Increasing Judge Strength: Impact on Reducing Pendency of Cases*

The 114th Law Commission Report on ‘Gram Nyayalayas’ by Justice (Retd.) D.A. Desai in 1986 contains this experience of a litigant, which was brought to its notice.

A litigant in search of justice since 1972 enriched his tale of woes at the workshop held in Benares University at Varanasi. According to him, on an average, there is a floating population of 50,000 litigants, including witnesses, who visit Varanasi District Court Compound daily. According to him, the average cost of transport, plus snacks works out to Rs.10 per day per individual. The longest distance one has to travel to reach court at Varanasi measures about 58 kms. Most of the places in the hinterland within the jurisdiction of District Court at Varanasi are not connected by rail with Varanasi. Bus transport apart from being hazardous is very uncomfortable and tedious. One is required to travel on an average 2 ½ to 3 hours one way. It does not require a genius to calculate this wasteful expenditure on what is euphemistically called search for justice…¹

The words could well be written in 2019, and they would still ring true about the plight of litigating citizens.

The Access to Justice Survey, 2017 by DAKSH investigated the paths to justice chosen by citizens who chose not to go to court. Of those who did not approach the courts, 26.8 per cent did not file a case in court because of the high costs of litigation, 21.5 per cent did not understand how to do so or found the legal system too complex, and 17.3 per cent said that they were deterred by how long courts take to resolve cases.² These responses show that a significant proportion of citizens have been obstructed from accessing the formal justice system because of problems inherent in the structure of the judiciary, and the processes of litigation and administration of the judiciary. None of the proposed or attempted solutions to these problems have evolved sufficiently to keep pace with the rapid increase in workload brought about by the significant growth of litigation in India in recent years.

The shortcomings of the formal justice system in making justice accessible led to the formation of Nyaya Panchayats (first conceptualised in the preindependence era) and Gram Nyayalayas (set up by an Act of the Parliament in 2009). One can safely say that both of these ideas have failed to take off from the ground. However, the continuing attraction of such and other ideas is because courts continue to fail the access to justice mandate on many counts— whether in terms of the distance that the citizen has to travel; procedural and process-related inflexibilities; or ultimately in rendering timely justice.

At the same time, courts have consistently demanded that more judges need to be appointed so as to render timely justice.³ The 120th Law Commission Report titled Manpower Planning in Judiciary: A Blueprint, published in 1987, and the 245th Report titled Arrears and Backlog: Creating Additional Judicial (Wo)manpower, published in 2014, spoke of how additional judges are needed in the judiciary. The reports did not consider how much of an impact more judges would have on the pendency and backlog numbers.

In this chapter, we evaluate whether setting up new courts benefits the litigant in terms of faster disposal of cases.

By new courts, we do not mean a new type of courts, for example, fast track courts or special courts. Here, we use the term ‘new court’ to refer to a new judicial post created in a specific judicial cadre. New courts selected for our purpose have been set up in the same court complex where other courts function. One can safely say that these new courts were not set up to alleviate hardships due to distance, and they also make use of the existing facilities and infrastructure belonging to existing courts. Therefore, we quantify the impact on time taken for disposal of cases on account of setting up new courts.

Factors Considered in Setting up New Courts

To answer the question we set for ourselves, we first sought to understand the factors that are considered when deciding to set up a new court. We did not find any document that lists the criteria used by the judiciary for such a process. During the course of informal discussions with a few judicial officers, we understand that no policy document for this purpose is in place. We were informed that the following factors are usually considered during this process.

1. New talukas: When new talukas are set up, it is generally expected that new courts catering to that jurisdiction will also be set up. However, we do not find court complexes in each taluka in the country and can only conjecture reasons for this.
2. Docket size per judge: The High Court generally monitors the docket size of each judge (the average number of cases that form the workload of the judge). Where it is felt that the docket size has become unmanageable (there is no specified number), new courts are set up.
3. Requests from the bar or litigants: In some cases, new courts are set up based on requests from litigants and members of the bar who are inconvenienced by the distance they have to travel to court complexes.
4. Other considerations: As with any other large institution that wields significant socio-economic power, when faced with such choices, the dynamics of individuals in power, be it within the judiciary or without, affect the final decision. Therefore, as with public services, such as railway stations, bus stations, post offices, etc., the choice of whether, and where to, open a new court is a mix of rational and political considerations.

Process of Setting up New Courts in an Existing Court Complex

1. The High Court recommends the setting up of a new court. Recommendations of the High Court are in most cases those of the full court based on findings from a committee that has been set up for this purpose.
2. The committee considers submissions of the bar and litigants and other material relevant to the matter in coming to its conclusion.
3. The state government then follows the recommendation of the High Court.

