3WLOSFirst OR95%CrIOR95%CrIOR95%CrIOR95%CrIOR95%CrIOR95%CrI GA(1)0.15(0.09,0.25)0.18(0.11,0.29)0.17(0.10,0.29)0.15(0.09,0.25)0.18(0.11,0.29)0.15(0.09,0.24) GA(2) 2.47(1.60,3.78)2.23(1.42,3.47)2.26(1.43,3.55)2.45(1.58,3.74)2.22(1.43,3.41)2.43(1.61,3.74) BWT0.88(0.71,1.10)0.91(0.72,1.13)0.91(0.72,1.14)0.87(0.70,1.09)0.91(0.73,1.14)0.85(0.68,1.06) BWT2 1.82(1.62,2.04)1.77(1.58,1.99)1.81(1.61,2.03)1.86(1.66,2.08)1.79(1.60,2.01)1.88(1.68,2.10) GA(1) ×BWT0.37(0.22,0.62)0.40(0.24,0.68)0.40(0.23,0.68)0.36(0.22,0.61)0.40(0.24,0.68)0.36(0.22,0.60) GA(1) ×BWT2 0.80(0.71,0.91)0.82(0.72,0.93)0.81(0.71,0.92)0.80(0.70,0.90)0.81(0.72,0.92)0.80(0.71,0.90) BWT×GA(2) 1.21(0.84,1.74)1.17(0.80,1.69)1.15(0.79,1.68)1.21(0.84,1.73)1.16(0.80,1.67)1.20(0.84,1.73) Male1.43(1.27,1.62)1.42(1.26,1.61)1.42(1.25,1.60)1.42(1.26,1.61)1.42(1.26,1.61)1.42(1.26,1.61) Steroids0.41(0.35,0.48)0.41(0.35,0.48)0.42(0.36,0.49)0.43(0.36,0.50)0.41(0.35,0.48)0.43(0.37,0.51) SCBU0.62(0.40,0.93)0.46(0.28,0.75)0.73(0.46,1.16)1.14(0.72,1.72)0.64(0.38,1.04)1.09(0.84,1.43) NICU2.22(1.82,2.73)2.68(2.18,3.30)1.79(1.48,2.18)1.33(1.10,1.60)2.01(1.64,2.47)0.93(0.80,1.08) OROddsratio;CrICredibleinterval GA(1)andGA(2)denotesplinetermsforgestationalageatbirth;BWTbirthweight AllcontinuouscoefficientswerestandardisedsoORareforaonestandarddeviationincrease *SCBUoddsratiocomparingspecialcarebabyunitstolocalneonatalunits(LNUs);NICUoddsratiocomparingneonatalintensivecareunitstoLNUs
7.4.5 NNU and network effects
Standard deviation of NNU and network effects
Figures 7.1 compares the between-NNU and between-network standard deviation (σu and σv) for each of the six weights. Figure 7.2 compares σu across all six weights and figure 7.3 does the same for σv. The posterior mean of σu was highest for the LOS weighting (0.31) and lowest for the First weighting (0.14). For comparison, the between-NNU standard deviation was 0.27(0.07,0.46) for the same model for non-transferred infants (without the MM, model 5 in chapter 6). For weights Beta3 and First, which attribute the most weight to initial part of stay, σu was more uncertain with posterior mass near zero, see figures 7.1 (d) and (f).
The σv was fairly similar across models (posterior mean of around 0.23) but slightly less for the First weighting (0.20). This is similar to the result of σv 0.22 (0.03,0.4) in non-transferred infants. In contrast to non-transferred infants only (figure 6.6 (e)) σu was more uncertain than σv, and of lower magnitude for three weighting schemes (Beta2, Beta3 and First ), see figures 7.1 (c),(d) and (f).
( a )
0 2 4 6
0.0 0.2 0.4 0.6
( d )
0 2 4 6
0.0 0.2 0.4 0.6
( b )
0 2 4 6
0.0 0.2 0.4 0.6
( e )
0 2 4 6
0.0 0.2 0.4 0.6
( c )
0 2 4 6
0.0 0.2 0.4 0.6
( f )
0 2 4 6
0.0 0.2 0.4 0.6
σu σv
Figure 7.1: Posterior distribution for σu and σv for each MM weighting: (a) Equal, (b) LOS, (c) Beta2, (d) Beta3, (e) WLOS and (f) First
0 2 4
0.0 0.2 0.4 0.6 0.8
value
density
MM weighting Equal LOS Beta2 Beta3 WLOS First
Figure 7.2: Posterior distribution comparing σu (between-NNU SD) across all multiple mem-bership weights
0 2 4 6
0.0 0.2 0.4 0.6
value
density
MM weighting Equal LOS Beta2 Beta3 WLOS First
Figure 7.3: Posterior distribution comparing σv (between-network SD) across all multiple mem-bership weights
Comparison of NNU effects across models
Figure 7.4 shows the correlation of individual NNU effects for each pair of weights, and the distribution of posterior means of NNU effects by NNU level. The lowest correlation (0.64) was between the LOS and First weightings and the highest correlation (0.98) was between the LOS and WLOS weightings. Overall the First weighting was not well correlated with the other weights (0.64-0.83) while the WLOS weighting correlated well with all weights (0.9 or greater) except First. Within NNU level, correlation between weighting schemes was generally lowest for SCBUs and highest for NICUs. Similarly to the analysis of non-transferred infants shown in figure 6.7, the lower level NNUs were more shrunk towards the mean. Shrinkage was most apparent in the Beta2, Beta3 and First weightings, corresponding to the lower σu seen in these models. There were a few outlying NNUs which were particularly apparent for the Equal, LOS and WLOS weightings.
