Retinal detachment after phacoemulsification in refractive surgery clinics: a large series analysis with variable follow-up during 16 years

Abstract

Purpose

To determine the long-term incidence of pseudophakic retinal detachment (PRD) after phacoemulsification and the weight of the main risk factors in the appearance of such complication in a large sample. To implement a customized formula and a software calculation program able to quantify the risk of suffering PRD applicable to all lens extraction patients.

Methods

Retrospective cumulative risk analysis conducted on 178,515 eyes operated under similar conditions in a group of refractive surgery clinics (Clínica Baviera SL) located in a relatively limited geographical area (Spain). A survival analysis was performed and the data were modelled using the Weibull regression to determine the risk over a period of 16 years and to estimate the association of different risk factors: sex, age, axial length (AXL) of the eye, intraoperative posterior capsule rents (PCR), and YAG laser capsulotomies. The resulting estimates were translated into a predictive equation for hazard rates and survival probabilities. Later, an application was developed to make prediction available for the clinical community in order to estimate the potential risk of any hypothetical case before lens surgery.

Results

Globally, 1521 (0.85%) cases of PRD were diagnosed during the period. The risk for PRD was significantly greater in males (5.48 [2.94–10.2]; p < 0.001), in long eyes (1.24 [1.21–1.26]; p < 0.001), and also after posterior capsule rents (13.97 [11.61–16.82]; p < 0.001). Posterior capsule rupture increased the risk of PRD up to fourteen times.

Conclusions

From weaker to stronger impact, age, axial length, sex, and intraoperative posterior capsule rent were significant risk factors for the appearance of PRD after lens extraction.

Appendix

The survival function gives the probability of surviving beyond time t. So, it represents the probability for the absence of retinal detachment before t. The hazard function h(t) is the instantaneous rate of failure having the units 1/t or in our case 1/month. The cumulative hazard function measures the total amount of risk that has been accumulated up to time t. In other words, the cumulative hazard rate records the number of times we would expect (mathematically) to observe failures over a given period, if only the failure event were repeatable.

The resulting estimates were translated into the predictive equation for hazard rates and survival probabilities.

The hazard function of the Weibull distribution is defined as:

Considering that intercept and scale parameters define shape of the Weibull distribution and are used for the prediction, these coefficients can be used to make predictions about survival probability, instantaneous hazard rate, and cumulative hazard rate.

Let

$$ Shape=\frac{1}{Scale}=\frac{1}{e^{0.736}} $$

and

$$ Scale={e}^{40.913-1.083 xAXL-1.284 xMale-5.086 xPCR} $$

Then, the hazard function of the Weibull distribution is defined as:

$$ h\left(t/ AXL, sex, PCR\right)=\frac{shape}{scale}\ x\ {\left(\frac{t}{scale}\right)}^{\left( shape-1\right)} $$

The cumulative hazard is defined as

$$ H\left(t/ AXL, sex, PCR\right)={\left(\frac{t}{scale}\right)}^{(shape)} $$

The survival function is given by:

$$ S\left(t/ AXL, sex, PCR\right)={e}^{-{\left(\frac{x}{scale}\right)}^{shape}} $$

For example, an eye with ALX = 23.5 mm from a male patient and without complications has the following cumulative hazard at 10 years:

$$ Shape=\frac{1}{Scale}=\frac{1}{e^{0.736}}=0.4790262 $$

and

$$ Scale={e}^{40.913-1.083x23.5-1.284x1-5.086x0}=1.4376207\ x\ {10}^6=1437621 $$

So,

$$ H\left(t/ AXL, sex, PCR\right)={\left(\frac{t}{scale}\right)}^{(shape)}={\left(\frac{120}{1437621}\right)}^{(0.4790262)}=0.011128 $$

Now, assume that the same eye had a surgical complication (PCR):

$$ Shape=\frac{1}{Scale}=\frac{1}{e^{0.736}}=0.4790262 $$

$$ Scale={e}^{40.913-1.083x23.5-1.284x1-5.086x1}=4326.4386505=4326.439 $$

$$ H\left(t/ AXL, sex, PCR\right)={\left(\frac{t}{scale}\right)}^{(shape)}={\left(\frac{120}{4326.439}\right)}^{(0.4790262)}=0.1795648 $$

where the consequences of the complication can be seen clearly, as the hazard increased by 17.9 times