The foregoing points have been corroborated by the High Court of Karnataka in its response to the RTI application we filed. The response stated that:

1. The Committee for Establishment, Abolition, and Alteration of Jurisdiction of Courts is responsible for this process. This is a permanent committee.
2. The following factors are considered in setting up new courts: ‘The overall pendency of cases according to criteria, accessibility/transportation facility, that is, conveyance from one place to another, jurisdiction, geographical condition, representations from concerned Bar Associations, opinion furnished by the concerned Principal District and Sessions Judge.’
3. These factors have not been codified in any rules, regulations, or handbook.

The process for the transfer of cases to the new courts varies based on the cadre of the judicial post created. The response to the RTI stated:

[I]f the new Courts are Civil Judge or Senior Civil Judge & JMFC and Addl. CJM Courts, the Principal District Judge will transfer the cases to the new courts from pre-existing courts considering the pendency and jurisdiction. If the new Courts are Addl. District Courts on the basis of the recommendation made by the Principal District and Sessions Judge, the High Court will permit the Principal District and Sessions Judge to transfer the cases from preexisting Courts to the new courts.⁶

Evaluation: The Impact of New Courts

In this chapter, we evaluate the impact of three new courts set up in the Mysuru and Chamarajanagar districts of Karnataka. These districts have historically been administered as one unit and were bifurcated only in 1998. They have many socio-economic and geographical similarities. These districts are predominantly rural in nature and have only one urban centre (Mysuru city). There is no special distinguishing feature in either of these districts that make the judiciary in these districts stand out either positively or negatively. These districts can, therefore, be considered to be representative of subordinate courts in India and suitable for our analysis without requiring adjustments for data.

The two districts had 56 judicial posts between 1 January 2000 and 18 August 2014, when three new courts were then notified.⁷ The three new courts were:

1. Additional Civil Judge and Judicial Magistrate First Class at Krishna Raja Nagar;
2. Additional Civil Judge and Judicial Magistrate First Class at Heggada Devana Kote;
3. II Additional Civil Judge and Judicial Magistrate First Class at Nanjanagud.

These three new courts are located in the existing court complexes at these locations. Therefore, no additional advantage of bringing the courts closer to the citizens has been created.

We consider a sample of data relating to cases filed between the years 2000 and mid-2018 for courts in these districts. The data set consists of 3,72,144 cases filed in these districts in this period, of which 3,10,303 were disposed as of 1 July 2018. There were also 61,896 cases that were pending as of 1 July 2018.

In Part A of this section, we provide an overview of how courts in Mysuru and Chamarajanagar are functioning; while in Part B, we discuss our hypotheses and analyse whether new courts help improve the functioning of courts in these two districts.

Part A: Overview of the Functioning of Courts in Mysuru and Chamarajanagar

In order to assess the impact of new courts, it is necessary to have a brief overview of the composition of cases in the dataset and understand how long cases take to progress through the system. The following data points will help in getting an overview of the functioning of the courts during this period.

figure 4.1.1.Distribution of Pendency and Disposal Times in the Dataset

From Figure 4.1.1, we note that most of the disposed cases were disposed within the 0–2 years’ bracket, and of the cases that were pending, the majority of them were pending for more than two years.

Before proceeding with our analysis in this chapter, it is important to set out the definitions of key terms used in our analysis:

1. Court versus Court Complex. In this chapter, ‘court’ refers to an individual judicial post, and ‘court complex’ refers to the physical location of one or more courts.
2. New Courts versus Transfer Courts versus Control Courts. The ‘New Courts’ analysed in this chapter are the three new courts established in the districts of Mysuru and Chamarajanagar in 2014, to which cases were transferred on 18 August 2014. The ‘Transfer Courts’ analysed in this chapter are the courts from which cases were transferred to the New Courts, and which are located in the same court complexes as the corresponding New Courts. The ‘Control Courts’ are those courts which are not New Courts and did not have cases transferred to Transfer Courts.

The terms ‘treatment’ and ‘control’ belong to terminology from experiment-based research. In an experiment, some subjects undergo a ‘treatment’ of some nature and are compared to other subjects that did not, which is the ‘control’ group.

A summary of the functioning of the New Courts since the date on which they were set up, and similar courts situated in the same complexes, has been provided.

figure 4.1.2.Comparison of Disposal Times in Years

As seen in Figure 4.1.2, the proportion of cases that have taken over two years to be disposed is higher in the New Courts (28.9 per cent) when compared with the Transfer Courts (24.01 per cent).

