La Tutela Asistencial en el Derecho Comparado

The dependent variable used in this model is mortality which takes the value one if the infant died while admitted to a neonatal unit and zero if the infant was otherwise discharged from neonatal care.

5.3.2

Control variables

A number of exogenous determinants of in hospital mortality are included in the model,

xi jt in model (6.7). These are widely used in similar models (Medlock et al., 2011).

The variables are gestational age and its square,14

birth weight z-score,15

maternal age, and dummies for whether an infant received antenatal steroids, and male sex.

In addition, I also include the local market forces factor (MFF) as a covariate. The MFF is estimated by the Department of Heath and represents the unavoidable cost differences in providing healthcare between areas, such as the cost of capital or labour inputs (Monitor, 2013). As has been emphasized throughout this chapter, the effect of interest is that due to increases or decreases to the expenditure (in real terms). However, we require this effect to be net of unavoidable differences in the cost of inputs since shifts in the labour market may affect the level of inputs to neonatal care without affecting the overall level of expenditure in real terms. It is for this reason the MFF is included.

5.3.3

Estimation

The linear panel instrumental variables model described in equation (6.7) can be esti- mated in a number of ways. Most commonly, models of this type are estimated either using the two stage least squares (2SLS) estimator (this is the one step generalised

14_{Measured using ultrasound.}

methods of moments (GMM) estimator) or using the two step GMM (2SGMM) esti- mator. Both provide consistent estimators under the same set of assumptions, however the latter is more efficient and is used here (Cameron and Trivedi, 2005b).

To ensure consistency of the 2SGMM estimator in this framework it is necessary to assume that the instruments are strongly exogenous. In particular, let z_{i jt} be the vector of instrumental variables (which in this case has dimension 1×2), and let ˜u_{i jt} = u_{i jt}−u¯_{i j} be the mean differenced errors from equation (6.7). Then, it is assumed that

E(z′_{i js}u˜i jt) =0fors,t=1, ...,T.

For the primary analysis, observations are weighted by the inverse of the probabil- ity of being born in each of the hospitals with neonatal units in this study. Since there are more likely to be observations from high volume units, the probability of observing the unit costs in high volume units is higher, the weighting is designed to counter this. The effects of interest are the returns to medical expenditure within neonatal healthcare

as a whole. The results are tested for sensitivity to the weighting scheme utilised in

Section 5.5.

5.3.4

Other Issues

Missing data

Both the NNRD and the NHS Reference Cost Data contain missing observations (Table 2.2 in Chapter 2). Not all admissions in England are observed in the NNRD. This is due to two reasons: firstly, not all English neonatal units contribute and provide permission to use their data to the NNRD (overall, records from 165/170 units are available); secondly, the location of the maternal residence may be missing from the data set. While the data are available for the large majority of infants, there will be neonatal units for which we only observe a subset of the population. For the individual model this is only a problem if the subset of missing infants are significantly different from the subset of included infants. Since I do not possess data on the missing infants this cannot be tested empirically; however, I do not believe the infants differ since the data are likely to be either missing completely at random or missing at random

numbers of units).

Heterogeneous Effects

The effects of interest and those estimated from the model in (6.7) are the marginal effects of neonatal healthcare expenditure averaged over the patient population, which isγ in the model. Nonetheless, for policy purposes, as well as clinical and economic

interest, the effects within certain sub-populations may also be of interest.

In many studies of mortality in neonatal units, the sample of infants under investi- gation is often restricted in some way. This is in part due to concerns that the mortality model may not be appropriate for all infants—those factors predicting mortality for one subset of the patient population are not successful predictors for another. Simi- larly, the causes of death may vary between different patient groups, which may be affected to a lesser or greater extent by increasing factor inputs to each unit. It is as- sumed in this chapter that increased HRG unit costs result from increased labour and capital inputs to neonatal units (this is further examined in Section 5.6). However, there are additional factors that may influence patient clinical outcomes between units above and beyond the levels of factor inputs. Infants admitted to higher volume neona- tal units at the hospital of birth have been shown to have a reduced risk of mortality (Chapter 4 and Watson et al. (2014)); this may be driven, in part, by the experience of clinicians within these units. Moreover, the accumulation of specific human capital on these units may enable them to more effectively deploy the resources available in the production of neonatal healthcare, as such there may further be differences in technical efficiency between units.