Table 7.8 shows the precision of the NNU effects, as measured by the average SD.
The lower the σu (figure 7.2), the more information is borrowed and the greater the precision. NNU effects had the most uncertainty for SCBUs and the least for NICUs, consistent with differences in size.
Figures 7.5 to 7.8 show caterpillar plots for SCBUs, LNUs, NICUs and networks.
Across all levels of NNU, the largest log OR were generally produced by the LOS weight-ing and the smallest by First and Beta3, consistent with the between-NNU SD (figure 7.2) and shrinkage of posterior means (figure 7.4). There was considerable overlap in the credible intervals, even for NICUs, with wider intervals for the larger effects produced by the LOS weight, consistent with the precision in table 7.8.
For most SBCUs there was little difference between the smallest and largest OR compared with the uncertainty. SCBU 36 had a substantial difference between the smallest and largest NNU effect, which can also be seen in figure 7.4. This NNU had 178 admissions, all of which were transfers in and all survived to discharge. Therefore the Equal and LOS weightings do not reflect the lower intensity of care, resulting in a very low (though uncertain) log OR for this NNU.
For LNUs the differences across models were slightly bigger than for SCBUs, but generally small relative to uncertainty. For NICUs there were more differences observed across the range with less of a consistent pattern. Credible intervals were a little smaller for NICUs, though still much larger than the differences across weights. There were a few LNUs and NICUs where both the largest and smallest estimates of the OR were on the same side of zero, but the credible intervals always included zero. As with the results in chapter 6, differences between weightings may be meaningful when expressed as the
probability of exceeding a certain threshold. For example for SCBU 104, the probability of the OR exceeding 1.2 (equating to a log OR of 0.18) is 31% for the LOS weighting but only 6% for the First weighting. Differences can also occur for NICU where the credible intervals are narrower; for example, for NICU 162 the probability of the OR exceeding 1.2 is 28% under the Equal weighting and 8% under the Beta3 weighting.
For LNUs and NICUs it was not always the case that NNUs with more extreme results had the bigger differences across weightings (as was observed when comapring models using caterpillar plots in chapter 6). This suggests that for a particular NNU, differences in the log OR across weightings are not solely driven by the overall between-NNU variance and amount of shrinkage, but also by how the weightings allocate care of infants treated in that NNU. This is consistent with the low correlation across weight-ings seen in figure 7.4 and suggests that choice of weightweight-ings will affect some NNUs differently to others. To investigate this I reordered the caterpillar plots by the propor-tion transferred, considering transfers in and out, and transfers within 24 hours. None of these plots showed any particular patterns. Figure 7.9 shows LNU effects ordered by the proportion of infants transferred out within 24 hours as an example, the remaining plots are provided in appendix F.
There were little differences between results for neonatal networks given the overall uncertainty, though the WLOS weight tended to produce effects closest to the null.
All SCBU LNU NICU Equal 0.25 0.31 0.25 0.21 LOS 0.28 0.33 0.28 0.22 Beta2 0.22 0.25 0.22 0.18 Beta3 0.18 0.20 0.19 0.16 WLOS 0.25 0.30 0.25 0.20 First 0.14 0.15 0.14 0.13
Table 7.8: Posterior mean standard deviation for NNU effects, averaged over NNU, MM models
EqualLOSBeta2Beta3WLOSFirst
Equal LOS Beta2 Beta3 WLOS First
0
Figure 7.4: Correlation of NNU effects across multiple membership weights
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Figure 7.5: Caterpillar plot for SCBU effects showing smallest and largest effects across multiple membership weights
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150152 1056 128139 163394528 112156714354689 16729 10716695176867 145157 11357136191 1177017 143136 132109 119101 1557385881040111263 153465972 12287374831 158168411432228290 124963095 1642527 13798 115
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Figure 7.6: Caterpillar plot for LNU effects showing smallest and largest effects across multiple membership weights