Figure 4.1.3 shows that cases that are pending for more than two years form about 69 per cent of the pending cases in New Courts while they constitute about 66 per cent in the Transfer Courts. The corresponding number for all courts in these districts is about 60 per cent.

From Figures 4.1.2 and 4.1.3, we may say that New Courts have not increased disposal timelines. On the contrary, the situation has worsened—the proportion of cases with a disposal time of more than two years is greater for New Courts and Transfer Courts, and pendency in the lowest age bracket (0–2 years) is actually smaller for New Courts and Transfer Courts.

figure 4.1.3.Comparison of Pendency, in Years

figure 4.1.4.Comparison of Proportion of Civil and Criminal Cases

Figure 4.1.4 shows that the balance of criminal cases and civil cases varies between New Courts, Transfer Courts, and Control Courts. For example, Control Courts have a much lower proportion of criminal cases than Transfer Courts—62.4 per cent, in comparison to 80.7 per cent. This could potentially bias comparisons between these groups, because criminal cases typically have lower disposal time and pendency than civil cases.⁸

figure 4.1.5.Comparison of Average Disposal Time across Six Years

Further, Figure 4.1.5 shows that in the immediate one year (2014 to 2015) following the creation of New Courts, graphs representing the disposal times of New Courts, Transfer Courts, and Control Courts are roughly parallel, implying that the New Courts had little impact on the amount of disposal time the courts were already taking.

Based on the foregoing analyses, it may be tempting to quickly conclude that New Courts have not helped in rendering timely justice. However, it must be noted that the metrics described previously do not give a complete picture to make a comparison between the New Courts, Transfer Courts, and Control Courts. One reason for this is that they do not enable us to estimate the extent of the relationship between which courts the cases are from and how this affects rates of case disposal. Another reason is that they do not account for factors like the nature of cases, duration for which they were pending, and changes (in workload, resources, and working style) at the courts over the period of analysis. The analysis shown above also does not account for gaps in the performance of Transfer Courts and other courts in the district that existed before the New Courts were set up. For example, variation in the types of cases and the complexity of their subject matter means that some types of cases may need more time for disposal than others. If the concentration of more demanding cases is higher in one region than another, the courts in that region will have higher average disposal time. Since both are necessary in order to make a valid comparison, we conducted further analyses as described in Part B of this section.

Part B: Hypotheses and Analyses

Given the limitations of the metrics used in Part A of this section in analysing the effect of New Courts, this part of seeks to go beyond those metrics in understanding how the life cycles of cases change once New Courts are introduced.

The court complexes chosen for the introduction of New Courts were chosen due to high demand, a relatively high volume of pending cases, and high average pendency, according to the Chief Administrative Officer of the Principal District Court, Mysuru.⁹ Therefore, in order to analyse the effect of establishing New Courts, we use methods that enable estimation of the difference in case disposal rates between New Courts, Transfer Courts, and Control Courts. These methods allow this comparison to be made while accounting for the influence of other factors.

Intuitively, cases should be disposed faster¹⁰ in New Courts than in Control Courts. This is because they have a lower workload and can thus, allocate more time to cases in each hearing or hear each case more frequently. Similarly, cases in Transfer Courts should also be disposed faster after the transfer since they too have a lower workload. The hypotheses that follow from these intuitions, and which we would like to test in this chapter, are given further.

1. For cases of age x, where all else is equal, cases in New Courts would have a higher chance of being disposed of at age x than cases in Control Courts;
2. Cases in Transfer Courts would also have a higher chance of being disposed of at age x than cases in Control Courts;
3. From the previous two hypotheses, we derive a third hypothesis, which is that the chance of disposal will be higher for cases from a wider pool, consisting of both New Courts and Transfer Courts, than for cases in the Control Courts, conditional on their being of the same age. This comparison enables estimation of the overall effect of the introduction of New Courts, in comparison to Control Courts.

The approach we use to test the hypotheses is ‘survival analysis’ or ‘duration analysis’, or the analysis of the duration of a state, and the probability¹¹ of transitioning (or not transitioning) to another state, commonly referred to as ‘failure’. It is typically used to estimate the probability of the occurrence of that transition, given the duration of the state. For example, in medicine, it has been used to estimate the probability of the death of a patient given the duration of an illness. In studying industrial reliability, it has been used to predict the probability of failure of mechanical components. In the context of legal cases, we use survival analysis to predict the probability that a case will be disposed or survive beyond a certain amount of time. Survival analysis can also be used to analyse the factors which influence these probabilities.

Survival analysis has been applied to court cases only relatively recently. We follow Datta, Prakash, and Sane¹² in using survival models for this purpose. They are especially appropriate for court cases for two reasons. The first is that survival models can be used to predict the instantaneous probability of disposal of a case, given its duration.¹³ The second reason is that survival models are specifically designed to utilise data in which some units of observation have not yet experienced a transition event.