The subgroups most often studied are those infants that are very low birth weight (VLBW; <1,500g) or very preterm (born at less than 33 weeks gestation) (see Chapter 3 for a review). A likelihood ratio test comparing the model in equation (6.7) estimated for the whole sample and separately for infants born at <33 weeks gestation and≥33 weeks gestation rejected the null hypothesis of no difference (p<0.001). To exam-

Table 5.1 Summary statistics of the sample Financial Year Variable 2009/10 2010/11 2011/12 2012/13 Whole Sample Nj 119 88 87 40 Ni 34,458 27,644 30,243 9,214 101,559 Birth weight (g) 2,743.3 (929.5) 2,783.4 (895.2) 2,835.2 (894.4) 2,809.6 (893.9) 2,798.7 (902.5) Gestational age (weeks) 36.4 (3.8) 36.7 (3.7) 36.9 (3.6) 36.7 (3.6) 36.7 (3.7)

% male 44.6 43.4 44.7 43.8 44.1

Mortality (%) 1.5 2.0 1.7 1.8 1.7

Average careday costa (£) 606.64 (171.23) 639.49 (148.62) 633.48 (154.66) 652.18 (163.13) 626.72 (160.40)

NjandNiare the number of neonatal units and the number of individual infants respectively.

Mortality is any in hospital mortality.

Birth weight, gestational age, and unit costs are mean (sd) values.

IC Unit Costs are averaged across providers and adjusted to 2012/13 GBP using the Health Services Cost Index (HSCI)

a _{These figures are averages over neonatal units rather than infants.}

ine heterogeneous effects of expenditure, I re-estimate the model for different patient groups by gestational age (the whole sample,≤32+6, and≤26+6). In addition, effects are estimated separately for different volume neonatal units, and levels of factor inputs are examined in Section 5.6.

The analyses are conducted in R 3.0.1 and Stata version 13.

5.4

Results

5.4.1

Summary Statistics

Table 5.1 provides summary statistics for the sample included this study. Overall, 101,559 infants were included in the sample, of which 12,559 were born at ≤32+6 weeks+days gestational age, and 2,596 at ≤27+6 weeks+days gestational age. The re- ported costs per cot day at all levels of care are provided in Chapter 2. The mean (sd) cost per care day over all neonatal units in the sample was £626.72 (160.40).

There are clearly a much smaller group of infants in the sample for the financial year 2012/13. This is due to a smaller group of providers submitting their estimated costs in this year (see Section 2.4.2). In Section 5.5, the main results are re-estimated

5.4.2

Instrument Validity

The validity of the instruments has been established to some extent in the previous chapter, where it was shown that the characteristics of the nearest neonatal unit to the maternal residence were as good as randomly assigned. In particular, it was shown that, conditional on the infant’s socio-economic status, there was no evidence that in- fants differed in terms of observed characteristics by the characteristics of their nearest neonatal unit. This provides some evidence to suggest that the independence assump- tion is met (Altonji et al., 2005). However, such a comparison is not generally possible in the framework presented for this chapter, since the ‘treatment’ is continuous as is the instrumental variable. Moreover, the requirement is now that the within transformed nearest neonatal unit expenditure is conditionally independent of within transformed unobserved heterogeneity. One possible method could be to test for zero partial corre- lation of the within transformed instrumental variable with various within transformed observed characteristics, such as gestational age. However, only in the case where all of the variables, including the conditioning variables, are multivariate normally dis- tributed, which is not the case here, does this imply conditional independence (Baba et al., 2004). As such, the following test of overidentifying restrictions is relied upon to provide information about instrument validity in this case.

The exclusion assumption can be tested using Hansen’s J statistic. The J statistic tests the null hypothesis that the instruments are uncorrelated with the errors in model (6.7), construction of the statistic requires an overidentified model, i.e. one with a greater number of instruments than endogenous variables, which is the case here. The J-statistic is a heteroskedasicity and cluster robust form of the Sargan statistic (God- frey, 1988). The J-statistic for each model is shown with their respective models in table 5.3. In no cases was the null hypothesis of instrument validity rejected.

diture the hospital of birth are examined in two ways. Firstly, an F-test of the excluded instruments in the first stage regression provides a p-value of <0.001 in all cases, pro- viding strong evidence for an effect of the instruments neonatal unit expenditure at the hospital of birth. Secondly, an underidentification test— this tests the null hypothesis that the model is not identified due to irrelevant instruments—rejects this null hypoth- esis in all cases. The p-values are reported in table 5.3.