In the context of this chapter, this means that the probability of a case’s disposal (or survival) given its age can still be estimated using a dataset containing pending cases. This is not the case for other methods and approaches, which would require omission of pending cases from the dataset.¹⁴ This is because survival analysis has been specifically designed to estimate the probabilities of both occurrence and non-occurrence of an event.

Key concepts in survival analysis are the survival function and the hazard function. In our context, for court cases, the survival function tells us the probability of a case remaining pending past any chosen point in time. For example, the survival function tells us the probability that a case would remain pending for two years or more. The two-year cut off is an important one because it is the longest permissible disposal time as per the Case Flow Management rules (CFM rules) developed by the Justice M. Jagannadha Rao Commission.¹⁵

The hazard function is a related concept. In our context, for court cases, it gives the risk of a case getting disposed at any point of time.¹⁶ For example, we are interested in the two-year cut off for case disposal because of the CFM rules. We can then look at the hazard function to know the risk of a case being disposed at two years.

We also use the cumulative hazard function in this analysis. The cumulative hazard function is a more complex concept and is a little less intuitive to grasp; however, since one of the methods of analysis depends on it, it needs to be explained. The cumulative hazard function represents the ‘accumulation’ of hazard over time—if the hazard function captures the risk of occurrence of an event after a given amount of time, the cumulative hazard function captures the total amount of risk that a subject would have been exposed to in the time that has passed. This is difficult to interpret as it is rarely the case that an individual can experience multiple ‘failure’ events, and for court cases this would be equivalent to a case being disposed multiple times.¹⁷ However, estimating the cumulative hazard function is necessary as a step to estimating the hazard function.¹⁸ Modelling the hazard function directly when time is treated as a continuous variable is difficult,¹⁹ but the cumulative hazard function, from which we can infer the shape of the hazard function,²⁰ is much easier.

In this chapter, we use two models to compare the survival and hazard functions between New Courts, Transfer Courts, and Control Courts. These are the Kaplan-Meier estimator and the Royston-Parmar parametric model. These models and the motivations for choosing them are explained below. For greater clarification of the components and concepts, which are at the core of survival analysis, see Annexure I.²¹

The Kaplan-Meier Estimator

The Kaplan-Meier estimator is a method of estimating survival functions. We use it to estimate the probability that a case will be pending for longer than a specified amount of time. To interpret Kaplan-Meier statistics, it is most useful to plot them as graphs, where a higher curve indicates a higher probability of cases lasting longer than a given amount of time. The formula for the Kaplan-Meier estimator is given in Annexure II. We plot these curves separately for New Courts, Transfer Courts, and Control Courts. Based on the intuition that increasing the number of courts would help dispose of cases faster, we predict that the curves for New Courts and Transfer Courts will be lower than the curve for Control Courts.

The Royston-Parmar Parametric Survival Model

The Royston-Parmar Parametric Survival model (RP model)²² is a method of estimating cumulative hazard functions (and by extension, survival functions). In this instance, we use this model to estimate hazard curves for cases while adjusting for the variation in disposal times that can occur because of other characteristics, such as case types, or other factors, such as the number of cases pending in a court at a given point of time in a case’s life.

The RP model also enables the prediction of:

1. The direction of the difference in probability of case disposal—meaning whether one group has higher or lower probability than another—and
2. The degree of the difference in probability of case disposal. For example, whether one group has 1.5 times the probability of case disposal than another group.

The model can be used to estimate how the variation in the probability of case disposal is correlated with variables, such as whether a case is from a New Court, a Transfer Court, or a Control Court. In other words, this means we can see how much lower (or higher) the probability of disposal is at any point of time for New Courts or Transfer Courts in relation to Control Courts. This difference is quantified in the form of a number known as a ‘hazard ratio’. For court cases, the hazard ratio expresses the ratio of the probabilities of disposal between two groups. For our investigation, it will be the ratio between the probabilities of disposal for a treatment group consisting of either New Courts or Transfer Courts, and Control Courts. For example, for cases of a given age, a hazard ratio of 2 for cases in New Courts against a baseline of cases in Control Courts would mean that New Courts have twice the estimated probability of disposal for cases of a given age in both types of court.²³ If the rate of filings is the same for both groups, then in this example, New Courts would have twice the rate of disposal of Control Courts. In this chapter, we also use this model to account for the effects of other variables, which are the type of case and the year of filing, and to see if variation in courts’ workload is the cause for the results, we fit one model controlling for the number of filings in a given year.

Using case-level data, we fit two separate models for three different treatment groups: one model which compares cases from New Courts and Transfer Courts separately to cases from Control Courts, and a second model grouping cases from both New Courts and Transfer Courts together, comparing these with cases from Control Courts. Our prediction is that if New Courts are effective in helping reduce disposal times and dealing with the workload of cases, the probability of disposal of a case in the group consisting of cases from New Courts and Transfer Courts will be higher than for a case in Control Courts at any given point of time.

Findings

Kaplan-Meier Estimator

Figure 4.1.6 gives estimated survival functions for New Courts, Transfer Courts, and Control Courts. From the survival curve shown, it is apparent that the probability of a case continuing to remain pending beyond each point in time is, in fact, higher for New Courts. This difference is significant at the 95 per cent level of confidence.²⁴ This is evidence against the first hypothesis, which stated that cases in New Courts would have a lower chance of surviving past any given age as compared to Control Courts.

However, the opposite is true for Transfer Courts in comparison to the Control Courts. It shows that Transfer Courts perform slightly better than Control Courts for cases up to two years old, and this difference is statistically significant at the 95 per cent level of confidence. This is evidence in favour of the second hypothesis—that cases in Transfer Courts have a higher chance of disposal.

As per these estimates, the creation of New Courts has had only a minor impact on the disposal time of a case, and only in Transfer Courts, for cases pending for longer than the two-year cut off.

Figure 4.1.7 shows a separate estimate of the survival function for all cases in Treatment Courts against Control Courts. Survival curves in both graphs have a 95 per cent confidence interval (CI), meaning that the ‘true’ value is believed to fall within

figure 4.1.6.Kaplan-Meier Survival Estimates Comparing New Courts and Transfer Courts with Control Courts

figure 4.1.7.Kaplan-Meier Survival Curves Comparing Survival Times for Cases from Control Courts with Cases from both New Courts and Transfer Courts

this interval with 95 per cent probability. There is no statistically significant difference between cases from the pooled group of both New Courts and Transfer Courts and those from Control Courts for the critical first two years of a case’s life, and the curves are very close for all survival times. Apart from a brief dip for cases between two and three years old, the curve for the pooled group is higher for most of the age range. This is evidence against the third hypothesis that the overall effect of the New Courts would be to increase the chances of case disposal in the group consisting of cases from both New Courts and Transfer Courts.

Royston-Parmar Parametric Survival Model

The cumulative hazard ratios for New Courts and Transfer Courts are, in fact, associated with a lower probability of disposal at any given point of time, even when other factors are controlled for, such as the number of cases filed and the types of cases. These effects are statistically significant. The predicted hazard for New Courts is between 44.2 per cent and 40.4 per cent of that of Control Courts. Transfer Courts fare much better, but still perform poorly in comparison to Control Courts, at between 79.6 per cent and 92.6 per cent of Control Courts. This shows that New Courts and Transfer Courts are associated with a lower probability of disposal of cases as compared to Control Courts. This is evidence against the first and second hypotheses, which are that cases in New Courts and Transfer Courts have a higher chance of disposal, with all else being equal, relative to Control Courts.

Limitations

The court complexes where New Courts were introduced were chosen based on the fact that the older courts in their talukas (Transfer Courts) had a higher volume of pending cases than others in the district, and cases in Transfer Courts were pending for longer in comparison to cases in other courts in the district. This ruled out our ability to utilise research design where we would have been able to design an appropriate method to study the causal relationship between the introduction of New Courts and the course and outcome of a case in those jurisdictions. If more court complexes had been selected, and if they had been randomly (or ‘as-good-as-randomly’) designated to be sites where New Courts were introduced (and therefore, where Transfer Courts are), we could have treated the cases in Transfer Courts as being generally equivalent to those in Control Courts before the transfer. This would have brought us closer to the process of an experiment—called a ‘natural experiment’—and we could have made a causal claim regarding the effect of transferring cases on the chances of case disposal.

Therefore, the fact that there was little overall improvement after the transfer implies that some factor other than just the volume of cases causes judicial delay, perhaps some feature of the court locations in which the New Courts were introduced, such as administrative practices or infrastructure.

It would have also been preferable to use a random sample of court locations from across India in which new courts were introduced. This would have helped in generalising from the observations made in this chapter, as the results would have been less sensitive to local conditions and more representative of the ‘population’ of cases that we want to generalise to.²⁵

The metrics used provide only a limited picture of how cases are processed in the courts studied, as there are numerous factors, such as the subject matter of cases, the number of witnesses examined, among others, that influence the progress of cases through courts. The stages of cases at the time of transfer, for example, would influence their progress through New Courts, in case any stages would need to be heard again. This would explain why Transfer Courts improved post-transfer, but New Courts performed poorly in comparison. Analysing these factors as well might reveal that volume of cases alone is not the only factor influencing rates of disposal.