5.4.3

Main Results

Two sets of estimates are presented in this section. Firstly, those from the model treat- ing health care expenditure as exogenous, as shown in table 5.2; and secondly those treating expenditure as endogenous, provided in table 5.3. In the first case, as table 5.2 shows, all of the point estimates are negative, implying that aceteris parabisincrease in neonatal unit expenditure is associated with a reduction in the risk of mortality. The results are not statistically significant (at the 5% level) when considering the whole sample, although the estimates are significantly different from zero in the case of very preterm and extremely preterm infants. Full regression results from these models are presented in Section C.2 in Appendix C.

It is possible that infants are transferred to neonatal units that may be more ap- propriate for their care or that units spend more in response to an unobservably sicker patient cohort. This may mean infants at higher risk of mortality are transferred to units with greater inputs to neonatal care.16

If this is the case then the estimates pre- sented in table 5.2 may be biased upwards. Table 5.3 presents results, allowing for the endogeneity of neonatal unit expenditure. All the results in this table are negative and statistically significant (at the 5% level), and below the equivalent point estimates in table 5.2. These results suggest that a 10% increase in total neonatal unit expenditure leads to a 0.2 percentage point reduction in the risk of mortality among very preterm infants (on a mortality rate of 5.0%, see table 4.1, Chapter 4.

16_{Infants are transferred to higher volume neonatal units if they are at high risk of mortality (Gale}

et al., 2012b), these units differ in the levels of labour and capital inputs used in the provision of health care.

Table 5.2 Regression results treating expenditure as exogenous (1) (2) (3) Whole sample ≤32+6 ≤26+6 expenditure −0.0002 −0.0160∗∗∗ −0.0668∗∗∗ (0.001) (0.002) (0.008) N 101,559 12,777 1,729

1 ∗_p<0.05;∗∗_p<0.01;∗∗∗_{p<0.001. Cluster robust standard errors in parentheses.}

2 _{The dependent variable is in-hospital mortality. The control variables are gestational age, gesta-}

tional age squared, birth weight z-score, indicators for whether a full or partial course of antenatal steroids was administered and male sex, year fixed effects, region fixed effects, deprivation score quintile dummies, and place of birth fixed effects.

3 _≤32+6_{=infants born at≤32}+6_{weeks gestation.≤26}+6_{=infants born at≤26}+6_{weeks gestation.}

Table 5.3 Regression results treating expenditure as endogenous

(1) (2) (3) Whole sample ≤32+6 ≤26+6 expenditure −0.00219∗∗ −0.0227∗∗∗ −0.0720∗∗∗ (0.000744) (0.00198) (0.00604) N 101559 12776 1719 J statistic 0.761 0.897 0.694 J stat. p-value 0.102 0.118 0.461

1 ∗_p<0.05;∗∗_p<0.01;∗∗∗_{p<0.001. Cluster robust standard errors in parentheses.}

2 _{The dependent variable is in-hospital mortality. The control variables are gestational age, gesta-}

tional age squared, birth weight z-score, indicators for whether a full or partial course of antenatal steroids was administered and male sex, year fixed effects, region fixed effects, deprivation score quintile dummies, and place of birth fixed effects.

3 _≤32+6_{=infants born at≤32}+6_{weeks gestation.≤26}+6_{=infants born at≤26}+6_{weeks gestation.} 4 _{Neonatal unit expenditure at the hospital of birth is instrumented with neonatal unit expenditure at}

Table 5.4 Regression results treating expenditure as endogenous without inverse prob- ability weighting estimation.

(1) (2) (3) Whole sample ≤32+6 ≤26+6 expenditure −0.00243 −0.0172∗∗∗ −0.0461∗ (0.001) (0.005) (0.018) N 101,559 12,776 1,719 J-statistic 0.666 0.775 0.805 J stat p-val. 0.314 0.608 0.302

1 ∗_p<0.05;∗∗_p<0.01;∗∗∗_{p<0.001. Cluster robust standard errors in parentheses.}

2 _{The dependent variable is in-hospital mortality. The control variables are gestational age, gesta-}

tional age squared, birth weight z-score, indicators for whether a full or partial course of antenatal steroids was administered and male sex, year fixed effects, region fixed effects, deprivation score quintile dummies, and place of birth fixed effects.

3 _≤32+6_{=infants born at≤32}+6_{weeks gestation.≤26}+6_{=infants born at≤26}+6_{weeks gestation.} 4 _{Neonatal unit expenditure at the hospital of birth is instrumented with neonatal unit expenditure at}

the nearest neonatal unit to the maternal residence.

5 _{The estimator used for the primary results included an inverse probability weighting scheme for the}

place of birth—the results in this table do not include this weighting scheme.