Conclusion

Discussion on backlog in Indian courts tends to focus on the numerical strength of courts, and approaches the problem as a question of human resource allocation. Indian courts do suffer from a large number of vacancies in sanctioned judicial postings. However, the results provide evidence that inadequate judge strength may not be the only contributing factor for pendency and backlog, and perhaps there are other causes which must be explored. Administrative practices and procedures and their effect on performance, as well as deficiencies in other areas, such as infrastructure, availability or performance of personnel other than judges, and technological assistance, for example, should also be considered.

Since the results show that the New Courts and Transfer Courts are associated with worse performance overall, in terms of rates of disposal of cases, it may be revealing to explore patterns and trends in the purpose of hearings after cases have been transferred, and how these change as a result of the transfer.

There are many potential reasons why they did not have the desired effect of increasing the chances of case disposal, as described above. This topic would benefit from research into what causes delays in the life cycle of cases.

Further, research could also be conducted in the form of randomised controlled trials (RCTs) to evaluate the impact of changes in court strength on rates of disposal. There is great scope for exploration of the potential legal, procedural, administrative, and technical causes of delay by comparing courts along these factors and measuring their impact on rates of disposal. A more detailed examination may also be done of how much time is dedicated to hearing and disposing of cases, using methods such as those in the Zero Pendency Courts Pilot Project of Delhi High Court.²⁶

Annexure I—Methodology: Survival Analysis Concepts

1. Time—T. This is a random non-negative variable denoting the duration of a state. For our purpose, this will be the amount of time for which a case has been in courts. This will refer to disposal time for disposed cases, and the amount of time cases have spent in courts at the time of data collection for pending cases. The distribution of T is given by cumulative distribution function F(t) and density function f(t), where
2. Censoring—units which have not reached the event of interest are referred to as ‘rightcensored’. In our case, this refers to pending cases as they have not yet been disposed of.
3. Survival function—S(t). This represents the probability that T is greater than or equal to some time t. S(t) can be expressed as
4. Hazard function—h(t). This represents the instantaneous probability of leaving a state at time t, conditional on having reached time t before the event. In our case, it is the probability of disposal at. h(t) is defined by

Annexure II—Methodology: Kaplan-Meier Survival Function Estimator

The Kaplan-Meier estimator is used to estimate the survival function described in Annexure III. It depicts the estimated probability of survival at each recorded time of failure in the data. It is calculated²⁷ as

Where in event time ti,

1. ri is the number of units at risk of failure, which are cases pending at ti, and
2. di is the number of units which are subject to failure in the interval [ti, ti+1], meaning the number of cases that have been disposed of.

This estimator is calculated and plotted for each time period in the data, as an estimate of the survival curve, and typically shows a decline in probability of survival over time. We estimate the Kaplan-Meier statistics with 95 per cent confidence intervals.

Annexure Iii—Methodology and Results: Royston-Parmar Model²⁸

The class of models developed by Patrick Royston and Mahesh K.B. Parmar semi-parametric model which models the variation in the cumulative hazard function (probability that a case will be disposed at or later than a given point of time) that is associated with variation in a group of variables.²⁹ It is a more appropriate choice for our dataset than the more conventional parametric models, such as the Weibull Model or the exponential model, and the popular Cox Proportional Hazards model, which is semi parametric, because the effect of variables on probability of case disposal varies with the age of a case, violating the assumptions of that model, but the Royston-Parmar model performs better when accounting for non-proportional hazards.³⁰ The model can be used to fit both proportional hazards and proportional odds models, but the former are more applicable to the study of legal cases, given that the probability of a case’s disposal can vary with its age, and especially given that any dataset on court cases is bound to contain right-censored data.

The key feature of this model is that the ‘baseline’ hazard function, meaning the hazard function independent of the effect of the variables in the chapter, is estimated as a ‘restricted cubic spline’, where different subdomains within the domain of the function are parameterised as a cubic function, meeting at specified points called knots. In a restricted cubic spline, the function is constrained to be linear beyond the highest and lowest knots, called the boundary knots.

A restricted cubic spline function with k knots in positions k1, k2....kk can be written as

Where the j are the coefficients of the derived functions. The derived functions, also called basis functions, vj (x) for j = 2,3, ..., k – 1 are calculated as

In keeping with the advice of Royston and Parmar (2002), we fit models with four internal knots³¹ meaning that the models have five degrees of freedom. They advise against models with fewer knots on the grounds that they are potentially unstable, and they also comment that increasing the number of knots does little to improve model fit.

The model, with time-dependent covariates, can be written as follows:³²

in which

1. In H_i(t|x_i) is the restricted baseline cumulative hazard function, conditional on the variables in the model.
2. H_i(t|x_i) is the cumulative hazard function, t is time, and x_i represents a vector of the covariates.
3. s {ln (t)|y , k₀} is the restricted cubic spline function, which models the baseline log cumulative hazard, a function of:
   1. y, the coefficients of the derived variables,
   2. k₀, the number of knots,
   3. x_iB represents a vector of the variables we are interested in, weighted by coefficients.
4. Captures the time-dependent effects of the variables, which would include our primary (indicator) variables of which court a case is from, as well as others such as the stage of a case and the number of cases filed in that court in a year.
   1. There are D time-dependent effects:
   2. 8_k the coefficients of the derived variables for these effects, and
   3. k_j, the number of knots.

The RP model enables us to estimate hazard ratios for multiple variables independent from the effect that the others will have on the probability of disposal, which is the main advantage it offers above simply estimating survival functions using the Kaplan-Meier estimator. This means that we can quantify the overall difference in the hazard functions and measure difference between the hazard functions of two groups, and can account for the confounding factors mentioned earlier, including the types of cases and the location of a given court. However, the Kaplan-Meier estimator remains very useful because it does not make any distributional assumptions, being a non-parametric model—which the RP model does.

For a detailed but technical explanation of the model, see Royston and Parmar³³ and see Lambert and Royston³⁴ for the user-written Stata commands used.

Annexure IV—Royston-Parmar Model Results

Notes

* The authors would like to thank Renuka Sane, Anarghya K. Chandar, Manjula, Nitin Bakshi, and Ramandeep Randhawa for their advice and assistance.

1. Law Commission of India. 1986. One Hundred and Fourteenth Report on Gram Nyayalaya, p. 14. Available online at http://lawcommissionofindia.nic.in/101-169/Report114.pdf (accessed on 13 March 2019).
2. Padmini Baruah, Shruthi Naik, Surya Prakash B.S., and Kishore Mandyam. 2018. ‘Paths to Justice: Surveying Judicial and Non-judicial Dispute Resolution in India’, in Harish Narasappa, Shruti Vidyasagar, and Ramya Sridhar Tirumalai (eds), Approaches to Justice in India: A Report by DAKSH, p. 28, available online at http://dakshindia.org/Daksh_Justice_in_India/12_chapter_02.xhtml#_idTextAnchor011 (accessed on 27 August 2019).
3. Justice (Retd) T.S. Thakur (then Chief Justice of India). 2016. ‘Country Needs over 70,000 Judges to Clear Pending Backlog of Cases: CJI’, First Post, 9 May, available online at https://www.firstpost.com/india/cji-judges-governmentmodi-thakur-hc-2771338.html (accessed on 25 June 2019).
4. While this is unclear, we understand this to mean that there are thresholds for both volume and duration of pending cases, based on which the Principal District and Sessions Judge decides whether to or not to recommend the creation of a new court. This is based on our conversation with officials, including the Chief Administrative Officer at Mysuru District Court Complex.
5. SPIO No. 50/2019 dated 23 March 2019 from Office of the State Public Information Officer and Joint Registrar, High Court of Karnataka.
6. SPIO No. 50/2019 dated 23 March 2019 from Office of the State Public Information Officer and Joint Registrar, High Court of Karnataka.
7. District and Sessions Judge, Mysuru. (2014) Order No. ADMN/A/11626/2014, Mysore, dated 16 August 2014, available online at https://districts.ecourts.gov.in/sites/default/files/Case%20Transfer%20List_Nanjangud.pdf; District and Sessions Judge, Mysuru. (2014) Order No. ADMN/A/11654/2014, Mysore, dated 16 August 2014, available online at https://districts.ecourts.gov.in/sites/default/files/CaseTransferList_HDKote.pdf; District and Sessions Judge, Mysuru. (2014) Order No. ADMN/A/11656/2014, dated 16 August 2014, available online at https://districts.ecourts.gov.in/sites/default/files/CaseTransferList_KRNagar.pdf (accessed on 25 June 2019).
8. On the National Judicial Data Grid (NJDG) which is a source of aggregate statistics on court cases logged in the e-courts system, the 74.84 per cent of civil cases in subordinate courts in India have a disposal time under one year, as compared to 87.25 of criminal cases, as of 27 August 2019.
9. Interviewed by the authors in person.
10. We define disposal time to be the time between the date of filing and the date of disposal.
11. In broad terms, a probability is a quantification of the chance that an event will occur. It may take any value between 0 and 1. The closer to 1, the higher the chance that the event will occur, while the closer 0, the lower the chance it will occur, with a probability of 1 meaning that the occurrence is certain, and the probability of 0 meaning that its non-occurrence is certain.
12. Pratik Datta, B.S. Surya Prakash, and Renuka Sane. 2017. Understanding Judicial Delay at the Income Tax Appellate Tribunal in India. No. 17/208, available online at https://macrofinance.nipfp.org.in/PDF/DattaPrakashSane_WP_2017_208.pdf (accessed on 18 December 2019).
13. Datta, Prakash and Sane, Understanding Judicial Delay.
14. See Janet M. Box-Steffensmeier and Bradford S. Jones. 2004. Event History Modeling: A Guide For Social Scientists. New York: Cambridge University Press.
15. The rules were drafted by the commission upon order of the Supreme Court in Salem Advocate Bar Association v. Union of India, (2005) 6 SCC 344. The rules prescribe time limits for case disposal for different ‘tracks’ of case, with each case’s track being classified based on its subject matter. While endorsed by the Supreme Court in the ruling, the rules have not been enacted for all jurisdictions, which must be done separately for High Courts and subordinate courts.
16. This is the conditional risk of disposal, being conditional on the case not having been disposed of before the time considered. It cannot be considered a probability because the estimated probability of an event when time is treated as a continuous variable tends to zero. See J.D. Singer, J.B. Willett, and J.B. Willet. 2003. Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. New York: Oxford University Press, pp. 472–475.
17. T.G. Clark, M.J. Bradburn, S.B. Love, and D.G. Altman. 2003. ‘Survival Analysis Part I: Basic concepts and first analyses’, British Journal of Cancer, 89(2): 232–238.
18. Clark, Bradburn, Love, and Altman, ‘Survival Analysis Part I: Basic concepts and first analyses’, 232–238; Singer, Willett, and Willett. Applied Longitudinal Data Analysis.
19. Singer, Willett, and Willett, Applied Longitudinal Data Analysis.
20. See Annexure I.
21. See John D. Kalbfleisch and Ross L. Prentice. 2002. The Statistical Analysis of Failure Time Data (Wiley Series in Probability and Statistics), available at https://onlinelibrary.wiley.com/doi/book/10.1002/9781118032985.
22. Patrick Royston and Mahesh K. B. Parmar. 2002. ‘Flexible Parametric Proportional‐hazards and Proportional‐Odds Models for Censored Survival Data, with Application to Prognostic Modelling and Estimation of Treatment Effects’, Statistics in Medicine, 21(15): 2175–2197.
23. This is with the assumption of proportional hazards—for a more detailed explanation, see Royston and Parmar, ‘Flexible Parametric Proportional‐Hazards’.
24. Whenever the data used in an analysis is a sample from a ‘population’ which it is intended to represent (all cases in Indian subordinate courts, in this context), we want to be sure that the difference between two groups in the sample in any metric, such as disposal time, is not simply due to chance. We would want to ensure that our estimates of the metric for the sample are representative, and we can quantify the extent of the certainty that the outcome that we see is not due to chance—this is known as ‘statistical significance’. Survival curves in both graphs have a 95 per cent confidence interval (CI), meaning that the population value is believed to fall within this interval with 95 per cent probability.
25. This is sometimes referred to as ‘external validity’.
26. The High Court of Delhi. 2019. Zero Pendency Courts Project. New Delhi, available online at http://dakshindia.org/wp-content/uploads/2019/05/PublicNotice_3MRRIN3QTHN.pdf (accessed on 30 November 2019).
27. Edward L. Kapla and Paul Meier. 1958. ‘Nonparametric Estimation from Incomplete Observations’, Journal of the American Statistical Association, 53(282): 457–481.
28. Royston and Parmar, ‘Flexible Parametric Proportional‐Hazards’, pp. 2175–2197.
29. Royston and Parmar, ‘Flexible Parametric Proportional‐Hazards’, pp. 2175–2197.
30. Box-Steffensmeier and Jones, Event History Modeling.
31. Royston and Parmar, ‘Flexible Parametric Proportional‐Hazards’, pp. 2175–2197.
32. Paul C. Lambert and Patrick Royston. 2009. ‘Further Development of Flexible Parametric Models for Survival Analysis’, The Stata Journal, 9(2): 265–290.
33. Royston and Parmar, ‘Flexible Parametric Proportional‐Hazards’, pp. 2175–2197.
34. Lambert and Royston, ‘Further Development of Flexible Parametric Models’, pp. 265–290.